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Keywords:

  • shape-memory effect;
  • temperature-memory effect;
  • stimuli-sensitive polymers;
  • modeling;
  • mechanical properties

Abstract

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. CYCLIC THERMOMECHANICAL TESTING AND MODELING OF DUAL SHAPE-MEMORY POLYMERS
  5. CYCLIC THERMOMECHANICAL TESTING OF TRIPLE- OR MULTI-SHAPE AND TEMPERATURE-MEMORY POLYMERS AND RELATED MODELING APPROACHES
  6. FURTHER APPLICATION-ORIENTED MODELS
  7. CONCLUDING REMARKS
  8. Acknowledgements
  9. REFERENCES AND NOTES
  10. Biographical Information
  11. Biographical Information
  12. Biographical Information
  13. Biographical Information

Thermo-sensitive polymers, which are capable to exhibit a dual-, triple-, or multi-shape effect or a temperature-memory effect (TME), characterized by a controlled shape change in a predefined way, are of current technological interest for designing and realization of actively moving intelligent devices. Here, the methods for the quantitative characterization of shape-memory effects in polymers and recently developed thermomechanical modeling approaches for the simulation of dual-, triple-, and multi-shape polymers as well as materials that exhibit a TME are discussed and some application oriented models are presented. Standardized methods for comprehensive quantification of the different effects and reliable modeling approaches form the basis for a successful translation of the extraordinary achievements of fundamental research into technological applications. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013


INTRODUCTION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. CYCLIC THERMOMECHANICAL TESTING AND MODELING OF DUAL SHAPE-MEMORY POLYMERS
  5. CYCLIC THERMOMECHANICAL TESTING OF TRIPLE- OR MULTI-SHAPE AND TEMPERATURE-MEMORY POLYMERS AND RELATED MODELING APPROACHES
  6. FURTHER APPLICATION-ORIENTED MODELS
  7. CONCLUDING REMARKS
  8. Acknowledgements
  9. REFERENCES AND NOTES
  10. Biographical Information
  11. Biographical Information
  12. Biographical Information
  13. Biographical Information

A prerequisite of polymers that exhibit thermally induced shape-memory effects (SMEs) is their elastic deformability in combination with their thermosensitivity. In general, shape-memory polymers (SMPs) are materials that can be deformed and fixed into various temporary shapes, which are stable until specific response temperatures are exceeded. In contrast to other shape-changing polymers, which deform solely as long as a stimulus is applied, the recovery of the original permanent shape is actuated once the SMPs' response temperature is exceeded.1 A great advantage of SMPs is their ability to perform (complex) active movements, when the SME is initiated. So far, the majority of SMPs are dual-shape polymers (DSPs) that change from a temporary shape (A) to a memorized original shape (B) when activated.1–12 Besides, such dual-shape materials recently polymers with a triple- or multiple-shape capability have been introduced3, 13–20 as well as materials exhibiting a pronounced temperature-memory effect (TME).21–24

A key structural element of SMPs are switching domains related to a thermal transition, for example, a glass or melting transition (Ttrans = Tg or Tm), which act as reversible crosslinks and are responsible for fixation of the temporary shape. In SMPs, the segments forming the switching domains are connected to netpoints, which determine the permanent shape. They can be either of chemical (polymer networks) or physical nature (thermoplastics). Alternatively, the SME has also been shown for liquid crystalline elastomers, for which the thermal transition is characterized by a clearing temperature (Ttrans = Tcl) where the mesogenic units change from a nematic/smectic into an isotropic phase.25

In polymers, a specific thermomechanical treatment named shape-memory creation procedure (SMCP) or programing has to be applied for implementation of the shape-memory functionality. A conventional dual-shape creation procedure consists of deforming the polymer at temperatures above Ttrans, followed by cooling to temperatures below Ttrans while keeping the external load, whereby the reversible crosslinks solidify, and finally, the external stress is removed to obtain the fixed temporary shape. When such programed SMPs are heated again to temperatures above Ttrans, the original shape is recovered under stress-free conditions, whereas under constant strain recovery a characteristic recovery-stress is obtained. The driving force for the recovery process is the entropy gained by the switching chain segments, when moving from an oriented (programed) conformation to a random coil-like (recovered) conformation.

On the macroscopic level, the shape-memory properties of polymers are typically quantified by the extent of fixing the externally applied deformation εm in the temporary shape (shape fixity ratio Rf) and the percentage of recovering the original shape (shape recovery ratio Rr). One of the most common test procedures for examination of SMPs are cyclic thermomechanical tensile tests, which allow on the one hand side a precise control of the applied programing parameters and on the other hand provide a complete dataset describing the materials' stress-temperature-strain behavior with time. Therefore, additional characteristic measures such as the switching temperature Tsw from the obtained strain-temperature plot under stress-free recovery conditions and the temperature at recovery-stress maximum Tσ,max or the temperature at the inflection point Tσ,inf of the stress-temperature curve under constant strain conditions can be determined.26

Based on the numerous available experimental data in recent years, various qualitative and quantitative modeling approaches have been developed for description and prediction of polymers' thermomechanical as well as shape-memory properties. While the short-term objective of the theoretical approaches is a description of experimental data, the ultimate goal is a true prediction of the macroscopic shape-memory behavior for a particular polymer and application. Thereby, the model description should be capable to reproduce the influence of different essential programing parameters such as the deformation temperature Tdeform or the applied deformation εm on the shape-memory properties, whereby also morphological model aspects representing the polymers' molecular structure have to be considered. Currently, two different modeling approaches can be distinguished: the application of existing linear viscoelastic models consisting of coupled spring, dashpot, and frictional elements for modeling of SMPs.27–36 Such models were applied to polymer networks as well as thermoplastic materials. More recently, models have been proposed that consider in greater detail the nature of the specific thermal transition, Ttrans = Tg or Tm.37–49 First summaries of modeling approaches for SMPs with thermal actuation were published recently.50, 51

In this article, a brief overview about the characterization of SMPs via cyclic thermomechanical tensile tests and the related thermomechanical modeling approaches is given. While in the first section, the cyclic testing of DSPs and the most relevant concepts for constitutive theoretical prediction models are introduced in particular, in the next paragraph, the respective characterization and modeling approaches were extended to polymers, which are capable of a triple- or multi-shape effect and temperature-memory polymers. The following section addresses selected application-oriented thermomechanical tests and theoretical models including finite element (FE) approaches. Finally, the main challenges and future perspectives in cyclic thermomechanical testing and modeling of SMPs are discussed.

CYCLIC THERMOMECHANICAL TESTING AND MODELING OF DUAL SHAPE-MEMORY POLYMERS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. CYCLIC THERMOMECHANICAL TESTING AND MODELING OF DUAL SHAPE-MEMORY POLYMERS
  5. CYCLIC THERMOMECHANICAL TESTING OF TRIPLE- OR MULTI-SHAPE AND TEMPERATURE-MEMORY POLYMERS AND RELATED MODELING APPROACHES
  6. FURTHER APPLICATION-ORIENTED MODELS
  7. CONCLUDING REMARKS
  8. Acknowledgements
  9. REFERENCES AND NOTES
  10. Biographical Information
  11. Biographical Information
  12. Biographical Information
  13. Biographical Information

Cyclic Thermomechanical Testing of Dual-Shape Polymers

Cyclic thermomechanical uniaxial tensile, bending, or compression tests are widely used to characterize SMPs, because a complete dataset of stress-temperature-strain over time can be generated. Such as modeling of stress–strain relationships is possible by fitting a theoretical model to existing datasets; in the same way, cyclic thermomechanical experiments serve as basis to evaluate and to fit theoretical models. As compared with a stress–strain relationship, where a constant strain rate is applied until a desired elongation is reached, which might be regarded as a single-step procedure, the thermomechanical evaluation of DSPs is a multistep procedure involving the creation of a temporary shape (called SMCP) and the recovery of the original shape under different conditions.

The first step during SMCP is the elongation of the sample to the programing strain εm at a temperature Tdeform, which is above the transition temperature Ttrans of the switching segment [see Fig. 1(a)]. At εm, the sample will be hold for a certain time to allow the sample to equilibrate. Subsequently, the sample will be cooled to Tlow, which is below Ttrans, either under constant strain (εm) or constant stress conditions (σm = const.) resulting in a maximum deformation ε(σm) = εl. During the cooling procedure, the formerly flexible switching segment will be fixed during the crystallization of the polymer chains, if Ttrans = Tm, or during the transition from the rubbery into the glassy state, if Ttrans = Tg. After Tlow has been reached, the sample is unloaded and the temporary shape εu is obtained. The degree of how well the applied deformation εm or εl can be maintained is called the shape-fixity ratio Rf. Rf is calculated according to eq 1, while N is the number of repeated measurement cycles, if the sample is cooled under strain controlled conditions, or according to eq 2, if the sample is cooled under stress controlled conditions.

  • equation image(1)
  • equation image(2)

The recovery process can be investigated under stress-free (σ = 0 MPa) conditions to observe the shape recovery due to entropy elastic behavior of the switching segment above Ttrans, when the polymer is heated to ThighTtrans. The temperature, at which the shape change occurs, is called the switching temperature Tsw. The recovered shape is determined as εp and the shape-recovery ratio Rr, which defines the degree of the shape recovery, can be obtained after one or more cycles, where each cycle is composed of the SMCP followed by the recovery procedure, and is defined in eq 3, if the programing was conducted under strain controlled conditions, or under stress controlled conditions (eq 4).

  • equation image(3)
  • equation image(4)

The stress-temperature-strain diagram in Figure 1 shows a simplified recovery process, where the sample fully recovers its original shape to εp = ε0. Typically, εp remains higher than ε0 due to irrecoverable strain. Alternatively, the sample can be reheated under constant strain (ε = const.) conditions to measure the evolution of the stress at increasing temperatures. Here, the characteristic values that can be obtained from the stress–temperature curve for thermoplastic materials are the peak recovery stress σmax and the respective temperature Tσ,max. Above Tσ,max, the recovery stress is reduced again due to softening of the polymer. In contrast to thermoplastic materials, the stress increases continuously for polymer networks and σmax is maintained even at higher temperatures. The characteristic temperature Tσ,inf is thus determined by the inflection point of the stress–temperature curve.26

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Figure 1. (a) Schematic illustration of a σ-T-ε diagram obtained in cyclic thermomechanical tensile tests consisting of a heating-cooling-heating shape-memory creation procedure (SMCP) and recovery under stress-free conditions with characteristic states: (1) start and end point of the cycle (0, Thigh, ε0 = εp); (2) after end stretching (σ(εm), Thigh, εm); (3) after cooling at constant strain (σm, Tlow, εm); (4) after unloading before the recovery step starts (0, Tlow, εu). (b) Schematic representation of the states of the test cycle by the standard linear solid (SLS) model.

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Modeling of Dual-Shape Polymers

A schematic representation of a stress-temperature-strain diagram obtained in a cyclic thermomechanical tensile test of a thermoplastic DSP is shown in Figure 1(a), whereby in Figure 1(b) a simple viscoelastic model consisting of an elastic spring and a Maxwell model connected in parallel at different characteristic steps of the test cycle is illustrated. This model is called the standard linear solid (SLS).52 The elastic spring with a Young's modulus of Eeq represents the equilibrium response on stress by the permanent netpoints (hard segments). The nonequilibrium branch is presented by spring and dashpot in series. The dashpot has a viscosity η or a characteristic relaxation time τ = η /Er , which depend strongly on temperature, representing the temperature dependent chain mobility of the switching segments (reversible crosslinks). At first, the viscosity of the dashpot is very low at Thigh, as depicted in state 1 in Figure 1. At Thigh, the deformation takes place so that the energy is stored mainly in the left spring of the equilibrium branch (see state 2 in Fig. 1), and the spring with modulus Er of the Maxwell unit is almost undeformed compared with the initial state. During cooling to Tlow, which is below Ttrans, the viscosity or relaxation time of the dashpot increases by orders of magnitude. In state 3, the external load/stress has been removed at Tlow. Because of the high viscosity, the Maxwell unit behaves like an elastic spring under constant stress. The stress free state (σ = 0) generates a redistribution of stored elastic energy in both springs combined with only a very small deformation εm − εu, because the modulus of the spring in the Maxwell unit of this model is in general much higher than the one in the equilibrium branch ErEeq. So, the deformation of the DSP at Thigh is fixed. For the next step of the cycle, it is important to note that the deformation of the spring in the Maxwell unit is compressive, whereas the sample itself is still elongated. During heating, the sample from Tlow to temperature above Ttrans, the viscosity in the dashpot is dramatically decreased, and the force, created through the spring of the Maxwell unit moves at Tsw the viscous extension back to zero, and the original shape (state 1) is recovered.

For the understanding of the mechanism of the SME two features of the dashpot play an important role: (i) the viscous strain, which is frozen and locked at Tlow, and (ii) the tremendous dependence of viscosity on temperature, which allows above Ttrans to unlock viscous strain and to bring back the original shape.

The whole thermomechanical cycle has been at first theoretically described and modeled by Tobushi et al.34, 35 The model extended the SLS model with a slip element to account for dissipated energy due to internal friction, which results in an incomplete recovery. The model expressed the fact that during stress free recovery at a specific temperature, a certain part of the extension remained as irrecoverable strain. A comparison of experimental and calculated data35 for a segmented polyurethane composed of amorphous ether-based soft segments consisting with a Tg around 45 °C, which contained adipic acid and bisphenol A moieties extended with ethylene or propylene oxide and crystallizable hard segments synthesized from 4,4′-diphenylmethane diisocyanate (MDI) and 1,4-butanediol (BD) are shown in Figure 2. For a maximum extension of εm = 20%, all steps of the cycle: (1) stretching, (2) cooling, (3) unloading are qualitatively well described, as well as including the ε(T)-curve (not shown) during the stress-free recovery (4).

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Figure 2. Modeling of a cyclic thermomechanical test of a segmented polyurethane with a maximum extension of εm = 20% using an extended standard linear solid (SLS) model with additional slip element due to account for internal friction (Reprinted from Ref.35, © 2001, with permission from Elsevier).

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This model is a first example of a general approach to calculate thermomechanical properties of DSPs based on its viscoelastic properties. Other rheological models consisting of spring, dashpot, and frictional elements were applied to SMPs, for example, by Lin and Chen.31 These models were further developed and stepwise adapted to the specific nature of the thermal transition in the polymer, either a glass transition with Ttrans = Tg40, 41, 43, 53, 54 among others or a melting transition Ttrans = Tm.33, 37, 38 The models for SMPs with crystallizable switching segments followed a mechanical approach, in which the stress–strain behavior is described as a combination of spring or dashpot units,33 or the observed expansion and contraction is predicted based on so-called “constitutive equations” for a rubbery phase, a semicrystalline phase, the crystallization and melting process, which are adjusted to predict the conditions of a specific SMP.37

The current capability of viscoelastic models is demonstrated on the 3D finite deformation constitutive model for amorphous SMPs recently developed by Westbrook et al.,55 which is shown in Figure 3.

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Figure 3. 1D rheological representation of the constitutive model for amorphous SMPs55 with thermal expansion element in series with parallel mechanical elements consisting of an equilibrium branch (spring) and nonequilibrium branches of Maxwell elements for one glassy and m rubbery nonequilibrium branches of different relaxation times (Reprinted from Ref.55, © 2011, with permission from Elsevier).

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The authors investigated an acrylate-based covalently crosslinked polymer network (Tg = 42 °C). Isothermal uniaxial compression experiments were conducted at strain rates of 0.01/s and 0.1/s. To explore the rubbery and glassy behavior, the isothermal uniaxial compression tests were performed at various temperatures between 0 and 100 °C in 10 K increments. Further cyclic experiments, both under constrained and free conditions during the recovery step were carried out. For constrained recovery, the programing took place at Tdeform = Thigh = 60 °C, the unloading (fixing) took place at Tlow = 10 °C, and the recovery again at Thigh = 60 °C. During constrained recovery, a stress overshoot peak for an initial compression deformation is observed on the stress–temperature graph [Fig. 4(a)]. At stress-free recovery experiments of samples programed at Tdeform = 40 °C and unloaded at Tlow = 10 °C, the recovery temperature was varied from Thigh = 30, 35, 40, to 50 °C. As it becomes obvious from Figure 4(b), the recovery behavior is strongly dependent on Thigh.

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Figure 4. Modeling of experimental recovery data of an acrylate-based covalently crosslinked polymer with the constitutive model, presented in Figure 3. (a) Comparison between experiment and simulation for the stress response during constant strain recovery. (b) Comparison between experiment and simulation for the strain recovery during isothermal heating at different temperatures TH2 under stress-free condition. Samples were programed at Thigh = TH1 = 40 °C (Reprinted from Ref.55, Figures 2 and 3, © 2011, with permission from Elsevier).

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These experiments were modeled with a viscoelastic model where every material point moves in space under conditions, which can be represented in 1D by the rheological model presented in Figure 3, where a thermal expansion element is arranged in series with mechanical elements. The mechanical elements consist of an equilibrium branch composed of an elastic spring with a Young's modulus of Eeq, a glassy nonequilibrium branch represented by a Maxwell element based on an elastic spring and a dashpot characterized by a relaxation time τg = ηg/Eg, which are placed in series, and several further Maxwell elements, presenting the rubbery nonequilibrium branches. This model represents an extension of the simple SLS model. The glassy branch describes the segmental relaxation of the polymer. This most fundamental relaxation process defines the monomer friction coefficient and it is on the bottom of all other and longer time scale chain relaxation processes. The model considers a finite number of n different relaxation processes in the rubbery (or molten) state. For the thermal expansion, a multiparameter theory has been used,56 which describes the volume departure of the polymer in the nonequilibrium situation below the glass transition. The elastic behavior of the DSP above Tg is modeled by a hyperelastic material model typically for rubbers, that is, the Arruda-Boyce eight chain model.57 For the nonequilibrium viscoelastic branches, one can assume that all branches follow the same viscous flow rules, but with different relaxation times. The relaxation times are temperature dependent. According to the thermo-rheological simplicity principle, a time-temperature superposition shift factor aT(T) can be determined, which relates all n + 1 relaxation times

  • equation image(5)

with i = 0,…,n to a reference relaxation time τmath image, where the shift factor is equal to 1. For temperatures below Tg, the shift factor can be determined from an Arrhenius-type behavior,58 and at temperatures close to or above Tg, the WLF equation59 can be used.

The authors implemented the constitutive model into a FE software package and fitted at first model parameters for several key features: (i) the overall behavior of the isothermal uniaxial compression results at a strain rate of 0.01/s, (ii) the location and magnitude of the stress overshoot peak in the constrained recovery experiments, and (iii) the overall behavior in stress-free recovery experiments at all Thigh values. It turned out that the number of nonequilibrium rubbery branches could be assessed to n = 2. The model was then capable to predict the strain rate dependency in the isothermal uniaxial compression experiments. For the constrained recovery conditions [see Fig. 4(a)], the model was able to capture magnitude and temperature location of the stress overshoot peak during heating. However, the overall behavior above 35 °C during cooling or heating and the location of the temperature at which the stress overshoot is still not well depicted. For the free recovery after a shape-memory cycle, the experimental results are well described [see Fig. 4(b)]. For ThighTg, the stress-free recovery behavior (both the recovery rate νrec and the temperature interval ΔTrec, where the transition from the temporary to the original shape starts (Tstart) and ends (Tend)) is equivalent excluding the thermal expansion for the case where Thigh > Tdeform.

The established model allows, for example, to study the influence of the heating rate on the recovery behavior up to the question of how fast the SMP can recover its memorized shape, if it could be heated instantaneously, or to simulate a magnetosensitive SMP composite to determine the effect of changing the particle size and concentration on the free recovery behavior.

The just discussed model represents implicitly also a tool to study the influence of the programing parameters Tdeform and εm on the recovery behavior of the SMP due to the incorporated temperature dependency of the relaxation times. It should also be mentioned that this constitutive model needs 23 parameters. The model of Srivastava et al.60 is currently the most elaborated with 45 parameters. The effort in the parameter description, together with the often mathematically challenging formulation of these models, is at present a disadvantage for a wider application of these kind of models in the SMP research. From this point of view, simple modeling concepts, which only focus on the essential aspects of the shape-memory behavior, are of special interest.

An example is the approach of Bonner et al.61 to predict the recovery time of SMPs depending on programing parameters. A simple Kelvin–Voigt model (elastic spring in parallel with a dashpot) is used to analyze data of a transient stress dip test, where a sample is stretched at constant rate up to a certain maximum length, then the stretching direction is very quickly reversed for a short time, and finally, the strain development as function of time is observed and the recovery stress σR is measured. It was found that σR is a linear function of λ2 − 1/λ where λ is the draw ratio, further that σR decreases with increasing deformation temperature, and increases with increasing strain rate. It turned further out that the ratio of the recovery stress to the total stress is a good approximation invariant to the three programing variables Tdeform, εm, and strain rate equation image. The shape recovery of the SMP occurs when the spring component of the Kelvin–Voigt model or the stored stress in the material exerts a force capable of deforming the viscous component or the dashpot element of the model, which typically occurs at the temperature of shape recovery.

Into the same direction of a simplified model with a few characteristic parameters aims also the recently modified SLS model.36 The simple analytical solution allows to predict the nonisothermal free recovery of an amorphous DSP by only eight calibration parameters obtained by relatively quick dynamic mechanical thermal analysis (DMTA) measurements.

For the second set of general modeling approaches to calculate thermomechanical properties, the polymers' morphology is the starting point. Covalently crosslinked amorphous DSPs are described as a two-phase material composed of a glassy and rubbery phase. Liu et al.42 developed a constitutive model where the total strain ε can be represented as sum ε = ϕfεf + (1 − ϕfa of two strain contributions from the frozen phase and the active phase. The strain in the frozen (glassy) phase εf can be determined from three contributions, that is, the (stored) entropic stain, the internal energetic strain, and the thermal strain. In the active phase, the strain deformation εa consists of two parts: the external stress induced entropic strain and the thermal strain.

The essential idea of this type of models is shown in Figure 5(a). In the glassy state at Tlow, the major phase of a polymer is the frozen phase composed of frozen bonds, where conformational motions of chain segments are locked. By heating over a deformation temperature Tdeform, the volume fraction of the frozen phase is reduced, and at the same time, the fraction of the active phase with free conformational motion is increasing till the polymer is at Thigh in a practically full rubbery state. This process is assumed as fully reversible.

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Figure 5. Sketch of the two-phase model. (a) Polymer phase at T = Tlow << Ttrans (left) at T = Ttrans (middle), and T = Thigh >> Ttrans (right). (b) Curves of the frozen volume fraction ϕf for normalized temperatures (see eq 7) presented through the generalized function (8) with two parameters a and b (Reprinted from Ref.62, © Springer Verlag 2012, with kind permission from Springer Science and Business Media).

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From a thermodynamic point of view, the frozen volume fraction ϕf is an internal state variable of the system and it is assumed that ϕf depends only on the temperature (T). Based on experimental results (a free strain recovery response during heating, where the sample has experienced predeformation εpre and strain-storage process), an analytical phenomenological function

  • equation image(6)

can be determined. The two numerical parameters cf and n can be fitted from the experimental strain ratio data. Very recently, Kazakeviciute-Makovska et al.62 analyzed Liu's law (6), and other ϕf(T) relations obtained by different researchers43, 44, 47, 48, 53 and proposed a modified general function based on reduced temperature values

  • equation image(7)

with two parameters a and b, and following shape

  • equation image(8)

where a can be positive or negative, and b > 0. The influence of these parameters on the T-dependency of the frozen volume fraction is shown in Figure 5(b). Parameter a shifts the transition curve relative to Tdeform, and b determines the width of the transition. The parameters a and b for the generalized evolution law for the frozen volume fraction may be obtained in a systematic way from stress–strain experiments. A simple approach has been used by Volk et al.,47 who assumed that the frozen volume fraction function [see Fig. 6(b)] is given by the normalized stress free recovery profile presented in Figure 6(a), that is, ϕf(T) = ε (T)/εm. Based on the generalized evolution law of the frozen volume fraction ϕf, it was possible to model several experimental sets of thermomechanical tests,63, 64 including the already discussed experiments of Tobushi et al.34

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Figure 6. Approximation of frozen volume fraction for a polystyrene-co-butadiene copolymer network as normalization of the extension recovery ϕf(T) = ε (T)/εm. (a) Stress free strain recovery. (b) Frozen volume fraction fitted by normalized extension data (Reprinted from Ref.47, with permission from IOP Publishing Ltd.).

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The two-phase approach was confirmed by Wang et al.48 Based on this theory, Chen and Lagoudas40, 53 reported an approach to describe the thermomechanical properties of SMPs under large deformations, where general constitutive functions of neo-Hookean type for nonlinear thermo-elastic materials are used for the active and frozen phases. This model was applied to analyze experimental cyclic tests for a polystyrene-based SMP network.47, 64 Figure 7 presents the comparison of experiment and modeling for different maximum extension values.

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Figure 7. σ-T-ε profile for 10%, 50%, and 100% extension experiments of a polystyrene-co-butadiene copolymer network and model predictions: (a) 10% extension, (b) 50% extension, and (c) 100% extension (Reprinted from Ref.47, with permission from IOP Publishing Ltd.).

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The model was calibrated by calculating values for model parameters (coefficient of thermal expansion, shear moduli, and the frozen volume fraction) using the data of the thermomechanical test with εm = 25%. Based on these data, the model allows to predict in qualitative agreement the full σ-T-ε tensile tests for small as well as large εm of 10%, 50%, and 100%. The model failed to capture the irrecoverable extension at the end of the recovery step. The model was also used to predict the stress free and constrained recovery curves for a polyurethane SMP, which were found to be in good agreement with experimental data.65

Despite its successes, the two-phase approach has a strong limitation. As Diani et al. discuss in ref.66, the volume fraction of each phase in such models must be given as a function of temperature ϕf = ϕf(T). This function is obtained from fitting experimental shape-memory data at a certain heating rate. Therefore, the resulting models can fit these experimental data but cannot predict the shape-memory behavior of the material under different heating rates or heating profiles.

Another important aspect was highlighted by Nguyen et al.43 with an own model development based on the nonequilibrium character of the glassy state. The authors pointed out that the concept of two mixed phases (frozen/active) is not in true agreement with the physical processes of the glass transition and thus results in “nonphysical” parameters, such as the volume fractions of the glassy and rubbery phases. Instead, it would be necessary to consider, as primary molecular mechanism, the time-dependent structural and stress relaxation of the glass forming polymer material. The model developed under this relaxation concept seems to reproduce the stress-free strain–temperature response, the temperature and strain-rate dependent stress–strain response, and important features of the temperature dependence of the shape memory response well.67 The modeling approach allowed recently to study the effect of physical aging (up to 180 days) on the stress free recovery of (meth)acrylate-based polymer networks.68 Another application of this stress-relaxation concept was the modeling of experiments where a SMP network was programed by cold compression.69

As extension of the discussed “two-phase” models, Kim et al.70 developed especially for shape-memory polyurethanes (SMPUs) a constitutive model consisting of three phases. SMPUs consist of hard and switching domains. The switching domains can form a variable state ranging from a rubbery (active) to a rigid (frozen) phase depending on temperature. Hard domains act as fixed (permanent) netpoints. The three-phase model divides the SMP into one hard segment phase that governs the viscoelastic behavior and two switching segmented phases (frozen and active phase) that undergo a reversible phase transformation as function of temperature. A three-element viscoelastic model (two springs and a dashpot) was used to present the hard segment phase. For the two switching segment phases, a Mooney-Rivlin solid model (hyperelastic spring) was used. The two hyperelastic springs for the frozen and active switching segment phases were linked in the model as series or parallel. The stresses in each phase were calculated using hyperelastic and viscoelastic equations, and combined into the total stress. The material properties for the constitutive equations were determined by differential scanning calorimetry and a series of uniaxial tensile stress–strain tests at three temperature conditions. Simulations of cyclic thermomechanical tests gave good agreement with experimental data and showed a certain dependence on the assumed linking model (parallel or series).

CYCLIC THERMOMECHANICAL TESTING OF TRIPLE- OR MULTI-SHAPE AND TEMPERATURE-MEMORY POLYMERS AND RELATED MODELING APPROACHES

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. CYCLIC THERMOMECHANICAL TESTING AND MODELING OF DUAL SHAPE-MEMORY POLYMERS
  5. CYCLIC THERMOMECHANICAL TESTING OF TRIPLE- OR MULTI-SHAPE AND TEMPERATURE-MEMORY POLYMERS AND RELATED MODELING APPROACHES
  6. FURTHER APPLICATION-ORIENTED MODELS
  7. CONCLUDING REMARKS
  8. Acknowledgements
  9. REFERENCES AND NOTES
  10. Biographical Information
  11. Biographical Information
  12. Biographical Information
  13. Biographical Information

Programing Procedures for Triple-Shape Polymers

Polymers containing at least two distinct domains having significantly different thermal transition temperatures (Ttrans,B and Ttrans,A) are able to memorize two temporary shapes and, hence, are called triple-shape polymers (TSPs).13, 71 When such a TSP is heated to Thigh, which is above the two transition temperatures Ttrans,B and Ttrans,A, both switching domains are in the rubbery elastic state and it can be easily deformed, for example, by stretching to εm = 50%. Cooling to Tmid, which is below Ttrans,B but above Ttrans,A, results in the fixation of domain B by crystallization or vitrification (depending on the nature of Ttrans,B, which can be a Tg or Tm), whereas domain A is still in the flexible state. Hence, cooling to Tmid affects only domain B, but not domain A, and unloading of the sample at Tmid results in the temporary shape εB. In a next step, the sample is stretched by an additional proportion to 100% at Tmid and cooled to Tlow, which is below Ttrans,A. During this step, only domain A is affected, because the cooling step only passes one thermal transition, which is Ttrans,A (either Tg or Tm). Unloading at Tlow results in the second temporary shape εA. To fix the temporary shape εB, different programing procedures have been described.3 The stress-free recovery of a crosslinked multiphase polymer network is shown in Figure 8 for different εB and εA.13

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Figure 8. TSP: Recovery of shapes B and C by heating a crosslinked multiphase polymer network from Tlow to Thigh. A constant heating rate of 1 K min−1 was applied. By different combinations of εB and εA, different recoveries can be achieved: solid line, εB = 50% and εA = 100%; dashed line, εB = 30% and εA = 100%; dotted line, εB = 50% and εA = 120% (Taken from Ref. 13, © 2006 National Academy of Sciences, USA, reproduced by permission).

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As extension of the dual SME, the shape-fixity ratios Rf(C [RIGHTWARDS ARROW] B) and Rf(B [RIGHTWARDS ARROW] A) for TSPs quantifying the difference between two shapes together with the overall fixity Rf(C [RIGHTWARDS ARROW] A) are described in eqs 911

  • equation image(9)
  • equation image(10)
  • equation image(11)

Recovery of TSPs is generally conducted under stress-free conditions (σ = 0 MPa) to observe the shape recovery. The sample is heated from Tlow to Thigh to observe a change in shape. The heating rate should be chosen as constant to really investigate whether the material shows a triple-shape effect.13, 71, 72 Upon heating, the sample contracts to the recovered shape B at εmath image when exceeding the switching temperature from shape A to B (Tsw(A [RIGHTWARDS ARROW] B)), at which the domain B is still in the glassy or semicrystalline state. The final shape C at εmath image is recovered when the sample reaches Tsw(B [RIGHTWARDS ARROW] C).

The recovery of the two memorized shapes in TSPs is calculated in analogy to DSPs. The shape-recovery ratios can be calculated for the recovery of the first recovery step Rr(A [RIGHTWARDS ARROW] B), the second change in shape Rr(B [RIGHTWARDS ARROW] C), and the total shape recovery Rr(A [RIGHTWARDS ARROW] C) according to the eqs 1214.

  • equation image(12)
  • equation image(13)
  • equation image(14)

Different material design concepts such as covalently crosslinked multiphase polymer networks13, 15, 71–73 or thermoplastic polymers containing two thermal transitions can be used as switching domains or copolymers with a broad thermal transition18, 74, 75 as well as multimaterial approaches17, 76 (which, in general, combine two dual-shape materials) have been reported for the realization of TSPs.

Programing Procedures for Multi-Shape Polymers

Polymers that exhibit a broad thermal glass transition, such as perfluorosulfonic acid ionomer (PFSA) with a ΔTg from 55 to 130 °C, are also able to memorize and recover more than two predefined shapes. A multishape creation procedure involves to heat the sample to Thigh, where all domains (i = 1,…,n) are in the rubbery phase, then to stretch the sample to the programing strain of shape S1, εS1, and finally to cool below the highest transition temperature Ttrans,1 to the deformation temperature Td1, where S1 is fixed and the sample can be unloaded. In the next step, the process of stretching at Td(i), cooling to Td(i+1) and unloading is repeated until the desired number of temporary shapes is obtained and Tlow, where all n domains are in the glassy state. The shape-fixity rate, which is a measure of how well the temporary shapes can be maintained, is increased the lower the transition of the domain, because more domains are already in the glassy state. Hence, these multishape polymers can, depending on the programing procedure, show a dual-, triple-, and multi-SME as illustrated in Figure 9. Recovery of such a multishape programed sample is achieved by heating the sample from Tlow to Thigh under stress-free conditions, as shown in Figure 10(b). In contrast to the TSP example shown in Figure 8, the recovery of the different shapes was realized with a discontinuous heating regime.77 The broad ΔTg of PFSA can be treated as ensemble of sharp transitions, whereby each particular sharp transition acts as a controlling unit with a specific Ttrans,i. This current point of view is the result of recent model considerations. First, Sun and Huang78 proposed that such SMPs consist of “tiny units of a dual part system” composed of an elastic spring as elastic part, and in parallel to this a thermoresponsive element representing the so-called transition part. In heating and cooling processes, the thermoresponsive element shows between the temperature values Ts and Tf a linear function of “hard portion in the transition part.” At T = Ts, the hard portion is 100% and at T = Tf the hard portion is 0%. The authors argued that under these idealized conditions it is possible during the programing to store stepwise contributions of elastic energy at certain elongations when the SMP is stepwise cooled from Tf to Ts. It becomes comprehensible that the stored elastic energy may be released stepwise in a free recovery during stepwise heating from Ts to Tf and creates the (entropic) driving force for this multi-SME. The basis is a single broad thermal transition, which can be assumed as integral distribution of an infinite number of “tiny units” showing all a separate sharp transition. So within the transition range, a portion of the transition part is glassy, whereas the rest is in a rubbery state. Based on the ideas of Sun and Huang very recently, the first quantitative model to predict the thermomechanical cycle of a multishape memory effect has been developed by Yu et al.77 and applied to the experimental PFSA data. The authors used the already introduced finite deformation model of Westbrook et al.55 (see Fig. 3). In the model, individual nonequilibrium branches represent different relaxation modes of polymer chains with different relaxation times. As the temperature increases in a staged manner, for a given temperature, different numbers of branches (or relaxation modes) became shape-memory active or inactive. The main equations of the model are the relations for the total stress σ (t), for the elastic strain εmath image(t), and the viscous strain εmath image(t) (the strain in the dashpot) in the ith individual nonequilibrium branch.

  • equation image(15)
  • equation image(16)
  • equation image(17)

For i = 0, τi = τg, and E0 = Eg. As discussed before, the relaxation times in the individual branches are strongly temperature dependent (see eq 5). Following the SMCP, eq 15 was solved for total strain ε (t) under the condition of the temperature and time dependent total stress. The individual elastic and viscous strain values are calculated with eqs 16 and 17. During stress free recovery (σ = 0), eq 15 was solved for the total recovery strain ε (t) with the left hand being zero.

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Figure 9. Temporal development of temperature T, stress σ (above), and strain ε (below) in cyclic thermomechanical tests of different SMCP for perfluorosulfonic acid ionomer (PFSA) with a ΔTg from 55 to 130 °C in comparison with a theoretical modeling approach (eqs 1517). (a) Dual-shape cycle. (b) Triple-shape cycle. (c) Multishape cycle (Reproduced from Ref.77, with permission of The Royal Society of Chemistry).

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Figure 10. Evolution of viscous strain εmath image(t) (the strain in the dashpot) in the glassy (G) and the seven nonequilibrium rubbery branches of the 1D rheological model presented in Figure 3 to describe the recovery after different SMCPs presented in Figure 9. (a) Dual-shape recovery of the single Maxwell elements. The superposition results in the free recovery presented in Figure 9(a). (b) Multishape cycle presented in Figure 9(b) (Reproduced from Ref.77, with permission of The Royal Society of Chemistry).

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As already illustrated in Figure 3, each domain i can be treated as a Maxwell element with the same spring constant but different damping constants, or retardation times, within the rubbery phase. With the model presented by eqs 1517, all dual-, triple-, and multi-shape recoveries can be well predicted.

Programing Procedures for Temperature Memory Effects in Polymers

If a multishape polymer such as PFSA is programed into a DSP at a certain Tdeform, which is within ΔTg and above a certain number of j transition temperatures, where j is below a maximum values n (1 ≤ jn) Ttrans,j, j domains will be fixed into the temporary shape, once cooled to Tlow, whereas all nj domains with a higher transition temperature will not be affected by the programing procedure. When heated from Tlow to Thigh, the entropy elastic recovery will be completed above Ttrans,j; hence, the response temperature (e.g., Tsw or Tσ,max) of the sample will correspond to the deformation temperature Tdeform. This so-called TME describes polymers with the capability to remember the temperature at which they were deformed and by reversing this deformation upon reheating above the deformation temperature. Therefore, both Tsw and Tσ,max can be related to Tdeform.22 The dependency of Tsw and Tσ,max toward Tdeform is presented in Figure 11. The relationship of the deformation and the recovery temperature, which is shown experimentally in Figure 11(a), can be understood by application of the model presented in Figure 3. In analogy, a similar behavior was found for this model when applied to PFSA with n = 7 domains, as illustrated in Figure 10(a), which in principle would implicate seven different Tsw.77 These so-called temperature-memory polymers might exhibit a broad thermal Tg,18, 23, 24, 79 a broad thermal melting transition Tm22, 29 as well as a combination of two thermal transitions.21 It should be emphasized again that in contrast to a multishape memory programing procedure, which requires the application of multiple deformations at various temperatures within a single programing protocol, a TME is characterized by several subsequent dual-shape test cycles, where different deformation temperatures are applied in subsequent cycles.

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Figure 11. Temperature-memory properties of a polymer network having a broad melting transition temperature. (a) Strain-temperature recovery curves for the same polymer, which was stretched at different Tprog (solid line: 0 °C; dashed line: 25 °C; dotted line: 50 °C; dash-dotted line: 75 °C; dash-double dotted line: 100 °C). (b) Relation of the response temperatures Tsw and Tσ,max on Tdeform. Filled squares: Tsw determined in five subsequent cycles with increasing Tdeform = 0, 25, 50, 75, 100 °C; open squares: five subsequent cycles with decreasing Tdeform = 100, 75, 50, 25, 0 °C. Filled circles Tσ,max determined in five subsequent cycles with increasing Tdeform = 0, 25, 50, 75, 100 °C; open circles: five subsequent cycles with decreasing Tdeform = 100, 75, 50, 25, 0 °C (εm = 75%, Tlow = −10 °C, and Thigh = 110 °C). The dashed trend line represents Tsw or Tσ,max = Tdeform (Taken from Ref. 22, © Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, reproduced with permission).

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FURTHER APPLICATION-ORIENTED MODELS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. CYCLIC THERMOMECHANICAL TESTING AND MODELING OF DUAL SHAPE-MEMORY POLYMERS
  5. CYCLIC THERMOMECHANICAL TESTING OF TRIPLE- OR MULTI-SHAPE AND TEMPERATURE-MEMORY POLYMERS AND RELATED MODELING APPROACHES
  6. FURTHER APPLICATION-ORIENTED MODELS
  7. CONCLUDING REMARKS
  8. Acknowledgements
  9. REFERENCES AND NOTES
  10. Biographical Information
  11. Biographical Information
  12. Biographical Information
  13. Biographical Information

Cyclic thermomechanical tests are the basic experiments for determination of the polymers' thermomechanical properties required as key datasets for constitutive viscoelastic and viscoplastic models as presented in the previous sections. Application oriented testing and modeling, however, requires the investigation of additional parameters, for example, aqueous physiological environment, as well as different thermomechanical settings, for example, the time-dependent shape-recovery at a constant recovery temperature. For example, the TME might be used to generate several temporary shapes at different deformation temperatures and to simulate their recovery behavior by application of a constant recovery temperature. Additionally, device components having more complex geometries such as cardiovascular stents need rather structural-dependent shape-memory and shape-recovery modeling. This is achieved by the FE analysis, which, besides investigation of the recovery kinetics in constant environments, will be presented in the following.

Modeling of Shape Recovery Kinetics

SMP-based materials intended for regenerative biomedical applications require, besides their biocompatibility and degradability, mainly an open porous structure for the cells to infiltrate and to regenerate functional tissue while the material is degraded over time. Furthermore, the nutrition and waste exchange as well as cell–cell crosstalks can be maintained by a porous structure, which is called scaffold. Typically, autologous cells are seeded in vitro onto the scaffold until they have proliferated and migrated throughout the scaffold, while the cell-scaffold is then implanted in the defect site of the patient. These cells, however, need an active environment such as mechanical strains to proliferate well and to prevent dedifferentiation. In this context, recently, mechanically active scaffolds based on SMPs were introduced, which can undergo autonomous, controlled shape changes (e.g., pore geometry) under physiological conditions.80 Such scaffolds are intended to serve as model scaffolds for investigating the mechanical stimulation of mechanosensitive cells such as mesenchymal stem cells in vitro or in vivo. The feasibility of actively moving scaffolds was demonstrated using model scaffolds prepared from radio-opaque copolyetherurethane composites (PEUC) with a broad mixed glass transition in the range from 20 to 90 °C, where originally square-shaped pores were temporarily fixed in an expanded circular shape at different Tdeform.80 It could be demonstrated that the kinetics of the shape change obtained under physiological conditions could be adjusted by variation of Tdeform in the range from 40 °C to 60 °C between 1 and 6 h. In further work, it was investigated how the variation of physical parameters applied during programing such as Tdeform and εm influence the recovery behavior of this copolyetherurethane (PEU).54 A theoretical model was developed, which was able to describe the different shape recovery kinetics observed for radiopaque PEU composites based 3D substrates under isothermal conditions (37 °C in water), which could be adjusted by variation of the deformation temperature (Tdeform) applied during the programing step.80 Systematic stress relaxation experiments were carried out with a tensile tester at seven different deformation temperatures (Tdeform = 0, 25, 37, 50, 60, 70, and 80 °C) for strain values εm = 100%, 150%, 200%, or 250%. Figure 12(a) displays the typical stress relaxation curves for the largest applied strain of εm = 250% at four Tdeform. Figure 12(b) shows the stress σ0 at the beginning of the relaxation process for different strain values εm..

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Figure 12. Modeling of relaxation experiments for an actively moving scaffold. (a) Relaxation experiments for PEU. (a-a′) εm = 250% and Tdeform = 25, 37, 60, and 80 °C. (a-b′) Stress at the beginning of the relaxation process for different εm and Tdeform. (b) Modeling of experimental stress relaxation curves for PEU with a simplified model of Figure 3 consisting out of a spring and two Maxwell units. (b-a′) Tdeform = 25 °C, εm = 100%, 150%, 200%, and 250%. (b-b′) At εm = 250% and Tdeform = 25, 37, 60, and 80 °C (Reprinted from Ref.54, © 2010, with permission from Elsevier).

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At a certain Tdeform value, the initial stress increases with strain εm, and at constant elongation, the initial stress becomes drastically smaller with increasing Tdeform. The applied model consisted of one spring and two Maxwell units in parallel. It could be understood as simplification of the model shown in Figure 3 without thermal expansion component and only two Maxwell branches. The fits of the relaxation curves for four elongations at Tdeform = 25 °C with the applied model are shown in the upper graph of Figure 12(b). The model describes well the experimental curves. The viscous element in the “fast” Maxwell unit has a relaxation time in the range of 102 s, the “slow” unit of about 103 s. At constant strain [see Fig. 12(b) below], the situation is more complex. The initial strong drop of stress-values changes with temperature, but also the final values of the relaxed stress after long observation times depend not proportionally on Tdeform. The information from the stress relaxation experiments of PEU was applied to model the isothermal recovery of PEUC scaffolds at 37 °C. It was found that the “fast” relaxation can be neglected, and the viscoelastic properties of PEU can be described by the simple SLS model. The calculated recovery ratio according to this model agreed well with the experimental data (Fig. 13). It can be seen that the model is qualitatively capable to present the Tdeform influence on an isothermal recovery calculation (fastest recovery if Tdeform is close to Thigh = 37 °C).

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Figure 13. Fit of experimental free recovery ratio Rapp values at Thigh= 37 °C for PEU based scaffolds, which were programed at different Tdeform-values (Reprinted from Ref.54, © 2010, with permission from Elsevier).

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Modeling Extension Toward Real Devices

A current task is to combine the developed 1D deformation models with more sophisticated model approaches to describe quantitatively experimental data. These future calculations may be realized by implementation of a thermomechanical model into a FE analysis. This combination is currently a trend in SMP modeling investigations, because it allows to model the shape-memory properties of real devices. Examples are the already mentioned stent structure,46 or of a flat diamond-lattice–shaped specimen.60 An instructive example is the simulation of a series of shape-memory torsion tests of a flat sheet prepared from an covalently crosslinked epoxy polymer network with Ttrans = Tg.66 The time–temperature dependency of the thermoelastic behavior of the polymer network was tested by detailed DMTA measurements using dynamic frequency sweeps at 0.2% strain for frequencies ranging from 0.01 to 63 Hz, and at temperatures between 40 °C and 60 °C. With the time–temperature superposition principle, a storage modulus master curve was constructed, and respective parameters of a generalized Maxwell model out of 12 branches were fitted to this curve. Together with time-temperature parameters determined with the WLF equation and coefficients of linear thermal expansion for glassy and rubbery state from thermal mechanical analysis experiments, it was possible to predict the torsion shape memory response of the epoxy material in very good agreement with the experimental data (Figure 14b, c). In a FE calculation, a sheet of 90 × 10 × 1.6 mm3 was presented by a network of 50 × 10 × 4 = 2000 of 8-node linear brick hybrid elements (Figure 14a).

The combined approach should help to design SMP devices with large deformation requirements, such as stents and deployable structures, based on its prediction results of the shape memory response of polymers with varying composition, structure, and geometry, and under varying thermomechanical cycling conditions. The presented approach seems transferrable to other shape memory polymers, which are intrinsically viscoelastic materials with time–temperature-dependent properties.

A further example for combining a general 3D constitutive model on the micromechanical level with FE-simulation of simple devices is the work of Baghani et al.81 Considering the small strain regime, the total strain is additively decomposed into four parts: (i) a SMP-related strain consisting out of glassy and rubbery parts, (ii) a strain contribution from hard segments (similar to ref.70), and contributions from irreversible (iii) and thermal strains (iv). The general model was verified using three different experimental datasets. First, the experimental strain and stress recovery curves of the epoxy-based polymer network used by Liu et al.42 were simulated (11 material parameters), ignoring time-dependent effects and the hard segment contribution. As second example, data of a SMP composite (hollow glass microballoons dispersed in a epoxy-based SMP matrix) were used,82 which were analyzed before49 with the simplified two-phase concept.42 With 19 material parameters, the overall trend in shape recovery for both regimes (stress free and constant strain) could be simulated in good agreement with the experimental data. Also the experiments of Volk et al.64 could be well represented using 15 material parameters. Based on the verified micromechanical models with the material parameters of the Liu experiment, but assuming a hard segment volume fraction of 0.33, that it is possible to solve boundary value problems, for example, for a 3D beam and a medical stent. The beam had a length of 100 mm, 12.5 mm width, and 10 mm height and was under fully clamped boundary conditions at one end. For certain stress, strain rate, and holding times, a full thermomechanical test cycle was calculated over 1000 min, including a stress-free recovery. Once FE calculations performed successfully for simple structures as the beam, also more complicated devices can be simulated, as was demonstrated for a medical SMP stent.

The pioneering studies for the FE-based simulation of the thermomechanical cycle of three-dimensional SMP structures, including a realistic SMP stent, were carried out by Reese et al.46 and Srivastava et al.60 By incorporation of the two-phase model of Liu et al.42 into a FE calculation, Reese et al.46 were able to calculate the deformations of a realistic stent structure consisting of a SMP during a thermomechanical cycle. At the same time, Srivastava et al.60 conducted large strain compression experiments for a tert-butyl acrylate (tBA) based SMP network, calibrated with these data the material parameter of a constitutive model considering large deformations, and used FE modeling to simulate the behavior of a cylindrical stent. The stent was made by photopolymerization of tBA with the crosslinking agent poly(ethylene glycol) dimethacrylate with diamond shaped perforations when it is inserted in an artery. The stent was modeled as a tube made from a nonlinear elastic material. Figure 15(a) shows the initial undeformed stent. Figure 15(b) shows the stent after radial compression at Thigh = 60 °C, and Figure 15(c) shows snapshots of the stent inside the artery during shape-recovery at 22, 42, and 60 °C. The aforementioned examples show the capability of FE calculations, once constitutive models of the specific SMP material have been established, to be a useful and appropriate tool for design, analysis, and optimization of 3D structures made of SMPs. Despite the promising results regarding real device applications, a current disadvantage for FE simulations of 3D-structures is the lack of 3D constitutive approaches. So far, only a few 3D models are available, which are capable to assess large strains.41, 46, 55, 60, 8114

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Figure 14. Simulation of a series of shape-memory torsion tests of a flat sheet prepared from an epoxy network. (a) Finite element (FE) simulation of the torsion shape recovery of the sample representative mesh when heated at 1 K min−1 a 360° deformation. (b) Model simulation results and experimental data of the shape recovery process for the epoxy under various heating rates. (c) Model prediction of the isothermal shape recovery as a function of time at 42 °C (Reprinted from Ref.66, © 2012, with permission from Elsevier).

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Figure 15. Finite element (FE) simulation of a cylindrical stent made from tBA/poly(ethylene glycol) dimethacrylate with diamond-shaped perforations. For clarity, the mesh has been mirrored along relevant symmetry planes to show the full stent and artery. (a) Undeformed original stent. (b) Deformed stent. (c) Shape recovery of the stent inside the artery at different temperatures (Reprinted from Ref.60, © 2010, with permission from Elsevier).

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CONCLUDING REMARKS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. CYCLIC THERMOMECHANICAL TESTING AND MODELING OF DUAL SHAPE-MEMORY POLYMERS
  5. CYCLIC THERMOMECHANICAL TESTING OF TRIPLE- OR MULTI-SHAPE AND TEMPERATURE-MEMORY POLYMERS AND RELATED MODELING APPROACHES
  6. FURTHER APPLICATION-ORIENTED MODELS
  7. CONCLUDING REMARKS
  8. Acknowledgements
  9. REFERENCES AND NOTES
  10. Biographical Information
  11. Biographical Information
  12. Biographical Information
  13. Biographical Information

SMEs of polymers are the result of the polymer network's structure/morphology in combination with the application of specific programing procedures (SMCPs). While in the past, the focus was mainly concentrated on the synthesis of new SMPs for variation of the shape-memory properties toward the requirements of the desired application; recently, the influence of the variation of physical parameters during SMCP or recovery on the SME of polymers is target of intensive research efforts. An impressive example for the influence of programing parameters on the SME is the TME, where a polymer material is capable to memorize the deformation temperature, whereby the SME occurs upon reheating above the deformation temperature, and in this way, the polymers' response temperature can be easily adjusted. In this context, the applied processing technologies for programing of SMPs turned out as a versatile toolbox for adjusting the shape-memory properties of polymers by solely physical methods, which should strongly support the translation of the scientific achievements into (industrial) applications of SMPs as one and the same material can be adjusted to the requirements of different applications.

Along with the development of more complex programing procedures for tailoring the materials' shape-memory capability at the same time highly sophisticated testing protocols such as cyclic thermomechanical tests have been developed allowing a comprehensive quantitative characterization of the polymers' thermomechanical behavior with time during programing and shape recovery. The obtained complete stress-temperature-strain datasets were the basis for the development of various qualitative and quantitative modeling approaches for description and prediction of shape-memory properties. Also a substantial progress could be achieved in the theoretical approaches for the description of experimental thermomechanical data. While the first constitutive model approaches allowed only to describe some main features of SMPs, the recently introduced advanced thermomechanical constitutive models are able to represent the materials behavior (e.g., the stress–temperature-strain development with time) in a very accurate way and further implementation of FE models allows the simulation of particular SMP-based devices (e.g., stents).

To achieve significant progress in this area, it will be necessary to close the currently existing gap between the complex theoretical model descriptions containing numerous parameters, which require an extensive characterization of the polymers, and real application-related issues. In this context, on the one hand, pragmatic and simple validated models with few parameters, for example, obtained by standard thermomechanical tests such as DMTA,36 have to be provided by theorists, which can be applied by engineers for design and development of shape memory polymers, and on the other hand, more sophisticated 3D constitutive models are required as basis for reasonable FE studies on SMP-based devices.

Further research activities on the theoretical approaches are necessary, which investigate, for example, the influence of holding times during programing as well as the relevant influence parameters in the real application such as constraints from the surrounding environment or fluctuations in temperature or humidity. Finally, for the design of novel SMPs, it would be very helpful, if multiscale modeling approaches can be developed, which combine the prediction of the molecular behavior (e.g., influence of small molecules such as additives or water) with the macroscopic directed motion of a SMP-based device.

REFERENCES AND NOTES

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. CYCLIC THERMOMECHANICAL TESTING AND MODELING OF DUAL SHAPE-MEMORY POLYMERS
  5. CYCLIC THERMOMECHANICAL TESTING OF TRIPLE- OR MULTI-SHAPE AND TEMPERATURE-MEMORY POLYMERS AND RELATED MODELING APPROACHES
  6. FURTHER APPLICATION-ORIENTED MODELS
  7. CONCLUDING REMARKS
  8. Acknowledgements
  9. REFERENCES AND NOTES
  10. Biographical Information
  11. Biographical Information
  12. Biographical Information
  13. Biographical Information
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Biographical Information

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. CYCLIC THERMOMECHANICAL TESTING AND MODELING OF DUAL SHAPE-MEMORY POLYMERS
  5. CYCLIC THERMOMECHANICAL TESTING OF TRIPLE- OR MULTI-SHAPE AND TEMPERATURE-MEMORY POLYMERS AND RELATED MODELING APPROACHES
  6. FURTHER APPLICATION-ORIENTED MODELS
  7. CONCLUDING REMARKS
  8. Acknowledgements
  9. REFERENCES AND NOTES
  10. Biographical Information
  11. Biographical Information
  12. Biographical Information
  13. Biographical Information
Thumbnail image of

Matthias Heuchel studied chemistry and got his Ph.D. in Physical Chemistry at University of Leipzig. 1997-99 he was Marie-Curie-Fellow at the Department of Chemical Engineering, University of Edinburgh. In 2000 he joined the Polymer Physics group of GKSS and is currently Senior Researcher in the Department of Polymer Engineering of the Institute of Biomaterial Science at the Helmholtz-Zentrum Geesthacht in Teltow, Germany. His research interests range from atomistic computer simulation of polymers to thermomechanical modeling of shape-memory polymers.

Biographical Information

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. CYCLIC THERMOMECHANICAL TESTING AND MODELING OF DUAL SHAPE-MEMORY POLYMERS
  5. CYCLIC THERMOMECHANICAL TESTING OF TRIPLE- OR MULTI-SHAPE AND TEMPERATURE-MEMORY POLYMERS AND RELATED MODELING APPROACHES
  6. FURTHER APPLICATION-ORIENTED MODELS
  7. CONCLUDING REMARKS
  8. Acknowledgements
  9. REFERENCES AND NOTES
  10. Biographical Information
  11. Biographical Information
  12. Biographical Information
  13. Biographical Information
Thumbnail image of

Tilman Sauter studied Mechanical Engineering at Technical University of Munich and Medical Engineering at the Royal Institute of Technology Stockholm. He obtained his degrees in 2010 and currently works for his PhD project on the shape-memory properties of polymeric scaffolds for biomedical applications in the Department of Polymer Engineering of the Institute of Biomaterial Science at the Helmholtz-Zentrum Geesthacht in Teltow, Germany.

Biographical Information

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. CYCLIC THERMOMECHANICAL TESTING AND MODELING OF DUAL SHAPE-MEMORY POLYMERS
  5. CYCLIC THERMOMECHANICAL TESTING OF TRIPLE- OR MULTI-SHAPE AND TEMPERATURE-MEMORY POLYMERS AND RELATED MODELING APPROACHES
  6. FURTHER APPLICATION-ORIENTED MODELS
  7. CONCLUDING REMARKS
  8. Acknowledgements
  9. REFERENCES AND NOTES
  10. Biographical Information
  11. Biographical Information
  12. Biographical Information
  13. Biographical Information
Thumbnail image of

Karl Kratz received his diploma in Chemistry and doctor's degree from the University Bielefeld. At first he worked a scientific project manager and director resources in the industry on the development of degradable shape-memory polymers. Currently he holds the position of a senior research associate and is head of the Polymer Engineering Department of the Institute of Biomaterial Science at the Helmholtz-Zentrum Geesthacht. His primary research interests are design, development and characterization of biomaterials and stimuli-sensitive polymers.

Biographical Information

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. CYCLIC THERMOMECHANICAL TESTING AND MODELING OF DUAL SHAPE-MEMORY POLYMERS
  5. CYCLIC THERMOMECHANICAL TESTING OF TRIPLE- OR MULTI-SHAPE AND TEMPERATURE-MEMORY POLYMERS AND RELATED MODELING APPROACHES
  6. FURTHER APPLICATION-ORIENTED MODELS
  7. CONCLUDING REMARKS
  8. Acknowledgements
  9. REFERENCES AND NOTES
  10. Biographical Information
  11. Biographical Information
  12. Biographical Information
  13. Biographical Information
Thumbnail image of

Andreas Lendlein is the Director of the Institute of Biomaterial Science at Helmholtz-Zentrum Geesthacht in Teltow, Germany and Member of the Board of Directors of the Berlin-Brandenburg Centre for Regenerative Therapies. He is a professor at the University Potsdam and Honorary Professor at Freie Universität Berlin as well as Member of the Medical Faculty of Charité University Medicine Berlin. He completed his Habilitation in Macromolecular Chemistry in 2002 at RWTH Aachen University and received his doctoral degree in Materials Science from the Swiss Federal Institute of Technology (ETH) in Zürich. His current research interests include (multi)functional polymer-based materials, biomaterials and their interaction with biological environments as well as the development of medical devices and controlled drug delivery systems especially for regenerative therapies.