ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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Recently Published Articles
- Strategies for stiffness analysis of laminates with microdamage: combining average stress and crack face displacement based methods
Article first published online: 29 JUN 2015 | DOI: 10.1002/zamm.201400296
Many approximate analytical models have been developed to calculate stress state between intralaminar cracks with the aim to predict the degradation of certain elastic property (most often axial modulus or shear modulus) of cross-ply laminate. Often they are plane stress solutions and laminate constants like Poisson's ratios cannot be considered. On the other hand the so called GLOB-LOC approach, presented in WWFE III, allows calculation of any thermo-elastic property of a general symmetric laminate with an arbitrary number of cracks in each layer provided that two local parameters – average and normalized crack opening displacement (COD) and crack face sliding displacement (CSD) are known. In this paper relationships are derived expressing these two parameters (COD and CSD) with average value of transverse stress and in-plane shear stress perturbation between cracks. Expressions are exact and independent on the approximations in the stress model. As examples, average perturbation functions for two shear lag models and Hashin's variational model are used to calculate damaged laminate properties that would not be available in original formulation: Poisson's ratio and thermal expansion coefficients. Predictions are compared with test data for GF/EP laminates and with more accurate predictions based on FEM calculations.
- Modeling and experimental investigations of elastic and creep properties of thermoplastic polymer nanocomposites
Jānis Zicāns, Remo Merijs Meri, Mārtiņš Kalniņš, Roberts Maksimovs and Juris Jansons
Article first published online: 25 JUN 2015 | DOI: 10.1002/zamm.201400288
The study is devoted to prediction of elastic and creep properties of thermoplastic polymer nanocomposites reinforced with anisodiametric nanoadditives (either carbon nanotubes, CNTs, or montmorillonite clay, MMT) by considering structural hierarchy of the nanocomposites and the nanofillers itself. The nanocomposites analysed have been based on both synthetic and biodegradable thermoplastic polymer matrices (polyethylene, PE, and plasticized starch, PS, respectively) with potential applications in packaging, building/construction and energetics. It has been demonstrated that modulus of elasticity, stress at break as well as stress at yield of the investigated polymer nanocomposites significantly increase upon introduction of a minor amounts of the aforementioned nanofillers into the polymer matrices. Gain in the modulus of elasticity of the investigated PS based nanocomposites has been described by applying the algorithm of stage-by-stage calculation of the elastic constants of the multiphase-systems containing anisodiametric plate-like nanoparticles with complex structure. Change of the modulus of elasticity of the investigated PE based nanocomposites has been described by applying the theoretical model based on micromechanics approach in consideration of distribution quality of CNTs within the polymer matrix. Creep resistance of neat PE and its nanocomposites in the investigated time frame has been described according to the Findley power law, in spite of the fact, that addition of CNTs increases creep rate to some extent, being the consequence of the nanofiller effect on both crystallinity degree of the polymer matrix as well as viscoelastic properties in the interfacial regions.
- Deformations near an elliptical hole with surface effect in a laminated anisotropic thin plate
Xu Wang and Peter Schiavone
Article first published online: 25 JUN 2015 | DOI: 10.1002/zamm.201400271
This work is concerned with the coupled stretching and bending deformation around an elliptical hole with surface energy in a laminated and inhomogeneous anisotropic elastic thin plate within the context of the Kirchhoff theory. A closed-form full-field solution is derived by using the octet formalism recently developed by Cheng and Reddy (2002, 2003, 2004, 2005) and by incorporating a simplified version of the surface elasticity model. In particular, explicit real-form expressions of the hoop membrane stress resultant, hoop bending moment, in-plane displacements and slopes on the mid-plane along the edge of the elliptical hole are obtained.
- On mathematical problems for viscoelastic multi-mechanism models in the isothermal case
Nils Hendrik Kröger, Michael Wolff and Michael Böhm
Article first published online: 12 JUN 2015 | DOI: 10.1002/zamm.201400171
We deal with special kinds of viscoelastic multi-mechanism models (MM models) in series connection. The MM models under consideration consist of a finite number of rheological Kelvin-Voigt elements and, possibly, a thermoelastic element. An important new item is the possible coupling between the KV elements leading to a new quality. After dealing in short with the modeling, we investigate two resulting three-dimensional mathematical problems in the isothermal case. In particular, we show existence and uniqueness of weak solutions for the corresponding initial-boundary value problems for displacements, stresses and partial strains.
- Crack closure effects in thermal fracture of functionally graded/homogeneous bimaterials with systems of cracks
Vera Petrova and Siegfried Schmauder
Article first published online: 11 JUN 2015 | DOI: 10.1002/zamm.201400294
In the presented model the microstructure of a functionally graded material (FGM) is accounted in two ways: via FGM properties and by distributed small cracks which could be on grain boundaries of the material. The contribution to the solution of material gradation of FGM and of material structure reflected via geometry of distributed cracks is investigated. Besides, some additional effects arising due to possible crack closure and contact of crack surfaces are taken into account in the model and its contribution is also assessed. The goal of this investigation is to show these affects and to estimate the contribution on the SIFs of each of these, if they are strong or can be neglected.