Yielding of a curved bar consisting of two layers subject to pure bending is investigated. It is assumed that both layers of the bar are in a state of plane stress and Tresca's yield criterion is used to detect onset of plasticization. Analytical expressions are obtained for the bending moments corresponding to the elastic limit leading to plastic flow. The results show that, depending on material properties and dimensions of the layers, different cases for plastic deformation may occur. Yielding may emerge at the inner or outer surface of the bar or at the interface between two layers. Furthermore, a critical case in which yielding commences at the outer and interface surfaces simultaneously was observed. Numerical results for real engineering materials are presented in graphical form.

The requirements for accurate numerical simulations are increasing steadily. Modern high precision physics experiments now exceed the achievable numerical accuracy of standard commercial and scientific simulation tools. One example are optical resonators for which changes in the optical length are now commonly measured to 10^-15 precision. The achievable measurement accuracy for resonators and cavities is directly influenced by changes in the distances between the optical components. If deformations in the range of 10^-15 occur, those effects cannot be modeled and analyzed anymore with standard methods based on double precision data types. New experimental approaches point out that the achievable experimental accuracies may improve up to the level of 10^-17 in the near future. For the development and improvement of high precision resonators and the analysis of experimental data, new methods have to be developed which enable the needed level of simulation accuracy. Therefore we plan the development of new high precision algorithms for the simulation and modeling of thermo-mechanical effects with an achievable accuracy of 10^-20. In this paper we analyze a test case and identify the problems on the way to this goal.

A direct time integration method is presented for the solution of the equations of motion describing the dynamic response of structural linear and nonlinear multi-degree-of-freedom systems. It applies also to large systems of second order differential equations with fully populated, non symmetric coefficient matrices as well as to equations with variable coefficients. The proposed method is based on the concept of the analog equation, which converts the coupled N equations into a set of single term uncoupled second order ordinary quasi-static differential equations under appropriate fictitious loads, unknown in the first instance. The fictitious loads are established from the integral representation of the solution of the substitute single term equations. The method is simple to implement. It is self starting, unconditionally stable and accurate and conserves energy. It performs well when large deformations and long time durations are considered and it can be used as a practical method for integration of the equations of motion in cases where widely used time integration procedures, e.g. Newmark's, become unstable. Several examples are presented, which demonstrate the efficiency of the method. The method can be straightforward extended to evolution equations of order higher than two.

New rate-independent finite elastoplastic equations are proposed in unified forms applicable to all loading-unloading cases. A departure from the classical elastoplastic equations is that these new equations are not subjected to and hence free from the usual extrinsic restrictive conditions, including the yield condition as well as the loading-unloading conditions. Such free equations are of Eulerian rate type and assume the same smooth form for all possible stresses and for all strain rates. It is demonstrated that the essential representative features of finite elastoplastic deformations, namely, the yield behavior and the loading-unloading behavior in the traditional sense, may be derived from and hence naturally incorporated as intrinsic physical characteristics into the free elastoplastic equations proposed in a more realistic sense and, in particular, the classical notions characterizing these features are found to exhibit novel, perhaps more profound physical meanings in the new equations. Furthermore, the strong discontinuity in tangent moduli at transition from elastic to plastic state, involved in the traditional formulation, is shown to be replaced by a smooth transition. Implications are discussed in respects of constitutive implications and numerical treatment.

The purpose of this paper is to take into account the derivative by moisture content of polymer volume in order to establish a diffusion law within the so-called “thermodynamical approach” for a polymer material which experiences a hygro-mechanical load. In this study, the specific case corresponding to the existence of unsymmetrical hygroscopic boundary conditions was investigated.

We constructed a functional DNA molecule model on the basis of a flexible helicoidal sensor, specifically, a pretwisted hollow nano-strip. We study in this note the helicoidal nano-sensor model with a pretwisted strip axial extension corresponding to the overstretching transition of DNA from dsDNA to ssDNA. Our model and the DNA molecule have similar geometrical and nonlinear mechanical features unlike models based on an elastic rod, accordion bellows, or a combination of “multiple soft and hard linear springs”, presented in some recent publications.

The multiple definitions of permeability and tortuosity employed by investigators modifying the basic equations of dynamic poroelasticity pose a problem as some resulting analyses produce results conflicting with those of other investigators. When the same words are used to describe different definitions of different concepts, the problem is compounded. These problems were highlighted in recent applications of acceleration wave analyses of dynamic poroelasticity. Wilmanski [40] and Coussy [14] applied acceleration wave analysis to their own systems of dynamic poroelastic equations and found contradictory results. In one case the wave speed depends upon tortuosity and in the other case a dependence upon permeability (and tortuosity) was not allowed. This means that acceleration waves in the Wilmanski [40] analysis cannot exhibit dispersion at lower frequencies. Harmonic wave analyses applied to the same systems of dynamic poroelastic equations predict a dependence of wave speed upon permeability. The acceleration wave analysis of a system of dynamic poroelastic equations is dependent upon the definitions of tortuosity used by the investigators. Wilmanski [40] and Coussy [14] each used their own definition of tortuosity.

An adhesive unilateral contact of elastic bodies with a small viscosity in the linear Kelvin-Voigt rheology at small strains is scrutinized. The flow-rule for debonding the adhesive is considered rate-independent and unidirectional, and inertia is neglected. The asymptotics for the viscosity approaching zero towards purely elastic material involves a certain defect-like measure recording in some sense natural additional energy dissipated in the bulk due to (vanishing) viscosity, which is demonstrated on particular 2-dimensional computational simulations based on a semi-implicit time discretisation and a spacial discretisation implemented by boundary-element method.

In this paper we present a model for transport of substance with sedimentation governed by a water flow in a shallow basin. The model is developed by using a dimension reduction technique in an infinite layer. The concentration of substance is modeled by a 2D-approximation, corrected in the vertical direction. In applications 2D-models are often used in shallow basins as it was illustrated for instance in [Legović T., Limić N., Valković V., Estuar. Coast. Shelf Sci. 30, 619–654, (1990)]. Here we establish the acceptability criterion for the reduction, based on the mass conservation law. Thus we discuss the existence of solutions to the original 3D-model and the deduced 2D-model with L₁ source terms. For the conclusion we prove that the relative error of sedimentation rates for the original and deduced model tends to zero as the distance from the source of substance tends to infinity.

We study stability of a rotating compressed nano-rod clamped at one and free at the other end. By using the Euler method of adjacent equilibrium configuration, we determine critical values for angular speed and compressive force. Post-critical shape of the rod is obtained by solving the non-linear system of equilibrium equations for several values of parameters.

We present some new persistence results for the non-periodic two-component Camassa-Holm (2CH) system in weighted L_p spaces. Working with moderate weight functions that are commonly used in time-frequency analysis, the paper generalizes some recent persistence results for the Camassa-Holm equation [2] to its supersymmetric extension. As an application we discuss the spatial asymptotic profile of solutions to 2CH.

This article is concerned with the mechanical behavior of heterogeneous composite plates with elastic moduli and layered geometries varying through the thickness direction and periodically along the in-plane directions. By using the concept of decomposition of the rotation tensor, we first formulate the three-dimensional elastic problem in an intrinsic form for application to the geometrically nonlinear problem. The variational asymptotic method is then exercised, leading to simultaneous homogenization and dimensional reduction to construct an effective and simple model suitable for plates with in-plane periodicity. In particular, having obtained the refinement terms up to the second order, we develop a refined plate model, namely a generalized Reissner-Mindlin model that is capable of capturing the transverse shear deformations. In order to deal with realistic and complex plate geometries and constituent materials efficiently and conveniently, the proposed model is implemented into a single unified formulation suitable for incorporation into a commercial analysis package. Numerical results computed herein for a few examples are compared to similar results available in the literature to demonstrate the application and performance of the present model.

We prove regularity results and, as a consequence, uniqueness for a system of partial differential equations arising in the study of dynamic electrowetting phenomena and more general electrokinetic processes in three space dimensions. The system consists of Stokes equations coupled with equations for the motion of electric charges, Poisson equation for computing the electric field generated by such charges and a Cahn-Hilliard equation for a phase field describing two fluids with different material parameters. The deduction and existence of weak solutions for this system was established in an earlier paper (Christof Eck et al., On a phase-field model for electrowetting, Interfaces Free Bound. 11 (2), 259–290, (2009)).

The classical continuum model does not describe the mechanical behaviour of cellular materials. To model the size-dependent mechanical properties of these materials, the extended continuum models such as the micropolar approach can be used. The reference data is extracted from the virtual experiments performed on an artificial open-cell foam specimens. With the proper set of the Cosserat parameters the detailed microstructural model can be described on the macroscopic level using the extended continuum approach. The parameter identification task is defined as a minimisation task, which is solved using the evolutionary computational framework.

A planar quantum waveguide is composed from two semi-strips of width 1 and a semi-strip of width H and the angle between strips is 2π/3. The spectrum of the Dirichlet problem in this waveguide is investigated. In particular, it is proved that there exists a critical width H_* for which the discrete spectrum is non-empty for any H ≤ H_* and conversely is empty for any H ≥ H_*. The critical width is estimated to be approximately H_* ≈ 1.25. Furthermore, the eigenvalue in the discrete spectrum is unique for 0 ≤ H ≤ H_*.

Structures made of Functionally Graded Materials (FGMs) show a gradual variation of material properties in one, two, or three directions. In this paper, an efficient low-order shell element with six nodal degrees of freedom (including the drill rotation) is presented, supplemented with a proper method for calculating effective elastic properties. This new FGM shell element can be coupled with 3D FGM beam elements on a single node. The numerical results indicate high effectiveness and accuracy of the proposed approach.

A classic problem in gas dynamics simulation is the occurrence of the carbuncle phenomenon, a breakdown of discrete shock profiles. We show that for high Froude number, this also occurs in shallow water simulations. Numerical evidence is given that commonly accepted cures developed for the numerics of gas dynamics should also work for shallow water flows.

One consider an anisotropic, unbounded elastic body containing three collinear, equal cracks subjected to asymmetrically tangential stresses, case corresponding to Mode II of classical Fracture. We determine the elastic state produced in the body using the formalism of Riemann-Hilbert problem and the representation of elastic stresses and displacements fields due to Lekhnitskii. Using the asymptotical analysis, we obtain the asymptotic values of the stress and the displacement fields in a vicinity of the cracks tips.

In this paper we present a sufficient and necessary condition to ensure the ellipticity of the bilinear form which is related to the one-equation coupling of finite and boundary element methods to solve a scalar free space transmission problem for a second order uniform elliptic partial differential equation in the case of general Lipschitz interfaces. This condition relates the minimal eigenvalue of the coefficient matrix in the bounded interior domain to the contraction constant of the shifted double layer integral operator which reflects the shape of the interface. This paper extends and improves earlier results [12] on sufficient conditions, but now includes also necessary conditions. Numerical examples confirm the theoretical results on the sharpeness of the presented estimates.

We derive an asymptotic one-dimensional model of a thin piezoelectric rod by means of a dimension reduction procedure. The rod is made from a heterogeneous material with a possibly varying cross-section and distorted ends. Asymptotically exact error estimates are derived. Representation formulas for effective moduli are established and, for a concrete piezoelectric material, we provide an explicit form.

Neglecting capillary pressure effects in two-phase flow models for porous media may lead to non-physical solutions: indeed, the physical solution is obtained as limit of the parabolic model with small but non-zero capillarity. In this paper, we propose several numerical strategies designed specifically for approximating physically relevant solutions of the hyperbolic model with neglected capillarity, in the multi-dimensional case. It has been shown in [Andreianov & Cancès, Comput. Geosci., DOI: 10.1007/s10596-012-9329-8, 2013] that in the case of the one-dimensional Buckley-Leverett equation with distinct capillary pressure properties of adjacent rocks, the interface may impose an upper bound on the transmitted flux. This transmission condition may reflect the oil trapping phenomenon. We recall the theoretical results for the one-dimensional case which are used to motivate the construction of multi-dimensional finite volume schemes. We describe and discuss a coupled scheme resulting as the limit of the scheme constructed in [Brenner & Cancès & Hilhorst, HAL preprint no.00675681, 2012] and two IMplicit Pressure – Explicit Saturation (IMPES) schemes with different level of coupling. We finally provide numerical evidences of the good behavior of the fully decoupled version of the IMPES scheme.

This paper addresses the problem of reflection and transmission of compression waves at the phase transition layer between the vapour and liquid phases of the same fluid. Within the framework of second gradient fluid modeling, we use a non-convex free energy in order to describe the phase transition phenomenon. A stationary solution for the fluid density is found for an infinite domain, and an analytical expression for the phase transition is presented. Then the propagation of linear waves superposed to this stationary solution is discussed, with particular attention to the behaviour in correspondence of the interfacial layer. The reflection and transmission of waves is studied and analized with the aid of numerical simulations, and an interesting phenomenon of mass adsorption at the interface is observed and discussed.

By Fourier-series expansion in thickness direction of the plate with respect to a basis of scaled Legendre polynomials, several equivalent (and therefore exact) two-dimensional formulations of the three-dimensional boundary-value problem of linear elasticity in weak formulation for a plate with constant thickness are derived. These formulations are sets of countably many PDEs, which are power series in the squared plate parameter. For the special case of a homogeneous monoclinic material, we obtain an approximative plate theory in finitely many PDEs and unknown variables by the truncation approach of the uniform-approximation technique. The PDE system is reduced to a scalar PDE expressed in the mid-plane displacement. The resulting second-order theory, considered as a first-order theory, is equivalent to the classical Kirchhoff theory for the special case of an isotropic material and equivalent to Huber's classical theory for an actual monoclinic material. However it remains shear-rigid as a second-order theory. Therefore, it is modified by an a-priori assumption to a theory for monoclinic materials, that presumes the former equivalences, considered as a first-order theory, but is in addition equivalent to Kienzler's theory as a second-order theory for the special case of isotropy, which implies further equivalences to established shear-deformable theories, especially the Reissner-Mindlin theory and Zhilin's plate theory. The presented new second-order plate theory for monoclinic materials is finally a system of two coupled PDEs of differentiation order six in two variables.

Liquefaction phenomena are encountered in many engineering applications, especially, in geomechanics and earthquake engineering. Drawing our attention to fluid-saturated granular materials with heterogeneous microstructures, the modelling is carried out within a continuum-mechanical framework by exploiting the macroscopic Theory of Porous Media (TPM) together with thermodynamically consistent constitutive equations. In this regard, the solid skeleton of the water-saturated soil is described as an elasto-plastic material with isotropic hardening and a stress-dependent failure surface. The underlying equations are discretised and implemented into the coupled porous-media finite-element solver PANDAS and linked to the commercial finite-element package Abaqus via a general interface. This coupling allows the definition of complex intial-boundary-value problems through Abaqus, thereby using the sophisticated material models of PANDAS. To reveal the capabilities of this approach, two types of simulations have been carried out. At first, in order to get a detailed understanding of the porous-media soil model under transient loading conditions, a cyclic torsion benchmark is computed. In a second step, specific liquefaction phenomena are addressed, where the underlying initial-boundary-value problems are inspired by practically relevant scenarios.

Biodegradable collagen matrices have become a promising alternative to traditional drug delivery systems. The relevant mechanisms in controlled drug release are the diffusion of water into the collagen matrix, the swelling of the matrix coming along with drug release, and enzymatic degradation of the matrix with additional simultaneous drug release. These phenomena have been extensively studied in the past experimentally, via numerical simulations as well as analytically. However, a rigorous derivation of the macroscopic model description, which includes the evolving microstructure due to the degradation process, is still lacking. Since matrix degradation leads to the release of physically entrapped active agent, a good understanding of these phenomena is very important. We present such a derivation using formal twoscale asymptotic expansion in a level set framework and complete our results with numerical simulations in comparison with experimental data.

We consider weakly coupled LQ optimal control problems and derive estimates on the sensitivity of the optimal value function in dependence of the coupling strength. In order to improve these sensitivity estimates a “coupling adapted” norm is proposed. Our main result is that if a weak coupling suffices to destabilize the closed loop system with the optimal feedback of the uncoupled system then the value function might change drastically with the coupling. As a consequence, it is not reasonable to expect that a weakly coupled system possesses a weakly coupled optimal value function. Also, for a known result on the connection of the separation operator and the stability radius a new and simpler proof is given.

In this work, we apply the fractional order theory of thermoelasticity to a 1D thermal shock problem for a half-space. Laplace transform techniques are used. The predictions of the theory are discussed and compared with those for the coupled and generalized theories of thermoelasticity. Numerical results are computed and represented graphically for the temperature, displacement and stress distributions.

Chaotic response is related to a dense set of unstable periodic orbits (UPOs) and the system often visits the neighborhood of each one of them. Moreover, chaos has sensitive dependence to initial conditions, which implies that the system evolution may be altered by small perturbations. Chaos control is based on the richness of chaotic behavior and may be understood as the use of tiny perturbations for the stabilization of an UPO enclosed in a chaotic attractor. It makes this kind of behavior to be desirable in a variety of applications, since one of these UPOs can provide better performance than others in a particular situation. In this work, an adaptive fuzzy sliding mode controller is combined with the close return method for the stabilization of UPOs in a chaotic pendulum. The adaptive fuzzy inference system is embedded in a smooth sliding mode controller to cope with both structured and unstructured uncertainties. Since noise contamination is unavoidable in experimental data acquisition, this work also investigates the effect of noisy signals on the used control law, verifying their influence on the system stabilization and on the required control action. Numerical results are presented in order to illustrate the ability of the proposed control scheme to track UPOs even in the presence of modeling inaccuracies and noisy input signals.

In this paper we obtain the existence and uniqueness in some Sobolev and L^p spaces for a Dirichlet-transmission problem for the Stokes and Brinkman equations on Lipschitz domains in ℝⁿ, n > 3. In the particular case n = 3 this problem describes the Stokes flow of a viscous incompressible fluid past a porous particle and in presence of a solid core. The flow within the porous particle is described by the Brinkman equation. In order to obtain the desired existence and uniqueness result, we use an indirect boundary integral formulation based on the layer potential theory for both Brinkman and Stokes equations. Some special cases, which refer to the Stokes flow past a porous particle with large permeability, respectively low permeability, are also analyzed.

In this investigation, the steady boundary layer flow of Casson fluid over a porous stretching/shrinking sheet is studied. The governing equations are transformed using similarity transformations and then solved analytically. In both stretching and shrinking sheet cases, the closed form exact solutions are obtained. The solution is always unique for stretching sheet case. On the other hand, in shrinking sheet case, the solution may exist or may not and if exists it may be unique or may be of dual nature; these all depend on the value of Casson parameter and wall mass transfer parameter. Also, the analysis reveals that for steady flow of Casson fluid stronger mass suction is needed.

In the paper, a general constitutive elastoplastic model for associated plasticity is investigated. The model is based on the thermodynamical framework with internal variables and can include basic plastic criteria with a combination of kinematic hardening and non-linear isotropic hardening. The corresponding initial value constitutive elastoplastic problem is discretized by the implicit Euler method. The discretized one-time-step constitutive problem defines the elastoplastic operator, which is formulated by a simple generalization of a projection onto a convex set. Properties of the so-called generalized projection are used for deriving basic properties of the elastoplastic operator like potentiality, monotonicity, Lipschitz continuity and local semismoothness. Further, hardening variables are eliminated from the projective definition of the elastoplastic operators, which yields relations among the models with hardening variables and the perfect plasticity model. Also a simplification of the operator for plastic criteria in eigenvalue forms is introduced. The simplifications are useful for a numerical implementation and can be used for deriving other properties like strong semismoothness of the elastoplastic operators for the classical plastic criteria or strong monotonicity of the stress-strain operator for some models with hardening. The derived properties can be important for convergence analyses of Newton-like methods and other mathematical and numerical analyses.

The background of this work is the problem of reducing the aerodynamic turbulent friction drag, which is an important source of energy waste in innumerable technological fields (transportation being probably the most important). We develop a theoretical framework aimed at predicting the behaviour of existing drag reduction techniques when used at the large values of the Reynolds numbers Re which are typical of applications. We focus on one recently proposed and very promising technique, which consists in creating at the wall streamwise-travelling waves of spanwise velocity (M. Quadrio, P. Ricco, and C. Viotti, J. Fluid Mech. 627, 161–178, 2009). A perturbation analysis of the Navier-Stokes equations that govern the fluid motion is carried out, for the simplest wall-bounded flow geometry, i.e. the plane channel flow. The streamwise base flow is perturbed by the spanwise time-varying base flow induced by the travelling waves. An asymptotic expansion is then carried out with respect to the velocity amplitude of the travelling wave. The analysis, although based on several assumptions, leads to predictions of drag reduction that agree well with the measurements available in literature and mostly computed through Direct Numerical Simulations (DNS) of the full Navier–Stokes equations. New DNS data are produced on purpose in this work to validate our method further. The method is then applied to predict the drag-reducing performance of the streamwise-travelling waves at increasing Re, where comparison data are not available. The current belief, based on a Re-range of about one decade only above the transitional value, that drag reduction obtained at low Re is deemed to decrease as Re is increased is fully confirmed by our results. From a quantitative standpoint, however, our outlook based on several decades of increase in Re is much less pessimistic than other existing estimates, and motivates further, more accurate studies on the present subject.

The subject of the paper is the numerical simulation of the interaction of two-dimensional compressible viscous flow and a vibrating airfoil. A solid airfoil with two degrees of freedom performs rotation around an elastic axis and oscillations in the vertical direction. The numerical simulation consists of the solution of the Navier-Stokes system by the discontinuous Galerkin method coupled with a system of nonlinear ordinary differential equations describing the airfoil motion. The time-dependent computational domain and a moving grid are taken into account by the arbitrary Lagrangian-Eulerian (ALE) formulation of the Navier-Stokes equations. The developed method is robust with respect to the magnitude of the Mach number and Reynolds number. Its applicability is demonstrated by numerical experiments.

This paper deals with the electromagnetic theory of microstretch elasticity. The full dynamic theory, which describes the interaction of electromagnetic fields with piezoelectric bodies, called piezoelectromagnetism, is considered. First, we derive the equations governing the bending theory of thin piezoelectromagnetic microstretch plates. Then, the boundary-initial value problem is formulated and a uniqueness result is presented. Finally, the effects of a concentrated charge density in an infinite plate are studied.

The Nonlinear Schrödinger (NLS) equation is a universal amplitude equation which can be derived for the description of small spatio-temporal modulations of an underlying carrier wave. The validity of this approximation for general dispersive wave systems possessing a quasilinear quadratic nonlinearity is an open problem that has remained unsolved for more than four decades. We report results on a systematic numerical simulation of such a quasilinear wave equation which strongly support the validity claim.

The Lyapunov first method generalized to the case of nonlinear differential equations is applied to the study of the instability of the equilibrium position of a mechanical system, whose motion is constrained by singular nonholonomic constraints. Starting from the results of S. D. Furta (On the instability of equilibrium position of constrained mechanical systems) three theorems on the instability are formulated. The first theorem considers the case of nonholonomic constraints that do not satisfy the condition of weak nonholonomity. The other two theorems are related to the case of weakly nonholonomic systems. In each of the formulated theorems it is shown that the minimum form of Maclaurin series for the potential energy has not a local minimum. Thus, a contribution has been made to the inversion of Lagrange's theorem.

This paper deals with the buckling of a column which is modeled by some finite rigid segments and elastic rotational springs and relating its solution to continuum nonlocal elasticity. This problem, which can be referred to Hencky's chain, can serve as a basic model to rigorously investigate the effect of the microstructure on the buckling behaviour of a simple equivalent continuum structural model. The buckling problem of the pinned-pinned discretized column is analytically investigated by introducing a Lagrange multiplier. Such a buckling problem is mathematically treated as an iterative eigenvalue problem. It is shown that the buckling load of this finite degree-of-freedom system is exactly obtained by a recursive formula involving Chebyschev polynomials. Euler's buckling load is asymptotically obtained at larger scales. However, at smaller scales, the buckling model highlights some scale effect that can be only captured by nonlocal elasticity for the equivalent continuum. We show that Eringen's nonlocal continuum is well suited to capture this scale effect. The small scale coefficient of the equivalent nonlocal continuum is then identified from the specific microstructure features, namely the length of each cell. It is shown that the small length scale coefficient valid for this buckling problem is very close to the one already identified from a comparison with the Born-Kármán model of lattice dynamics using dispersive wave properties.

We consider conservation laws with spatially discontinuous flux that are perturbed by diffusion and dispersion terms. These equations arise in a theory of two-phase flow in porous media that includes rate-dependent (dynamic) capillary pressure and spatial heterogeneities. We investigate the singular limit as the diffusion and dispersion parameters tend to zero, showing strong convergence towards a weak solution of the limit conservation law.

We study grain boundaries in the Swift-Hohenberg equation. Grain boundaries arise as stationary interfaces between roll solutions of different orientations. Our analysis shows that such stationary interfaces exist near onset of instability for arbitrary angles between the roll solutions. This extends prior work in [6] where the analysis was restricted to large angles, that is, weak bending near the grain boundary. The main new difficulty stems from possible interactions of the primary modes with other resonant modes. We generalize the normal form analysis in [6] and develop a singular perturbation approach to treat resonances.

In present paper the inverse problem on the identification of three non-homogeneous residual stress components in rectangular plate in steady-state vibration regime is considered. The equation building the iterative process of solving the inverse problem is formulated. An approach to the reconstruction of residual stresses is described on the basis of introduction the Airy prestress function. The technique of leading the inverse problem to a system of linear algebraic equations at each iteration is proposed. Results of conducting a series of computational experiments on the reconstruction are depicted and discussed.

In this paper, we study the supercritical aggregation equation. We prove the global well-posedness for small initial data lying in Besov spaces and the local well-posedness for arbitrary initial data. The Fourier localization technique and the Littlewood-Paley theory are the main tools used in the proof.

This paper presents an overview of modeling fractal media by continuum mechanics using the method of dimensional regularization. The basis of this method is to express the balance laws for fractal media in terms of fractional integrals and, then, convert them to integer-order integrals in conventional (Euclidean) space. Following an account of this method, we develop balance laws of fractal media (continuity, linear and angular momenta, energy, and second law) and discuss wave equations in several settings (1d and 3d wave motions, fractal Timoshenko beam, and elastodynamics under finite strains). We then discuss extremum and variational principles, fracture mechanics, and equations of turbulent flow in fractal media. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions and reduce to conventional forms for continuous media with Euclidean geometries upon setting the dimensions to integers. We also point out relations and potential extensions of dimensional regularization to other models of microscopically heterogeneous physical systems.

The existence of solutions is proved for the unilateral dynamic contact of a von Kármán-Donnell shell with a rigid obstacle. Both purely elastic material and a material with a singular memory are treated.

In this paper, we study the spatial behavior of three phase-field models. First, we consider the Cahn-Hilliard equation and we obtain the exponential decay of solutions under suitable assumptions on the data. Then, for the classical isothermal phase-field equation (i.e., the Allen-Cahn equation), we prove the nonexistence and the fast decay of solutions and, for the nonisothermal case governed by the Fourier law, we obtain a Phragmén-Lindelöf alternative of exponential type, respectively.

The motion of a chain of three identical bodies along a straight line in a dry-friction medium is studied. The motion is excited and controlled by changing the distances between the bodies of the chain. An undulatory excitation mode is proposed, in which the distances between the adjacent bodies of the chain change periodically and the time histories of the distances in the pairs of adjacent bodies consecutively repeat each other with a constant time shift. It looks like a wave is running along the chain. The necessary and sufficient conditions for the system to be able to move from rest are established. For a specific excitation mode, in which the time histories of the distances between the bodies of the chain are defined as piecewise quadratic functions, a steady-state motion of the system is studied for the case where the friction force is small in comparison with the force necessary for a body of the chain to be moved from a state of rest through a distance characterizing the amplitude of oscillations of adjacent bodies during the excitation period.

This paper proposes a novel event-based control method for nonlinear systems that are input-output linearizable. A method for the design of an event-based state-feedback controller is proposed which approximates the disturbance rejection behavior of a continuous state-feedback system, referred to as reference system, with adjustable accuracy, while simultaneously reducing the feedback communication effort. The event-based control loop is shown to be input-to-state stable. A bound for the deviation between the behavior the event-based control loop and the reference system is derived. This bound is shown to be a function of the event threshold, which is a design parameter that can be freely chosen. Moreover, the deviation between the outputs of both systems is also proven to be bounded and can be made arbitrarily small by appropriately scaling the event threshold. The minimum time in between consecutive events is shown to be bounded from below by some bound which is explicitly determined. The efficiency of the new control method is demonstrated for a bioreactor example.

We prove that the stability problem of a vertical uniform rotation of a heavy top is completely solved by using the linearization method and the conserved quantities of the differential system which describe the rotation of the heavy top.

Optimal design problems for semiconductor devices with relevant thermal effects can be formulated by help of the energy transport model. In this paper we perform a sensitivity analysis to derive the first-order necessary condition for the optimization. Exploiting the special structure of the KKT system we use a special variant of the classical Gummel iteration to provide a very fast optimization algorithm. Numerical results for a ballistic diode underline the feasibility of our approach.

In this paper, the propagation of acoustic waves along a duct system, where a semi-infinite circular rigid pipe with a rigid end face is placed axially inside an infinite circular rigid pipe is analyzed rigorously. First, direct Fourier transform is applied and the problem is reduced into the solution of a modified Wiener-Hopf equation of the second type from which the reflection and transmission coefficients are determined. Then the bifurcated circular waveguide problem is solved by applying direct Fourier transform again to reduce the problem into the solution of a Wiener-Hopf equation and the resulting transfer coefficients are taken into account when applying the building block method. Building block method is one of the scattering matrix techniques where reflection and transmission characteristics of each discontinuity in a duct are first determined independently and then taken into account as scattering matrices in order to analyze the original problem. At the end of the analysis, numerical results are presented comparing two approaches of formulation and illustrating the effects of the radii of the pipes and frequency.

Free axisymmetric vibrations of a single-walled carbon nanotube (SWCNT) embedded in a nonhomogeneous elastic matrix are studied on the base of the nonlocal continuum shell theory. The effect of the surrounding elastic medium are considered using the Winkler-type spring constant which is assumed to be variable along the tube axis. The tube may be prestressed by external tensile forces. The Flügge type shell equations, including the initial membrane hoop and axial stresses, are used as the governing ones. The constitutive equations are formulated by considering the small-scale effects. Using the asymptotic approach, the SWCNT eigenmodes are constructed in the form of functions decreasing rapidly away from some “weakest” line which is assumed to be far from the tube edges. This study shows that introducing the small length scale parameter into the tube model allows to take into account inclusions in the surrounding elastic matrix which may results in the strong localization of some eigenmodes. The dependence of the natural frequencies and the power of the localization of the corresponding modes upon the constant of non-locality, tensile stresses and the nanotube radius is analyzed.

We study a dynamic problem for linearly electro-elastic materials, permitting piezoelectric effects. As a theoretical result, we state and prove the existence of a unique solution to the problem by using arguments of semi-linear evolutionary equations and semigroups of linear continuous operators. Then we introduce a fully discrete scheme to solve the problem numerically. Under certain solution regularity assumptions, we derive an optimal order error estimate. Finally, we present some numerical results on a two-dimensional test problem to illustrate the theoretical error estimate.

One of the main challenges of using photoelasticity has always been its complexity to determining all stress components, for it provides an unfinished solution. Indeed, the use of the Beltrami-Michell Boundary Value Problem remains of practical interest for the study of the stress-separation, when complemented by the photoelasticity analysis to acquire the Dirichlet conditions. The synergy of both is enhanced with the use of Finite Difference Method to work out a photoelastic-numerical hybrid method for stress analysis under plane conditions. On the other hand, while for photoelasticity specially, annular disks under diametral compressive load are usually used as standard models allowing to check the performance of any developed method; because theoretical solutions exist. A comprehensive study has been carried out to show the photoelastic-numerical method in order to investigate the in-plane stress distribution using isochromatic values only on the boundaries of an annular object subjected to diametral compression. Compared with a reference work, the obtained results are more than concluding. The method is fast in the analysis for a low cost.

We consider large deformations of curved thin shells in the framework of a classical Kirchhoff-Love theory for material surfaces. The geometry of the element is approximated via the position vector and its derivatives with respect to the material coordinates at the four nodes, and C¹ continuity of the surface over the interfaces between the elements is guaranteed. Theoretical background provides certainty concerning the boundary conditions, the range of applicability of the model, extensions to multi-field problems, etc. Robust convergence and accuracy of the resulting simple numerical scheme is demonstrated by the analysis of benchmark problems in comparison with other solutions.

This paper is concerned with a dual-mixed formulation for a three dimensional exterior Stokes problem via boundary integral equation methods. Here velocity, pressure and stress are the main unknowns. Following a similar analysis given recently for the Laplacian, we are able to extend the classical Johnson & Nédélec procedure to the present case, without assuming any restrictive smoothness requirement on the coupling boundary, but only Lipschitz-continuity. More precisely, after using the incompressibility condition to eliminate the pressure, we consider the resulting velocity-stress approach with a Neumann boundary condition on an annular bounded domain, and couple the underlying equations with only one boundary integral equation arising from the application of the normal trace to the Green representation formula in the exterior unbounded region. As a result, we obtain a saddle point operator equation, which is then analyzed by the well-known Babuška-Brezzi theory: in particular, the well-posedness of the formulation will be established.

The method of elastic multibody systems is frequently used to describe the dynamical behavior of the mechanical subsystems in multi-physics simulations. One important issue for the simulation of elastic multibody systems is the error-controlled reduction of the flexible body's degrees of freedom. By the use of second order frequency-weighted Gramian matrix based reduction techniques the distribution of the loads is taken into account a-priori and very accurate models can be obtained within a predefined frequency range and even a-priori error bounds are available. However, the calculation of the frequency-weighted Gramian matrices requires high computational effort. Hence, appropriate approximation schemes have to be used to find the dominant eigenspace of these matrices. In the current contribution, the matrix integral needed for calculating the Gramian matrices is approximated by quadratures using integral kernel snapshots. The number and location of these snapshots have a strong influence on the reduction results. Sophisticated snapshot selection methods based on Greedy algorithms from the reduced basis methods are used to construct the optimal location of snapshot frequencies. The method can be viewed as an automatic determination of optimal frequency weighting and as an adaptive learning of quadrature rules. One ingredient of Greedy algorithms is the need of error measures. To gain computational advantage two different error estimators are derived and used in the Greedy algorithm instead of the absolute or relative error.

An electrically conducting fluid is driven by a rotating disk, in the presence of a magnetic field that is strong enough to produce significant Hall currents. The disk is porous, allowing mass transfer through suction or injection. The limiting behavior of the flow is studied, as the magnetic field strength grows indefinitely. The flow variables are properly scaled, and uniformly valid asymptotic expansions of the velocity components are obtained through parameter straining. The leading order approximations show sinusoidal behavior that is decaying exponentially, as we move away from the disk surface. The two-term expansions of the radial and azimuthal surface shear stress components, as well as the far field inflow speed, compare well with the corresponding finite difference solutions; even at moderate magnetic fields.

The dynamic response of a cracked magnetoelectroelastic layer sandwiched between dissimilar elastic layers under anti-plane shear and in-plane electric and magnetic impacts is investigated by the integral transform method. Fourier transforms and Laplace transforms are applied to reduce the mixed boundary value problem of the impermeable crack to simultaneous dual integral equations, which are then expressed in terms of simultaneous Fredholm integral equations of the second kind. The stress field, electric field and magnetic field near the crack tip are obtained asymptotically, and the corresponding field intensity factors are further determined. Numerical results show that the stress intensity factors are influenced by the material properties, the electric and magnetic loadings, and the geometry. The crack initiation can be enhanced or retarded depending on the electric and magnetic loading, and the crack may propagate along its original crack line when the criterion of maximum hoop stress is applied.

The Riemann solutions without vacuum states for compressible duct flows have been completely constructed in the paper [11]. However, the nonuniqueness of Riemann solutions due to a bifurcation of wave curves in state space is still an open problem. The purpose of this paper is to single out the physically relevant solution among all the possible Riemann solutions by comparing them with the numerical results of the axisymmetric Euler equations. Andrianov and Warnecke in [2] suggested using the entropy rate admissibility criterion to rule out the unphysical solutions. However, this criterion is not true for some test cases, i.e. the numerical result for axisymmetric three dimensional flows picks up an exact solution which does not satisfy the entropy rate admissibility criterion. Moreover, numerous numerical experiments show that the physically relevant solution is always located on a certain branch of the L–M curves.

The paper analyzes the motion of nonholonomic mechanical systems composed of two particles with imposition of various nonlinear limitations to the velocities of the particles – parallelism of velocities, equality of the intensities of velocities and perpendicularity of velocities. The analysis for such systems includes: equations of constraints, reactions of constraints, i.e. the mode of variations of such constraints, trajectories of the points of the systems, linear integrals for generalized velocities, i.e. cyclical coordinates. It is clearly demonstrated on these models that in the case of nonlinear nonholonomic constraints the Hamiltonian effect, in the general case, has no stationary value. Lastly, the equations of brachistochronic motion of described systems are derived and the brachitochrones of specified points are determined.

We address an optimization problem related to a diffusive flow in a nonhomogeneous porous medium. More exactly, the purpose is to control by a flow parameter an optimal average of the solution in a subset of the domain. The state model is degenerate and ill-posed and this requires to develop a technique of optimization for a singular state system.

Classical plate buckling theory is obtained systematically as the small-thickness limit of the three-dimensional linear theory of incremental elasticity with null incremental data. Various a priori assumptions associated with classical treatments of plate buckling, including the Kirchhoff–Love hypothesis, are here derived rather than imposed, and the conditions under which they emerge are stated precisely.

Large amplitude free vibration behavior of thin, isotropic square plate configurations resting on Winkler type of elastic foundation are expressed in the form of simple closed-form solutions by using the Rayleigh-Ritz (R-R) method based on coupled displacement fields (CDF). Geometric non-linearity of von-Kármán type is taken into consideration. The in-plane displacement field variations used in the formulation of the R-R (CDF) method are derived by using the governing in-plane static differential equations of the plate which in turn simplifies the difficulty of assuming an in-plane displacement field variations of the plate. Accuracy and robustness of proposed closed-form solutions is compared to the available finite element formulation results. Proposed closed-form solutions are corrected for the simple harmonic motion (SHM) assumption using the well established harmonic balance method (HBM) which is applicable for the homogeneous form of cubic non-linear Duffing equation.

In space semi-discretized equations of elastodynamics with weakly enforced Dirichlet boundary conditions lead to differential algebraic equations (DAE) of index 3. We rewrite the continuous model as operator DAE and present an index reduction technique on operator level. This means that a semi-discretization leads directly to an index-1 system. We present existence results for the operator DAE with nonlinear damping term and show that the reformulated operator DAE is equivalent to the original equations of elastodynamics. Furthermore, we show that index reduction and semi-discretization in space commute if the discretization schemes are chosen in an appropriate way.

The majority of processes in composite materials involve a wide range of scales. Because of the scale disparity in multi scale problem, it's often impossible to resolve the effect of small scales directly. In this paper we perform multi scale modeling in order to analyze properties of composite materials with periodical structure under temperature and stresses influence. Each component has its own thermal and mechanical (elastic) properties. We replace differential equations with rapidly oscillating coefficients by homogenized equations having effective parameters, incorporating multi scale structure and properties of any component. The influence of any component's properties and of the layer thickness on the effective properties of whole sample has been studied. We perform comparison of results, obtained with and without account for thermostresses.

We study flow problems in unsaturated porous media. Our main interest is the gravity driven penetration of a dry material, a situation in which fingering effects can be observed experimentally and numerically. The flow is described by either a Richards or a two-phase model. The important modelling aspect regards the capillary pressure relation which can include static hysteresis and dynamic corrections. We report on analytical existence and instability results for the corresponding models and present numerical calculations. We show that fingering effects can be observed in various models and discuss the importance of the static hysteresis term.

For the approximation of steady state solutions, we propose an iterated defect correction approach to achieve higher-order accuracy. The procedure starts with the steady state solution of a low-order scheme, in general a second order one. The higher-order reconstruction step is applied a posteriori to estimate the local discretization error of the lower-order finite volume scheme. The defect is then used to iteratively shift the basic lower-order scheme to the desired higher-order accuracy given by the polynomial reconstruction. Hence, instead of solving the high-order discrete equations the low-order basic scheme is solved several times. This avoids that the high-order reconstruction with a large stencil has to be implemented into an existing basic solver and can be seen as a non-intrusive approach to higher-order accuracy.

In this paper we use a layer potential analysis to show the existence of solutions for a Dirichlet-transmission problem for pseudodifferential Brinkman operators on Sobolev and Besov spaces associated to Lipschitz domains in compact boundaryless Riemannian manifolds. Compactness and invertibility properties of corresponding layer potential operators on L^p, Sobolev, or Besov scales are also obtained.

In this work a simple and effective method is proposed to solve the problem corresponding to plane strain deformations of an N-phase decagonal quasicrystalline circular inclusion-matrix system in which the circular inclusion is bonded to the surrounding matrix through (N-2) co-axial interphase layers. We consider three kinds of thermomechanical loadings: (i) the matrix is subjected to a remote uniform stress field; (ii) the composite undergoes a uniform temperature change; (iii) the matrix is subjected to a uniform heat flux at infinity. We find that it is sufficient to manipulate three 8 × 8 real matrices, a 5 × 5 real matrix, and another 4 × 4 real matrix to arrive at the complete temperature and thermoelastic fields within the circular inclusion and the surrounding matrix, irrespective of the number of interphase layers existing within the composite system. Our results clearly indicate that the existence of the intermediate interphase layer(s) mean that the internal stresses within the circular inclusion are: (i) sextic functions of the two coordinates x₁ and x₂ under the loading of a remote uniform stress field; (ii) quadratic functions of the two coordinates under the loading of a uniform temperature change; (iii) cubic functions of the two coordinates under the loading of a remote uniform heat flux. The design of neutral and harmonic coated circular inclusions is also discussed as an application of the derived solution. Our analysis suggests that a coated inclusion can be made neutral only to a remote isotropic phonon stress field; whereas it can be made harmonic to any remote uniform phonon stress field.

We study the positivity of solutions of a class of semi-linear parabolic systems of stochastic partial differential equations by considering random approximations. For the family of random approximations we derive explicit necessary and sufficient conditions such that the solutions preserve positivity. These conditions imply the positivity of the solutions of the stochastic system for both Itô's and Stratonovich's interpretation of stochastic differential equations.

We give a short overview of an extended Discontinuous Galerkin and Spectral Difference Method using PKD polynomials on triangular grids. A corresponding exponential filter is used to avoid oscillations near discontinuous solutions and to give some stabilization for nonsmooth testcases.

The sedimentation of a polydisperse suspension with particles belonging to N size classes (species) can be described by a system of N nonlinear, strongly coupled scalar first-order conservation laws. Its solutions usually exhibit kinematic shocks separating areas of different composition. Based on the so-called secular equation [J. Anderson, Lin. Alg. Appl. 246, 49–70 (1996)], which provides access to the spectral decomposition of the Jacobian of the flux vector for this class of models, Bürger et al. [J. Comput. Phys. 230, 2322–2344 (2011)] proposed a spectral weighted essentially non-oscillatory (WENO) scheme for the numerical solution of the model. It is demonstrated that the efficiency of this scheme can be improved by the technique of Adaptive Mesh Refinement (AMR), which concentrates computational effort on zones of strong variation. Numerical experiments for the cases N = 4 and N = 7 are presented.

We investigate controllability properties of bilinear control systems, defined by classes of Toeplitz matrices. It is shown that the Lie algebra of all pseudo-circulant matrices coincides with the full matrix Lie algebra. This implies the controllability of associated bilinear control systems. As a by-product we deduce that every complex invertible matrix is the finite product of invertible Toeplitz matrices; moreover, every complex unitary matrix is shown to be a finite product of complex unitary Toeplitz matrices.

We construct and analyze sparse tensorized space-time Galerkin discretizations for boundary integral equations resulting from the boundary reduction of nonstationary diffusion equations with either Dirichlet or Neumann boundary conditions. The approach is based on biorthogonal multilevel subspace decompositions and a weighted sparse tensor product construction. We compare the convergence behavior of the proposed method to the standard full tensor product discretizations. In particular, we show for the problem of nonstationary heat conduction in a bounded two- or three-dimensional spatial domain that low order sparse space-time Galerkin schemes are competitive with high order full tensor product discretizations in terms of the asymptotic convergence rate of the Galerkin error in the energy norms, under lower regularity requirements on the solution.

The modelling of diffraction of time-harmonic electromagnetic or acoustic waves from obstacles and screens leads to boundary value problems for the three-dimensional Helmholtz equation with Dirichlet, Neumann, or other conditions on the boundary. A prominent example is the problem of diffraction from a quarter-plane in ℝ³, which admits an explicit solution. In this paper the Dirichlet and Neumann problems for the three-quarter-plane are solved by an algebraic trick: the matricial coupling of operators associated to “dual” boundary value problems, a kind of abstract Babinet principle.

We used cube corner, Berkovich, cono-spherical, and Vickers indenters to measure the indentation modulus of highly oriented bulk pyrolytic carbon both normal to and parallel to the plane of elastic isotropy. We compared the measurements with elastic constants previously obtained using strain gage methods and ultrasound phase spectroscopy. While no method currently exists to extract the anisotropic elastic constants from the indentation modulus, the method of Delafargue and Ulm (DU) [17] was used to predict the indentation modulus from the known elastic constants. The indentation modulus normal to the plane of isotropy was %sim; 20% higher than the DU predictions and was independent of indenter type. The indentation modulus parallel to the plane of isotropy was 2–3 times lower than DU predictions, was depth dependent, and was lowest for the cube corner indenter. We attribute the low indentation modulus to nanobuckling of the graphite-like planes and the indenter type dependence to the impact of differing degree of transverse stress on the tendency toward nanobuckling.

Cube corner, Berkovich, cono-spherical, and Vickers indenters have been used to measure the indentation modulus of highly oriented bulk pyrolytic carbon both normal to and parallel to the plane of elastic isotropy. The indentation modulus normal to the plane of isotropy was ~ 20% higher than the predictions of Delafargue and Ulm (DU) and was independent of indenter type. The indentation modulus parallel to the plane of isotropy was 2–3 times lower than DU predictions, was depth dependent, and was lowest for the cube corner indenter. The impact of differing degree of transverse stress on the tendency toward nanobuckling is assumed to be relevant.

In this work, the linear elastic material properties of differently textured variants of pyrolytic carbon are homogenized from the submicro- to the micro-scale. In high resolution transmission electron microscope (HRTEM) lattice fringe images, the microstructure of pyrolytic carbon manifests itself in terms of projections of graphene layers. According to their orientation distribution, different textures of pyrolytic carbon have been classified. Assuming a von Mises-Fisher distribution for the spatial orientation of single graphene layers, the orientation distribution function of the projected layers in the image plane is analytically found to be a modified Struve function. For each pyrolytic carbon texture, Maximum-likelihood estimates for the mean orientation and the concentration parameter of the von Mises-Fisher distribution are obtained numerically. Hereby, Fourier transformation and appropriate filters are used to determine the probabilities for discrete orientations of the graphene layers directly from HRTEM images. First- and second-order bounds of the linear elastic properties of pyrolytic carbon of the different textures are computed. Elastic constants of graphite and pyrolytic graphite have been used for modeling the elastic behavior of the graphene layers within a continuum mechanical setting. Due to the high anisotropy of all analyzed textures of pyrolytic carbon, the differences even between the second-order bounds are quite large.

In this work, the linear elastic material properties of differently textured variants of pyrolytic carbon are homogenized from the submicro- to the micro-scale. Assuming a von Mises-Fisher distribution for the spatial orientation of single graphene layers, the orientation distribution function of the projected layers in the image plane is analytically found to be a modified Struve function. For each pyrolytic carbon texture, Maximum-likelihood estimates for the mean orientation and the concentration parameter of the von Mises-Fisher distribution are obtained numerically. Hereby, Fourier transformation and appropriate filters are used to determine the probabilities for discrete orientations of the graphene layers directly from HRTEM images. First- and second-order bounds of the linear elastic properties of pyrolytic carbon of the different textures are computed.

The microstructure of carbon/carbon composites obtained by chemical vapor infiltration of carbon-fiber felts was studied comparatively by means of Raman spectroscopy, polarized light microscopy (PLM), scanning electron microscopy (SEM), and X-ray diffraction. The matrices, which are homogeneously textured according to PLM, exhibit pronounced spatial structural gradients at the sub-μm scale if investigated by means of Raman microprobe spectrometry. The Raman and SEM observations demonstrate that the high-temperature treatment correlates with the increasing development of the graphitic ordering in low- and high-textured pyrolytic carbon matrices.

The microstructure of infiltrated carbon-fiber felts has been studied by means of Raman spectroscopy, polarized light microscopy, scanning electron microscopy, and X-ray diffraction. It has been found that the high-temperature treatment correlates with the increasing development of the graphitic ordering in low- and high-textured pyrolytic carbon matrices.

Thermal expansion of differently-textured pyrolytic carbon matrices (pyrocarbons) of carbon/carbon composites was studied with a high temperature X-ray diffraction at temperatures ranging from 25°C to 1400°C. The composites were synthesized by chemical vapor infiltration of a carbon fiber felt, using methane as a carbon source. From the linear dependence of the lattice displacement on temperature, coefficients of thermal expansion (CTE) of the pyrocarbons were calculated. One-dimensional thermal expansion along the (002)-direction (c-axis) of the pyrocarbons was found to be proportional to the composite synthesis temperature. A correlation between CTE and pyrocarbon texture was found: low-textured pyrocarbon with an extinction angle (Ae) of 10° exhibits a smaller CTE of 2.02 × 10^-5 K^-1, whereas high-textured pyrocarbon with an Ae of 22° exhibits a considerably higher CTE of 2.65 × 10^-5 K^-1. However, CTE of high-textured pyrocarbon is still smaller than that of graphite, which is 2.9 ×10^-5 K^-1.

Thermal expansion of pyrolytic carbon matrices (pyrocarbons)of carbon/carbon composites has been studied at temperatures ranging from 25°C to 1400°C. One-dimensional thermal expansion along the (002)-direction (c-axis) of the pyrocarbons has been found to be proportional to the composite synthesis temperature. A correlation between the coefficient of thermal expansion (CTE) and pyrocarbon texture has been found: low-textured pyrocarbon with an extinction angle (Ae) of 10° exhibits a smaller CTE of 2.02 × 10^-5 K^-1, whereas high-textured pyrocarbon with an Ae of 22° exhibits a considerably higher CTE of 2.65 × 10^-5 K^-1.

Statistical analysis procedure is proposed to characterize volume, shape and orientation distribution of pores in chemical vapor infiltrated carbon/carbon composites. The microstructure data is provided by X-ray microtomography. To characterize orientation distribution of pores, probability distribution functions of pore volume, orientation angles and principal moments of inertia are constructed. Based on this information, a statistically significant range of pore geometry parameters is determined for evaluation of their contribution to the effective elastic properties of the material. Using the design of experiment approach, a subset of 53 pores is selected for the finite element simulations. The results are analyzed to construct a 3-factor stochastic model of a pore contribution to the overall elastic response based on its geometric parameters. It is determined that the non-dimensionalized surface to volume ratio factor plays an important role for pores in this type of material. A 4-factor model incorporating this ratio is proposed. The model is validated by direct finite element simulations for a set of 150 randomly selected pores not included in the initial subset. The accuracy of the proposed approach is compared with the traditionally used approximation of pores by equivalent ellipsoids.

Statistical analysis procedure is proposed to characterize volume, shape and orientation distribution of pores in chemical vapor infiltrated carbon/carbon composites. The microstructure data is provided by X-ray microtomography. Using the results of finite element analysis, 3-factor and 4-factor stochastic models are constructed to correlate the pore compliance contributions with their geometric parameters. The accuracy of the proposed approach is compared with that of the traditionally used approximation of pores by equivalent ellipsoids.