On a model for anisotropic creep of materials

We apply the concepts of proper moduli and states, revealing the structure of the generalized Hooke’s law, to a model of anisotropic steady-state creep of materials. The steady-state creep equations for incompressible materials are expressed in invariant form. The matrix of anisotropy coefficients of these materials reduces to block form with the nine independent components. We consider the special case of an orthotropic incompressible material for which the matrix of anisotropy coefficients corresponds to a nonor.     

Mathematical model of the yield contour for anisotropic materials

The paper is concerned with a relevant question of processing of experimental data. Our aim is to construct yield contours for various structural materials of complicated rheology. The problem amounts to determining the minimum of a target function of the contour coefficients and belongs to the class of problems of regression analysis. Three approaches are considered for constructing a yield contour from experimental data: manual adjustment, the coordinate descent method, and the steepest descent method. On the basis of these three methods we suggest a procedure which provides a result with the least error. A program to implement this procedure is developed.     

Development of an elastic-plastic constitutive model for highly anisotropic materials

Homogenization methods are used to obtain the effective properties of highly anisotropic materials such like textile reinforced composites. The state of the art is the utilization of this method to compute elastic properties. But the consideration of inelastic and anisotropic properties requires the application of more advanced techniques such as the FE²-method. Due to the high numerical effort induced by this approach, this paper presents a new method to evaluate inelastic properties of an heterogeneous elastic-plastic material. The parameters describing the inelastic properties require a modification of the return mapping algorithm which is used for the numerical implementation. Finally, the verification shows the accuracy of the results obtained with this new homogenization method. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

New exact multi-coated ellipsoidal inclusion model for anisotropic thermal conductivity of composite materials

The present study deals with a new micromechanical modeling of the thermal conductivity of multi-coated inclusion-reinforced composites. The proposed approach has been developed in the general frame of anisotropic thermal behavior per phase and arbitrary ellipsoidal inclusions. Based on the Green's function technique, a new formulation of the problem of multi-coated inclusion is proposed. This formulation consists in constructing a system of integral equations, each associated to the thermal conductivity of each coating and the reference medium. Thanks to the concept of interior- and exterior-point Eshelby's conduction tensors, the exact solution of the problem of multicoated inclusion is obtained. Analytical expressions of the intensity in each phase and the effective thermal conductivity of the composite, through homogenizations schemes such as Generalized self-consistent and Mori-Tanaka models are provided. Results of the present model are successfully compared with those issued from both analytical models and finite elements methods for composites with doubly coated inclusions. Moreover, the developed micromechanical model has been applied to a three phase composite materials in order to analyze combined effects of the aspect ratio and the volume fraction of the ellipsoidal inclusions, the anisotropy of the thermal conductivity of interphase, the thermal conductivity contrast between local phases on the predicted effective thermal conductivity.     

Galerkin-based energy-momentum time-stepping schemes for anisotropic hyperelastic materials

This paper is motivated by dynamic simulations of fiber-reinforced materials in light-weight structures, and has two goals. First of all, the introduction of energy-momentum schemes for nonlinear anisotropic materials, based on GALERKIN approximations in space and time, assumed strain approximations in time and superimposed algorithmic stress fields (compare [1]). Second, to show a variationally consistent design of energy-momentum schemes using a differential variational principle. We develop a discrete variational principle leading to energy-momentum schemes as discrete EULER-LAGRANGE equations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An anisotropic flow law for incompressible polycrystalline materials

New and explicit anisotropic constitutive equations between the stretching and deviatoric stress tensors for the two- and three-dimensional cases of incompressible polycrystalline materials are presented. The anisotropy is assumed to be driven by an Orientation Distribution Function (ODF). The polycrystal is composed of transversally isotropic crystallites, the lattice orientation of which can be characterized by a single unit vector. The proposed constitutive equations are valid for any frame of reference and for every state of deformation. The basic assumption of this method is that the principle directions of the stretching and of the stress deviator are the same in the isotropic as well as in the anisotropic case. This means that the proposed constitutive laws are able to model the effects of anisotropy only via a change of the fluidity due to a change of the ODF. Such an assumption is justified to guarantee that, besides knowledge of the parameters involved in the isotropic constitutive equation, the anisotropic material response is completely characterized by only one additional parameter, a type of enhancement factor. Explicit comparisons with experimental data are conducted for Ih–ice.     

An anisotropic flow law for incompressible polycrystalline materials

New and explicit anisotropic constitutive equations between the stretching and deviatoric stress tensors for the two- and three-dimensional cases of incompressible polycrystalline materials are presented. The anisotropy is assumed to be driven by an Orientation Distribution Function (ODF). The polycrystal is composed of transversally isotropic crystallites, the lattice orientation of which can be characterized by a single unit vector. The proposed constitutive equations are valid for any frame of reference and for every state of deformation. The basic assumption of this method is that the principle directions of the stretching and of the stress deviator are the same in the isotropic as well as in the anisotropic case. This means that the proposed constitutive laws are able to model the effects of anisotropy only via a change of the fluidity due to a change of the ODF. Such an assumption is justified to guarantee that, besides knowledge of the parameters involved in the isotropic constitutive equation, the anisotropic material response is completely characterized by only one additional parameter, a type of enhancement factor. Explicit comparisons with experimental data are conducted for Ih–ice. Dedicated to Prof. L.W. Morland on the occasion of his 70^th birthday Received: July 6, 2004; revised: November 8, 2004     

Analysis of a Large Eddy Simulation model based on anisotropic filtering

We consider a new Large Eddy Simulation model, derived with the introduction of suitable horizontal (anisotropic) differential filters. One main advantage of this filtering is that, for channel flows, there is no need for artificial boundary conditions. Hence, we can deal with some realistic problems, equipped with Dirichlet boundary conditions, in special bounded domains (at least those bounded only in one direction). Recent numerical results for a similar model, based on a derivation with wave-number asymptotics, are also recalled. After a detailed analysis of the properties of the differential filter, we prove that the resulting initial–boundary value problem is well-posed in suitable anisotropic Sobolev spaces, giving a strong mathematical support to the model we propose. Some remarks on higher-accuracy Approximate Deconvolution Models are also given in the last section.     

Inference for an anisotropic diffusion model

The vector sum of a white noise in an unknown hyperspace and an Ornstein-Uhlenbeck process in an unknown line is observed through sharp linear test functions over a finite time span. The parameters associated with the white noise (including the hyperplane) are determinable with precision and index the measure-equivalence classes in the relevant sample space. An intraclass relative density provides a basis for Bayesian inference of the remaining parameters.     

Stable elastic waves in anisotropic materials

Zusammenfassung Diese Arbeit befasst sich mit der Fortpflanzung von stabilen Wellen in einem anisotropen Medium infolge einer sich bewegenden Ladung an der Grenze des Materials. Wir behandeln besonders mobile Ladungen, deren Geschwindigkeit höher ist als diejenige der Wellen im Material. Das Problem wird als ebenes Spannungsproblem behandelt.

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This work was supported by the United States Atomic Energy Commission.     

Computation of the fundamental solution of electrodynamics for anisotropic materials

A new method for computation of the fundamental solution of electrodynamics for general anisotropic nondispersive materials is suggested. It consists of several steps: equations for each column of the fundamental matrix are reduced to a symmetric hyperbolic system; using the Fourier transform with respect to space variables and matrix transformations, formulae for Fourier images of the fundamental matrix columns are obtained; finally, the fundamental solution is computed by the inverse Fourier transform. Applying the suggested approach, the fundamental solution components are computed in general anisotropic media. Computational examples confirm robustness of the suggested method.     

Plane anisotropic rari‐constant materials

We consider here the existence of rari‐constant anisotropic layers and show that actually there are two distinct classes of such materials, mutually exclusive. Also, we show that the correct condition for establishing that a material is of the rari‐constant type is that the number of independent linear tensor invariants of the elastic tensors must reduce to one. We characterize these materials and show that they can be designed by using some basic rules of homogenization. Copyright © 2015 John Wiley & Sons, Ltd.     

Material properties of anisotropic materials with pores

An approach based on cavity compliance contribution tensor is utilized for evaluation of effective stiffness of anisotropic materials with irregularly shaped pores. The shapes considered in the present work were extracted from the X-ray computed microtomography of a carbon/carbon composite sample. The cavity contribution tensors of individual pores were calculated numerically and then employed in the micromechanical modeling procedure. It was shown that presence of pores with total porosity of p = 9.13% results in approximately 20% reduction in the material's Young's moduli. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A generalized polyconvex hyperelastic model for anisotropic solids

A generalized polyconvex hyperelastic model for anisotropic solids is presented. The strain energy function is formulated in terms of convex functions of generalized invariants and is given by a series with an arbitrary number of terms. The model addresses solids with orthotropic or transversely isotropic material symmetry as well as fiber-reinforced materials. Special cases of the strain energy function suitable for anisotropic elastomers and soft biological tissues are proposed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structure and properties of magnetic fibrous polymeric materials

Characteristic features of the filtration of liquids by magnetic fibrous polymeric materials (MFPM) are addressed; these materials are a set of fibers of a polymeric material containing a ferritic filler; they are adhesively bound at points of their intersection. It is demonstrated that variations in structural parameters (fiber thickness, distribution of fiber throughout the material, and its concentration), as well as the degree and direction of magnetization of the MFPM exert an influence on the efficiency of the liquid filtration. Optimum parameters for MFPM designed to purify liquids of ferromagnetic and nonmagnetic contaminants are given.A paper to be presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 291–297, May–June, 1995.