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Abstract: This paper is devoted to the effective behavior of linear viscoelastic heterogeneous materials with a particular emphasis on their transient response. First, two new asymptotic relations for the overall creep function are derived at short and large times. They are related to the retardation spectrum of the composite and involve second-order moments per phase of the stress field for the purely elastic and purely viscous problems. In the context of harmonic loadings, these relations provide exact frequential asymptotic conditions on the overall storage and loss moduli. Second, by making use of these asymptotic results, an approximate model is proposed. It consists in approximating the retardation spectrum of the composite by a single discrete Dirac mass. Its accuracy is assessed by comparison with exact analytical results, full-field simulations and collocation results for several classes of composites and polycrystals. [Copyright &y& Elsevier]

Abstract: A reduced model for the effective behavior of nonlinear composites, such as metal–matrix composite materials, has been recently proposed by the authors . It extends and improves on the Transformation Field Analysis of Dvorak by considering nonuniform transformation strains, also called plastic modes, and is referred to as the Nonuniform Transformation Field Analysis. The present study is devoted to the implementation of this new homogenized model into a structural computation. A brief account on the reduction procedure is given first. Then the time-integration of the model which is required at each integration point of the structural problem is performed by means of an implicit scheme. Two examples are discussed. The response of the homogenized structure is compared to the “exact” response of the actual heterogeneous structure computed with a very fine mesh. It is seen that not only the structural response is accurately captured by the NTFA model, but also the local stress field is correctly approximated. [Copyright &y& Elsevier]

The exact description of the overall behavior of composites with nonlinear dissipative phases requires an infinity of internal variables. Approximate models involving only a finite number of those can be obtained by considering a decomposition of the microscopic anelastic strain field on a finite set of transformation fields. The Transformation Field Analysis of Dvorak [Proc. R. Soc. Lond. A 437 (1992) 311] corresponds to piecewise uniform transformation fields. The present theory considers nonuniform transformation fields. Comparison with numerical simulations shows the accuracy of the proposed model. [Copyright &y& Elsevier]

Recent progress in the analysis of nonlinear composites or polycrystals suggests that higher-order moments of the local fields in individual phases could play a significant role on the effective properties of such composites. The present study is devoted to a detailed computational investigation of the first and second moment of the strain fields. It shows that the predictive schemes belonging to the class of secant methods underestimate significantly the second moments of the strain field. As a consequence, their predictions are too stiff in comparison with numerical simulations. [Copyright &y& Elsevier]

Numerical simulations of the behavior of composite materials have to take into account the complexity of their microstructural geometry. Realistic simulations involve a large number of degrees of freedom.FFT-based methods have proved their efficiency for mechanical problems (composites with linear elastic or elastic-plastic phases), and can often be much more efficient than classical finite element methods. However the iterative method initially proposed in Moulinec and Suquet (C.R. Acad. Sci. Paris II 318 (1994) 1417) requires a number of iterations roughly proportional to the contrast between the moduli of the individual phases. The improved method proposed in Eyre and Milton (J. Phys. III 6 (1999) 41) has a rate of convergence proportional to the square root of the contrast, but still cannot be applied to composites with infinite contrast (like porous materials). An alternate scheme based on augmented Lagrangians and Fourier Transforms has been proposed in Michel et al. (Comput. Modelling Eng. Sci. (2000) accepted) for highly contrasted or even infinitely contrasted materials.The efficiency of these three methods are compared as a function of the contrast between the phases. [Copyright &y& Elsevier]

This paper investigates the implementation of Field Dislocation Mechanics (FDM) theory for media with a periodic microstructure (i.e. the Nye dislocation tensor and the elastic moduli tensor are considered as spatially periodic continuous fields). In this context, the uniqueness of the stress and elastic distortion fields is established. This allows to propose an efficient numerical scheme based on Fourier transform to compute the internal stress field, for a given spatial distribution of dislocations and applied macroscopic stress. This numerical implementation is assessed by comparison with analytical solutions for homogeneous as well as heterogeneous elastic media. A particular insight is given to the critical case of stress-free dislocation microstructures which represent equilibrium solutions of the FDM theory. [ABSTRACT FROM AUTHOR]

Abstract: To exactly describe the macroscopic behaviour of composites with non linear dissipative constituents, it is necessary to take an infinitely large number of internal variables into account. Simplifying assumptions are usually adopted to reduce this number. A new method has been proposed [Michel JC, Suquet P. Nonuniform transformation field analysis. Int J Solids Struct 2003;40:6937–55], based on the transformation fields approach [Dvorak G. Transformation field analysis of inelastic composite materials. Proc Roy Soc Lond A 1992;437:311–27], but not taking transformation fields to be necessarily uniform. The interest of this new method has been shown in the case of composites with elastic–plastic constituents. Here we deal with composites having elastic–viscoplastic and porous elastic–viscoplastic constituents. In the latter case, the viscoplastic strain has a dilatational part. [Copyright &y& Elsevier]

Abstract: Understanding the flow of ice in glaciers and polar ice sheets is of increasing relevance in a time of potentially significant climate change. The flow of ice has hitherto received relatively little attention from the structural geological community. This paper aims to provide an overview of methods and results of ice deformation modeling from the single crystal to the polycrystal scale, and beyond to the scale of polar ice sheets. All through these scales, various models have been developed to understand, describe and predict the processes that operate during deformation of ice, with the aim to correctly represent ice rheology and self-induced anisotropy. Most of the modeling tools presented in this paper originate from the material science community, and are currently used and further developed for other materials and environments. We will show that this community has deeply integrated ice as a very useful “model” material to develop and validate approaches in conditions of a highly anisotropic behavior. This review, by no means exhaustive, aims at providing an overview of methods at different scales and levels of complexity. [Copyright &y& Elsevier]

Abstract: A digital image correlation (DIC) technique has been adapted to polycrystalline ice specimens in order to characterize the development of strain heterogeneities at an intragranular scale during transient creep deformation (compression tests). Specimens exhibit a columnar microstructure so that plastic deformation is essentially two-dimensional, with few in-depth gradients, and therefore surface DIC analyses are representative of the whole specimen volume. Local misorientations at the intragranular scale were also extracted from microstructure analyses carried out with an automatic texture analyzer before and after deformation. Highly localized strain patterns are evidenced by the DIC technique. Local equivalent strain can reach values as much as an order of magnitude larger than the macroscopic average. The structure of the strain pattern does not evolve with strain in the transient creep regime. Almost no correlation between the measured local strain and the Schmid factor of the slip plane of the underlying grain is observed, highlighting the importance of the mechanical interactions between neighboring grains resulting from the very large viscoplastic anisotropy of ice crystals. Finally, the experimental microstructure was introduced in a full-field fast Fourier transform polycrystal model; simulated strain fields are a good match with experimental ones. [Copyright &y& Elsevier]

The correspondence principle is customarily used with the Laplace-Carson transform technique to tackle the homogenization of linear viscoelastic heterogeneous media. The main drawback of this method lies in the fact that the whole stress and strain histories have to be considered to compute the mechanical response of the material during a given macroscopic loading. Following a remark of Mandel (1966 Mécanique des Milieux Continus (Paris, France: Gauthier-Villars)), Ricaud and Masson (2009 Int. J. Solids Struct. 46 1599-1606) have shown the equivalence between the collocation method used to invert Laplace-Carson transforms and an internal variables formulation. In this paper, this newmethod is developed for the case of polycrystalline materials with general anisotropic properties for local and macroscopic behavior. Applications are provided for the case of constitutive relations accounting for glide of dislocations on particular slip systems. It is shown that the method yields accurate results that perfectly match the standard collocation method and reference full-field results obtained with a FFT numerical scheme. The formulation is then extended to the case of time- and strain-dependent viscous properties, leading to the incremental collocation method (ICM) that can be solved efficiently by a step-by-step procedure. Specifically, the introduction of isotropic and kinematic hardening at the slip system scale is considered. [ABSTRACT FROM AUTHOR]