SUMMARY It is recognized that the convergence of FFT‐based iterative schemes used for computing the effective properties of elastic composite materials drastically depends on the contrast between the phases. Particularly, the rate of convergence of the strain‐based iterative scheme strongly decreases when the composites contain very stiff inclusions and the method diverges in the case of rigid inclusions. Reversely, the stress‐based iterative scheme converges rapidly in the case of composites with very stiff or rigid inclusions but leads to low convergence rates when soft inclusions are considered and to divergence for composites containing voids. It follows that the computation of effective properties is costly when the heterogeneous medium contains simultaneously soft and stiff phases. Particularly, the problem of composites containing voids and rigid inclusions cannot be solved by the strain or the stress‐based approaches. In this paper, we propose a new polarization‐based iterative scheme for computing the macroscopic properties of elastic composites with an arbitrary contrast which is nearly as simple as the basic schemes (strain and stress‐based) but which has the ability to compute the overall properties of multiphase composites with arbitrary elastic moduli, as illustrated through several examples. Copyright © 2011 John Wiley & Sons, Ltd.

2016-12-24T18:05:51

No abstract

In this study, we propose a micromechanics-based modification of the Gurson criterion for porous media subjected to arbitrary loadings. The proposed formulation, derived in the framework of limit analysis, consists in the consideration of Eshelbylike exterior point trial velocity fields for the determination of the macroscopic dissipation. This approach is implemented for perfectly plastic rigid von Mises matrix containing spherical voids. After the minimization procedure required by the use of the Eshelby-like trial velocity fields, we derive a two-field estimate of the macroscopic yield function. It is shown that the obtained closed-form estimate provides a significant modification of the Gurson criterion, particularly in the domain of low stress triaxialities. This estimate is first compared with existing criteria. Moreover, its accuracy is assessed through comparison with results derived from numerical exact two-field criterion and with recently available numerical bounds.

In this paper, we investigate the interfacial stress effects on the macroscopic yield function of ductile porous media containing nanosized spheroidal cavities. The solid matrix is assumed rigid-ideal plastic and of von Mises type with associated flow rule. We then perform limit analysis of a spheroidal unit cell containing a confocal spheroidal (prolate or oblate) cavity and subjected to arbitrary mechanical loadings. Voids size effects are captured by considering at the interface between the matrix and the cavity a surface stress model which relates the jump of the traction vector to the interfacial residual stress and interfacial plastic strain. This accounts for a thin shell of material in which occurs a strong plastic strain accumulation. We then provide a closed-form two-field based estimate of the overall dissipation which contains additional terms related to the interfacial plasticity. By taking advantage of this result, we derive parametric equations of the macroscopic yield surface of the nanoporous plastic material. The obtained estimates are assessed through comparisons with numerical data. Finally, it is shown that the resulting macroscopic criterion of the nanoporous material exhibits specific features such as (i) a dependence of the yield stress on the size of the spheroidal nanovoids, (ii) asymmetry between the yield stress in uniaxial tension and compression, (iii) more pronounced size effects for oblate voids than for prolate ones.

New expressions of the macroscopic criteria of perfectly plastic rigid matrix containing prolate and oblate cavities are presented. The proposed approach, derived in the framework of limit analysis, consists in the consideration of Eshelby-like trial velocity fields for the determination of the macroscopic dissipation. It is shown that the obtained results significantly improve existing criteria for ductile porous media. Moreover, for low stress triaxialities, these new results also agree perfectly with the (nonlinear) Hashin–Shtrikhman bound established by Ponte-Castañeda and Suquet

A computational homogenization method to determine the effective parameters of Mindlin's Strain Gradient Elasticity (SGE) model from a local heterogeneous Cauchy linear material is developed. The devised method, which is an extension of the classical one based on the use of Quadratic Boundary Conditions, intents to correct the well-known non-physical problem of persistent gradient effects when the Representative Volume Element (RVE) is homogeneous. Those spurious effects are eliminated by introducing a microstructure-dependent body force field in the homogenization scheme together with alternative definitions of the localization tensors. With these modifications, and by a simple application of the superposition principle, the higher-order stiffness tensors of SGE are computed from elementary numerical calculations on RVE. Within this new framework, the convergence of SGE effective properties is investigated with respect to the size of the RVE. Finally, a C 1-FEM procedure for simulating the behavior of the effective material at the macro scale is developed. We show that the proposed model is consistent with the solutions arising from asymptotic analysis and that the computed effective tensors verify the expected invariance properties for several classes of anisotropy. We also point out an issue that the present model shares with asymptotic-based solutions in the case of soft inclusions. Applications to anisotropic effective strain-gradient materials are provided, as well as comparisons between fully meshed structures and equivalent homogeneous models.

To cite this version:T.K. Nguyen, Vincent Monchiet, Guy Bonnet. A Fourier based numerical method for computing the dynamic permeability of periodic porous media. European Journal of Mechanics -B/Fluids, Elsevier, 2013, 37, pp