A micromechanics-based approach for the derivation of constitutive elastic coefficients of strain-gradient media

By T. Tran, V. monchiet, Guy Bonnet. 2012

97 citations recorded by the source corpus.

Abstract A micromechanics-based approach for the derivation of the effective properties of periodic linear elastic composites which exhibit strain gradient effects at the macroscopic level is presented. At the local scale, all phases of the composite obey the classic equations of three-dimensional elasticity, but, since the assumption of strict separation of scales is not verified, the macroscopic behavior is described by the equations of strain gradient elasticity. The methodology uses the series expansions at the local scale, for which higher-order terms, (which are generally neglected in standard homogenization framework) are kept, in order to take into account the microstructural effects. An energy based micro–macro transition is then proposed for upscaling and constitutes, in fact, a generalization of the Hill–Mandel lemma to the case of higher-order homogenization problems. The constitutive relations and the definitions for higher-order elasticity tensors are retrieved by means of the “state law” associated to the derived macroscopic potential. As an illustration purpose, we derive the closed-form expressions for the components of the gradient elasticity tensors in the particular case of a stratified periodic composite. For handling the problems with an arbitrary microstructure, a FFT-based computational iterative scheme is proposed in the last part of the paper. Its efficiency is shown in the particular case of composites reinforced by long fibers.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f9247ec38855800ed8ab1224547292e0c71fa93f

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Convergence of FFT‐based homogenization for strongly heterogeneous media (2015, methodology): “The Moulinec–Suquet discretization was successfully applied to various micromechanical problems, including thermoelasticity [39], piezoelectric composites [40], elasto-viscoplasticity in polycrystals at small and finite strains [41–45], permeability [46, 47], the mechanical behavior of polycrystalli”
Computational second-order homogenization of materials with effective anisotropic strain-gradient behavior (2020, methodology): “We show that the resulting method is consistent with results obtained by asymptotic expansion techniques [60].”
Geometrically nonlinear higher-gradient elasticity with energetic boundaries (2013, background): “• The papers which try to establish which “microscopical” structure may produce at a macroscopic level general- ized continuum theories: Forest et al. (2000, 2001); Tenek and Aifantis (2001); Sunyk and Steinmann (2003); Forest and Sievert (2003); Maranganti and Sharma (2007); Nikolov et al. (2007); ”