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A set of enhanced formulations for existing nonlinear homogenization schemes and their evaluation

Abstract : On the basis of non-biased comparative evaluations of various linearization procedures used in nonlinear homogenization, performed both at the global and local scales for power-law composites [37, 39, 40], we propose in this paper six ad hoc enhancements of some of the linearization procedures considered in [39]. Both "stress-strain" approaches (the secant and affine formulations) or "variational formulations" (the tangent second-order method [33]) are considered. The main idea consists in proposing alternatives for the usual reference strains used by the secant, affine and tangent second-order procedures. The new linear comparison composites generated by the linearization step around the chosen alternative descriptors of the strain field statistics explicitly account for either intraphase strain fluctuations or both inter- and intraphase strain fluctuations. As a first illustration, the relevance and limitations of the enhanced linearization procedures are tested for rigidly-reinforced and porous power-law composites. For isochoric loadings, it is shown that two variants of the enhanced tangent second-order formulation lead to accurate estimates of the exact effective response which are in good agreement with the efficient second-order scheme of Ponte Castañeda [35]. Further, the modified secant formulation provides good results for strongly nonlinear rigidly-reinforced composites away from low particulate volume fraction and the percolation threshold; however some new inherent limitations of secant formulations are also established. At last, a very discriminant situation is tested: it consists of a porous medium submitted to a pure hydrostatic loading at low pore concentrations. It is shown that one variant of the proposed enhanced second-order formulations leads to accurate estimates alike the efficient and more sophisticated formulations proposed in [3, 9].
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Amna Rekik, François Auslender, Michel Bornert. A set of enhanced formulations for existing nonlinear homogenization schemes and their evaluation. European Journal of Mechanics - A/Solids, Elsevier, 2015, pp.10.1016/j.euromechsol.2014.10.001. ⟨10.1016/j.euromechsol.2014.10.001⟩. ⟨hal-01071907⟩

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