A methodology for an accurate evaluation of the linearization procedures in nonlinear mean field homogenization

Amna Rekik (1) , Michel Bornert (1) , François Auslender (1) , André Zaoui (1)

1 LMS - Laboratoire de mécanique des solides

A systematic methodology for the evaluation of the linearization procedures sustaining mean field homogenization theories for nonlinear composite materials is proposed and applied as an illustration to various recently proposed ‘affine' and ‘second-order' formulations for nonlinear elasticity. It relies on the analysis of composites for which both the exact nonlinear homogenization problem and the homogenization problem associated with the ‘linear comparison material' defined by the linearization procedure can be solved numerically with the same accuracy and for the same microstructure. The comparison of the results then provides a rigorous evaluation of the effects of the sole linearization method.

Mots clés: Continuum mechanics; Homogenization; Nonlinear behavior; Linearization; Affine; Second order

Domaines: Mécanique des matériaux [physics.class-ph]

Amna Rekik, Michel Bornert, François Auslender, André Zaoui. A methodology for an accurate evaluation of the linearization procedures in nonlinear mean field homogenization. Comptes Rendus Mécanique, 2005, 333, pp.789-795. ⟨10.1016/j.crme.2005.10.002⟩. ⟨hal-00156073⟩