Damage and size effects in elastic solids: A homogenization approach

Abstract The paper presents a new procedure to construct micro-mechanical damage models able to describe size effects in solids. The new approach is illustrated in the case of brittle materials. We use homogenization based on two-scale asymptotic developments to describe the overall behavior of a damaged elastic body starting from an explicit description of elementary volumes with micro-cracks. An appropriate micro-mechanical energy analysis is proposed leading to a damage evolution law that incorporates stiffness degradation, material softening, size effects, unilaterality, different fracture behaviors in tension and compression, induced anisotropy. The model also accounts for micro-crack nucleation and growth. Finite element solutions for some numerical tests are presented in order to illustrate the ability of the new approach to describe known behaviors, like the localization of damage and size-dependence of the structural response. Based on a correct micro-mechanical description of the energy dissipation associated with failure, the model avoids significant mesh dependency for the localized damage finite element solutions.

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