Size effects for micro-fractured bodies under compressive loading. (English) Zbl 1299.74020

Summary: A two-scale damage model for micro-fractured media is constructed using the asymptotic homogenization method. At the small-scale level, we consider locally periodic microstructures of two-types: micro-cracks nucleating from pores and wing-type micro-cracks. Based on an energy criterion for micro-crack propagation we deduce the macroscopic damage model, without supplementary assumptions on the overall behavior. We show that the resulting two-scale model has the property of capturing a micro-structural length – the distance between neighbor micro-cracks. The influence of the micro-structural parameters on the effective behavior is studied. We illustrate the capacity of the model to predict size effects under compression loadings.


74A60 Micromechanical theories
74Q10 Homogenization and oscillations in dynamical problems of solid mechanics
74R10 Brittle fracture
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