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Quasi-brittle failure of heterogeneous materials : damage statistics and localization

Abstract : We propose a novel approach inspired from non-local damage continuum mechanics to describe damage evolution and quasi-brittle failure of disordered solids. Heterogeneities are introduced at a mesoscopic continuous scale through spatial variations of the material resistance to damage. The central role played by the load redistribution during damage growth is analyzed by varying the interaction function used in the non-local model formulation. The spatio-temporal evolution of the damage field is obtained from energy conservation arguments, so that the formulation is thermodynamically consistent. We analytically determine the onsets of localization and failure that appear controlled by the redistribution function. Damage spreading is characterized through a complete statistical analysis of the spatio-temporal organization of the precursors to failure. The power law increase of the rate of energy dissipated by damage and an extracted correlation length close to failure supports the interpretation of quasi-brittle failure as a critical phenomena. Indeed, we establish a connection between our damage model and the evolution law of an elastic interface driven in a disordered medium. It allows to identify the order and control parameters of the critical transition, and capture the scale-free statistical properties of the precursors within the mean field limit. Finally, we experimentally investigate the coaction of localized dissipative events and elastic redistributions in disordered media via compression experiments of two-dimensional arrays of hollow soft cylinders. Our experimental observations show a quantitative agreement with the predictions derived following our approach.
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Estelle Berthier. Quasi-brittle failure of heterogeneous materials : damage statistics and localization. Mechanics [physics]. Université Pierre et Marie Curie - Paris VI, 2015. English. ⟨NNT : 2015PA066588⟩. ⟨tel-01421842⟩

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