How criticality meets bifurcation in compressive failure of disordered solids
Résumé
Continuum mechanics describes compressive failure as a standard bifurcation in the response of a homogeneous solid to an increasing load: damage, that initially grows uniformly within the material, localizes in a thin band at failure. Yet, experiments recording the acoustic activity preceding localization evidence power law distributed damage precursors of increasing size, suggesting that compressive failure is a critical phenomenon controlled by the interplay between material disorder and long-range elastic interactions. We examine here this apparent contradiction by probing the spatial organization of the damage activity and its evolution until localization during compression experiments of 2D cellular solids. The intermittent damage evolution measured in our experiments is appropriately described by a non-stationary depinning equation derived from damage mechanics reminiscent of critical phenomena. In this description, precursors are damage cascades emerging from the interplay between the material disorder and the long-range stress redistributions following individual failure events. Yet, the divergence of their characteristic size observed in our experiments close to failure is not signature of a transition towards criticality, the system remaining at a fixed distance to the critical point at all stages of the damage evolution. Instead, it results from the progressive loss of stability of the material as it is driven towards localization. Our study shows that compressive failure is a standard bifurcation for which the material disorder plays a marginal role. It also shows that precursory failure events constitutes by-products of the evolution towards localization which can serve of warning signals for predicting the residual lifetime of structures.
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