How Criticality Meets Bifurcation in Compressive Failure of Disordered Solids

Abstract

Continuum mechanics describes compressive failure as a standard bifurcation in the response of a material to an increasing load: Damage, which initially grows uniformly in the material, localizes within a thin band at failure. Yet, experiments recording the acoustic activity preceding localization evidence power-law-distributed failure precursors of increasing size, suggesting that compressive failure is a critical phenomenon. 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 adequately described by a nonstationary depinning equation derived from damage mechanics and reminiscent of critical phenomena. In this description, precursors are damage cascades emerging from the interplay between the material's disorder and the long-range stress redistributions following individual damage events. Yet, the divergence of their characteristic size close to failure, which we observe in our experiments, is not the signature of a transition toward criticality. Instead, the system remains at a fixed distance to the critical point at all stages of the damage evolution. The divergence results from the progressive loss of stability of the material as it is driven toward localization. Thus, our study shows that compressive failure is a standard bifurcation for which the material disorder plays a marginal role. It also implies that the precursory acoustic activity behaves as a tracer of the evolution of materials toward failure and can therefore be used to assess their residual lifetime.