Abstract

Localization in a quasibrittle material is studied using a local second-gradient model. Since localization takes place in a medium assumed to be initially homogeneous, nonuniqueness of the solutions of an initial boundary value problem is then also studied. Using enhanced models generalizes the classical localization analysis. In particular, it is necessary to study solutions more continuous (that is, continuous up to the degree one) than the ones used in analysis involving classical constitutive equations. Within the assumptions done, it appears that localization is possible in the second-gradient model if it is possible in the underlying classical model. Then the study of nonuniqueness is conducted for the numerical problem, using different first guesses in the full Newton–Raphson procedure solving the incremental nonlinear equations. Thanks to this method, we are able to simulate qualitatively the nonreproducibility of usual experiment in the postpeak regime.

Keywords

continuum with microstructure, second gradient, finite element, bifurcation, strain localization, mode switching, reproducibility

Authors