Numerical Study on Crack Dilatancy Part I: Models and Stability Analysis

Abstract

Discrete cracks have been modeled with interface elements in which the tractions are related to the relative displacements of the crack sides. Three stages in the cracking process can be distinguished: (1) The linear‐elastic state; (2) the development state in which a tension‐softening model is used; and (3) the open‐crack state. For the open‐crack state five different crack‐dilatancy models have been implemented. Explicit relations have been derived for the tangential stiffness matrices of these models. The tangential stiffness relations turn out to be nonsymmetrical; this has major consequences for the stability of the discretized mechanical system. The stability has been analyzed via eigenvalue analyses of the tangential‐stiffness matrix. Here, marked differences appear between the various models. This observation may have broad implications for the convergence behavior of assemblies of continuous and discrete elements in which these material models are utilized.