ABSTRACT
Nonlinear continuum models with nonconvex elastic energies result in equilibrium equations that lose ellipticity at some critical level of deformation. Beyond this critical strain, discontinuous-strain solutions emerge, and due to the absence of an internal length scale, the equilibria computed using finite element methods strongly depend on the selected mesh size. In particular, this problem presents itself in nonlinear models of fracture. One such example is the Virtual Internal Bond (VIB) model (Gao and Klein, 1998; Klein and Gao, 1998, 2000; Zhang et al., 2001), where the constitutive law is found by averaging over a random network of cohesive bonds with nonconvex Lennard-Jones-type potentials. The model successfully predicts critical stress level and direction of the deformation zone for nucleation of fracture that appears as a localized zone of high strain. However, without an internal length scale it cannot predict the size of the localized deformation zone.
