Simulation of crack propagation based on eigenerosion in brittle and ductile materials subject to finite strains

In this paper, a framework for the simulation of crack propagation in brittle and ductile materials is proposed. The framework is derived by extending the eigenerosion approach of Pandolfi and Ortiz (Int J Numer Methods Eng 92(8):694–714, 2012. 10.1002/nme.4352) to finite strains and by connecting it with a generalized energy-based, Griffith-type failure criterion for ductile fracture. To model the elasto-plastic response, a classical finite strain formulation is extended by viscous regularization to account for the shear band localization prior to fracture. The compression–tension asymmetry, which becomes particularly important during crack propagation under cyclic loading, is incorporated by splitting the strain energy density into a tensile and compression part. In a comparative study based on benchmark problems, it is shown that the unified approach is indeed able to represent brittle and ductile fracture at finite strains and to ensure converging, mesh-independent solutions. Furthermore, the proposed approach is analyzed for cyclic loading, and it is shown that classical Wöhler curves can be represented.

A non-smooth regularization of a forward–backward parabolic equation

In this paper, we introduce a model describing diffusion of species by a suitable regularization of a “forward–backward” parabolic equation. In particular, we prove existence and uniqueness of solutions, as well as continuous dependence on data, for a system of partial differential equations and inclusion, which may be interpreted, e.g. as evolving equation for physical quantities such as concentration and chemical potential. The model deals with a constant mobility and it is recovered from a possibly non-convex free-energy density. In particular, we render a general viscous regularization via a maximal monotone graph acting on the time derivative of the concentration and presenting a strong coerciveness property.