Our work on rate-independent systems was stimulated by our search for evolutionary
material models for shape-memory alloys that are flexible enough to encompass nonlinear …

Under a pure tensile loading, cracks in brittle, isotropic, and homogeneous materials often
propagate such that pure mode I kinematics are maintained at the crack tip. However …

Phase-field approaches to fracture based on energy minimization principles have been
rapidly gaining popularity in recent years, and are particularly well-suited for simulating …

We present a new data-driven paradigm for variational brittle fracture mechanics. The
fracture-related material modeling assumptions are removed and the governing equations …

A variational model for the analysis of crack evolution is presented. The method considers
strong discontinuities that evolve according to the principles of cohesive fracture mechanics …

This chapter reviews mathematical approaches to inelastic processes on the surfaces of
elastic bodies. We mostly consider a quasistatic and rateindependent evolution at small …

In variational phase-field modeling of brittle fracture, the functional to be minimized is not
convex, so that the necessary stationarity conditions of the functional may admit multiple …

In the nonconvex case, solutions of rate-independent systems may develop jumps as a
function of time. To model such jumps, we adopt the philosophy that rate-independence …

This paper is devoted to a numerical implementation of the Francfort–Marigo model of
damage evolution in brittle materials. This quasi-static model is based, at each time step, on …

Although the phase field method has been widely used in the field of fracture, various
models exist, such as the second-order and fourth-order phase field model in the field of …