A variational asymmetric phase-field model of quasi-brittle fracture: Energetic solutions and their computation.

We derive the variational formulation of a gradient damage model by applying energetic rate-independent processes and obtain regularized fracture. The exhibits different behaviour at traction compression has state-dependent dissipation potential which induces path-independent work. will show how such provides natural framework for setting up consistent numerical scheme with underlying structure derivation additional necessary conditions global optimality in form two-sided inequality. These our criteria making better choice starting guess application alternating minimization to describe crack propagation as quasistatic evolution minimizers incremental functional. apply procedure two- three-dimensional benchmark problems we compare results solution weak Euler-Lagrange equations. observe that including inequality method, describe, some problems, an equilibrium path when starts manifest, is from one obtained solving simply stationariety