Irreversibility and alternate minimization in phase field fracture: a viscosity approach. (English) Zbl 1447.35312
Author’s abstract: This work is devoted to the analysis of convergence of an alternate (staggered) minimization algorithm in the framework of phase field models of fracture. The energy of the system is characterized by a nonlinear splitting of tensile and compressive strains, featuring non-interpenetration of the fracture lips. The alternating scheme is coupled with an \(L^2\)-penalization in the phase field variable, driven by a viscous parameter \(\delta \rightarrow 0\), and with an irreversibility constraint, forcing the monotonicity of the phase field only w.r.t. time, but not along the whole iterative minimization. We show first the convergence of such a scheme to a viscous evolution for \(\delta \rightarrow 0\) and then consider the vanishing viscosity limit \(\delta \rightarrow 0\).
Reviewer: Kaïs Ammari (Monastir)
MSC:
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
| 74R05 | Brittle damage |
| 74R10 | Brittle fracture |
| 74G05 | Explicit solutions of equilibrium problems in solid mechanics |
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