Analysis and simulation of a rate-independent phase-field damage model

Within this talk, the focus is on rate-independent damage models. Since the corresponding phase-field energies in general are non-convex, we are faced with a discontinuous evolution of the phase-field variable. Solution concepts have to be carefully chosen in order to predict discontinuities that are physically reasonable. We focus here on the concept of balanced viscosity solutions and develop a convergence scheme that combines alternate minimization with a local minimization ansatz due to Mielke/Efendiev, [EM06]. We proof the convergence of the incremental solutions to balanced viscosity solutions and illustrate the behaviour of the numerical scheme with some examples, [BRKM22].

[EM06] M. A. Efendiev, A. Mielke, On the Rate-Independent Limit of Systems with Dry Friction and Small Viscosity, Journal of Convex Analysis 13(1), 151-167, 2006.

[BRKM22] S. Boddin, F. Rörentrop, D. Knees, J. Mosler, Approximation of balanced viscosity solutions of a rate-independent damage model by combining alternate minimization with a local minimization algorithm, arXiv:2211.12940, 2022.

[RBKM24] F. Rörentrop, S. Boddin, D. Knees, J. Mosler, A time-adaptive finite element phase-field model suitable for rate-independent fracture mechanics, Computer Methods in Applied Mechanics and Engineering, vol. 431, p. 117240, 2024.