Prof. Dorothee Knees (University of Kassel)

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. In the
first part of the talk, we give an overview on concepts for rate-independent systems. In
the second part, we explain the concept of balanced viscosity solutions for damage
models in more detail and present a time-discretization scheme that combines
alternate minimization with a local minimization ansatz due to Mielke/Efendiev, [EM06],
in order to approximate this type of solutions. We proof the convergence of the
incremental solutions to balanced viscosity solutions and illustrate the behaviour of the
numerical scheme with some examples, [BRKM22, RBKM24].
[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.