Numerical approach to a model for quasistatic damage with spatial $BV$-regularization
- Bartels, Sören
- Milicevic, Marijo
- Thomas, Marita
2010 Mathematics Subject Classification
- 35K85 74R05 49J45 49S05 65M12
- Partial damage, damage evolution with spatial regularization, functions of bounded variation, semistable energetic solutions, numerical approximation
We address a model for rate-independent, partial, isotropic damage in quasistatic small strain linear elasticity, featuring a damage variable with spatial BV-regularization. Discrete solutions are obtained using an alternate time-discrete scheme and the Variable-ADMM algorithm to solve the constrained nonsmooth optimization problem that determines the damage variable at each time step. We prove convergence of the method and show that discrete solutions approximate a semistable energetic solution of the rate-independent system. Moreover, we present our numerical results for two benchmark problems.
- Proceedings of the INdAM-ISIMM Workshop on Trends on Applications of Mathematics to Mechanics, Rome, Italy, September 2016, E. Rocca, U. Stefanelli, L. Truskinovsky, eds., vol. 27 of Springer INdAM Series, Springer International Publishing, Cham, 2018, pp. 179--203, DOI 10.1007/978-3-319-75940-1_9 .