Perfect plasticity with damage and healing at small strains, its modelling, analysis, and computer implementation

Prof. Dr. Jan Valdman

June 18, 2015, 12:30 p.m. S2 416-1

The quasistatic, Prandtl-Reuss perfect plasticity at small strains is combined with a gradient, reversible (i.e. admitting healing) damage which influences both the elastic moduli and the yield stress. Existence of weak solutions of the resulting system of variational inequalities is proved by a suitable fractional-step discretisation in time with guaranteed numerical stability and convergence. After finite-element approximation, this scheme is computationally implemented and illustrative 2-dimensional simulations are performed. The model allows e.g. for application in geophysical modelling of re-occurring rupture of lithospheric faults. Resulted incremental problems are solved in MATLAB by quasi-Newton method to resolve elastoplasticity component of the solution while damage component is obtained by solution of a quadratic programming problem. This is a joint work with T. Roubicek (Prague).