Perfect plasticity with damage and healing at small strains, its modelling, analysis, and computer implementation
This work provides a theoretical and computational framework for modeling re-occurring rupture in lithospheric faults, which is a domain-specific geophysical problem.
The paper combines Prandtl-Reuss perfect plasticity with gradient damage and healing, proving existence of weak solutions via a fractional-step discretization and demonstrating computational implementation with 2D simulations.
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 resulted system of variational inequalities is proved by a suitable fractional-step discretisation in time with guaranteed numericalstability 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.