Uncertainty Quantification of Inifinitesimal Elastoplasticity

 

Bojana Rosić

Hermann Matthies

Miroslav Živković

 

We analyse the stochastic finite element method for a class of mixed variational inequalities of the second kind, which arises in elastoplastic problems. The quasi-static von Mises elastoplastic rate-independent evolution problem with linear isotropic hardening is considered with the emphasis on the presence of uncertainty in the description of material parameters. Within one time-step of backward Euler discretization, the stochastic finite element method leads to a minimisation problem for smooth convex functions on discrete tensor product subspaces, whose unique minimiser is obtained via the closest point projection method. To this end, we use a description in the language of non-dissipative and dissipative operators and introduce a well-developed stochastic Newton iterative algorithm for solving coupled nonlinear systems of equations. Finally, the proposed framework is demonstrated by a numerical simulation in plane strain conditions.

Key words: elastoplasticity, stochastic process, finite element method, stochastic method, stochastic algorithm.