Fokker-Planck linearization for non-Gaussian stochastic elastoplastic finite elements
- Author(s): Karapiperis, K;
- Sett, K;
- Levent Kavvas, M;
- Jeremić, B
- et al.
Published Web Locationhttps://doi.org/10.1016/j.cma.2016.05.001
Presented here is a finite element framework for the solution of stochastic elastoplastic boundary value problems with non-Gaussian parametric uncertainty. The framework relies upon a stochastic Galerkin formulation, where the stiffness random field is decomposed using a multidimensional polynomial chaos expansion. At the constitutive level, a Fokker-Planck-Kolmogorov (FPK) plasticity framework is utilized, under the assumption of small strain kinematics. A linearization procedure is developed that serves to update the polynomial chaos coefficients of the expanded random stiffness in the elastoplastic regime, leading to a nonlinear least-squares optimization problem. The proposed framework is illustrated in a static shear beam example of elastic-perfectly plastic as well as isotropic hardening material.