Simulation of inelastic materials and structures under uncertainties with Time-separated Stochastic Mechanics

The Time-separated Stochastic Mechanics is a novel method for the fast and accurate uncertainty quantification of materials and structures with inelastic material response, e.g., elasto-viscoplasticity. The stochastic behavior is approximated with a low number of deterministic but time-dependent basis functions multiplied by the stochastic but time-independent random variables. For each coefficient of the reduced-order model only a single additional FEM simulation has to be performed. Due to the special structure of the resulting equation system for the coefficients, a standard FEM solver can be used. Analytical and deterministic equations allow to compute the expectation and standard deviation of all quantities of interest. In this contribution the efficiency and accuracy of the Time-separated Stochastic Mechanics is presented for a variety of problems with viscoelastic, elasto-viscoplastic and damage material models. Compared to reference Monte Carlo simulations, the results are typically visually nearly indistinguishable while only a fraction of the computational cost is required.