TSM for visco-elastic materials

The TSM has successfully been derived for visco-elastic materials. Here, two internal variables need to be computed which approximate the usual viscous part of the total strain. These internal variables are time-dependent and thus also vary for varying loads; however, they are deterministic. The expectation and standard deviation for both the stochastic viscous part of the strains and the stresses is computed by means of the two internal variables and deterministic coefficients which depend on the stochastic behavior of the material. Once they are computed, they remain constant even if the external load is changing. This results in a computational effort which is doubled as compared to classical (deterministic) material models for visco-elasticity. However, for a Monte Carlo approach, at least 400 realizations need to be performed. This renders the TSM approach to be faster than Monte Carlo simulations by a factor of approximately 200.