Time-separated Stochastic Mechanics for structures with a coupled thermo-viscoelastic material under uncertainty

Time-separated Stochastic Mechanics (TSM) presents a new paradigm to take randomness in material models into account. This method achieves a significant reduction in the numerical costs of uncertainty quantification compared to classical methods. The TSM is based on a Taylor series of all field variables, i.e., displacements and internal variable in the random variables. For each random variable only a single additional system of equations has to be solved. This can be done with standard finite element software. For uncertainty quantification of a variety of inelastic materials and structures, the TSM has been successfully applied. Typically, nearly identical results to those obtained from reference Monte Carlo simulations can be obtained using TSM with a fraction of the computational cost. In this contribution, we present the application of TSM for structures with a coupled thermo-viscoelastic material. Due to the heat diffusion this problem is non-local in nature. Here, we apply TSM for the first time to non-local inelastic problems. Based on assumed random material parameters such as Young’s modulus, thermal conductivity and thermal expansion, the temperature field and the stress field are random as well. TSM enables the efficient calculation of the expectation and standard deviation as well as the probability distribution function of all quantities of interest. The efficiency and accuracy of the TSM for a number of numerical examples is quantified against reference Monte Carlo simulations.