Simulation of finite-strain viscoelastic structures under uncertainties using time-separated stochastic mechanics

Stochastic material parameters lead to uncertainties in the material response. In numerical simulations, the accurate quantification of those uncertainties is usually associated with high computational cost. Time-separated Stochastic Mechanics (TSM) is an efficient approach for the inclusion of randomness in engineering simulations [1]. It is based on the separation of the time-independent and stochastic variables from the time-dependent and deterministic basis. We extend TSM to the simulation of viscoelastic structures under finite strain, incorporating the finite element method. As basis for the extension serves a constraint-conforming material model for finite-strain viscoelasticity. It is derived using the procedure presented in [2] and incorporates the viscous volume-preserving constraint through a Lagrange multiplier. This allows the algorithmic treatment with implicit Euler time integration. The numerical results are compared to those of the Monte Carlo method and confirm the accuracy and numerical efficiency of the TSM approach. References [1] Hendrik Geisler et al. ”A new paradigm for the efficient inclusion of stochasticity in engineering simulations: Time-separated stochastic mechanics”. In: Computational Mechanics (2024). [2] Tobias Bode et al. ”On constraint-conforming numerical discretizations in constitutive material modeling”. In: Computational Mechanics (2024).