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

The accurate quantification of uncertainties in engineering simulations is typically characterized by high computational cost, particularly for finite-strain inelasticity where complex nonlinear kinematics and constraint enforcement create computationally demanding problems. Moreover, material parameters usually exhibit inherent and ineliminable stochastic variations. The resulting material response becomes inherently random which can significantly influence structural behavior. This work presents the successful extension of time-separated stochastic mechanics (TSM) to finite-strain viscoelasticity. Firstly, a constraint-conforming material model, which does not require the usual exponential mapping for numerical discretization, is formulated. The viscous volume preservation is incorporated through a Lagrange multiplier. This enables a straightforward algorithmic treatment with implicit Euler time integration. Secondly, the model is extended using TSM to efficiently account for stochasticity. TSM is based on the separation of the stochastic, time-independent variables from the deterministic, time-dependent basis and is applicable to material models involving differential equations. In a post-processing step, semi-analytical, closed-form expressions are derived enabling a highly efficient evaluation of the sensitivity of all resulting physical quantities with respect to the stochastically fluctuating input parameters. The numerical results demonstrate the superior performance of TSM regarding numerical efficiency in direct comparison to the Monte Carlo method, while maintaining high accuracy.