Simulation of the dynamic behavior of viscoelastic structures with random material parameters using time-separated stochastic mechanics

Abstract

Modeling and simulation of materials with stochastic properties is typically computationally expensive, especially for nonlinear materials or dynamic simulations. Time-separated stochastic mechanics (TSM) is a technique to efficiently compute the stochastic characteristics of stress and reaction force of materials. It has successfully been used for viscoelastic materials with random homogenized Young’s modulus. The method is based on a decomposition of time-invariant random variables and time-dependent but deterministic variables for the strain response at the material point. In this work, the TSM is extended for the dynamic analysis of stochastic viscoelastic materials. It is showcased that the TSM can efficiently approximate the expectation and variance of the reaction force and the stress for the dynamic simulation of a viscoelastic nonlinear material. Furthermore, generalized equations of the TSM are presented that increase the accuracy and allow for accounting of larger fluctuations of the material parameters. Transient time-domain simulations are performed for different boundary value problems and compared to Monte Carlo simulations to demonstrate the accuracy and computational efficiency of the method.