Time‐separated stochastic mechanics for simulating the visco‐elastic response of construction parts

In a series of papers, we investigated the problem of efficiently analyzing visco‐elastic materials with stochastic material properties. The related evolution equation could be solved analytically which allowed for a stochastic series expansion around the mean for the internal variable. This, in turn, gave access to analytical expressions for the stochastic stress and reaction force in a finite element setting such that expectation and variation could be expressed in terms of simple formulas. Consequently, our analysis separated the stochastic properties of the material from any boundary problem and any loads, i.e., the stochastic behavior was separated from all time‐dependent conditions such that we referred our method as time‐separated stochastic mechanics. Numerical results of our formulas were in excellent agreement to representative Monte‐Carlo (MC) simulations. This holds true for both material point computations as well as finite element simulations. Particularly for finite element simulations, the time consumption for our approach is smaller by orders of magnitude. In this contribution, we recall the basic aspects of our works and present a brief overview. After presenting the key idea of the TSM, we recall the numerical treatment and present several examples which we compare to Monte‐Carlo results. Our results show a similar quality as the reference solution but at a computational effort that is orders of magnitude smaller.