Time-separated stochastic mechanics

All physical measurements and production processes are subject to natural fluctuations. The fluctuations result from a whole range of factors such as measurement uncertainties, material impurities or environmental factors. These fluctuations impair the predictive ability of classical deterministic models, which contain no information about the fluctuations. Safety factors are therefore introduced, wall thicknesses are oversized or longer maintenance intervals are planned. However, this jeopardizes the achievement of the goals of resource efficiency and sustainability in mechanical engineering and construction. These considerations give rise to the research field of uncertainty quantification, i.e., the inclusion of information on fluctuations in numerical simulations.

Unfortunately, all existing strategies for including stochastic variables in numerical simulations have the disadvantage that they entail high numerical costs. In particular, the simulation time can increase by orders of magnitude. This prevents the inclusion of stochastics in industrial design practice. Developed at IKM, Time-separated stochastic mechanics is a new approach based on a stochastic series representation. The method comes with extremely low additional numerical costs and can be applied to almost arbitrarily complex material models. The method can be implemented directly in industrial software such as Abaqus and yields almost identical results compared to reference Monte Carlo simulations.