On a relaxation approach to modeling the stochastic behavior of elastic materials

Abstract

AbstractThe inclusion of information on the stochastic behavior of microstructures is a key issue for modeling materials with even higher precision. To this end, stochastic series expansions offer an elegant for accounting for randomness. A prominent example is the usage of the so‐called Chaos Polynomial Expansion in the context of the Stochastic Finite Element. Although providing the desired information, the numerical effort is highly increased even for the simple linear elastic case. We aim at improving the numerical efficiency by proposing a novel approach to modeling the stochastic behavior of microstructures: we divide the material (= integration) point into a subset of domains which can be interpreted, e.g. as crystal grains. Afterwards, we employ a stochastic series expansion for the elastic constants and strains in each domain. Appropriate energy relaxation results into effective (homogenized) elastic constants and strains which are stochastic. Calculation of expectation and variance is only a technical issue yielding analytical formulas which are basically free of any additional computational effort as compared to regular deterministic linear elastic calculations. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)