Stochastic inverse finite element modeling for characterization of heterogeneous material properties

The micro and meso-structural characteristics of materials present an inherent variability because of the intrinsic scatter in raw material and manufacturing processes. This problem is exacerbated in highly heterogeneous materials, which shows significant uncertainties in the macroscale material properties. Therefore, providing optimal designs and reliable structural analyses strongly depend on the selection of the underlying material property models. This paper is intended to provide insight into such a dependence by means of a stochastic inverse model based on an iterative optimization process depending only of one parameter, thus avoiding complex parametrizations. It relies on nonlinear combinations of material property realizations with a defined spatial structure for constraining stochastic simulations to data within the framework of a Finite Element approach. In this way, the procedure gradually deforms unconditional material property realizations to approximate the reproduction of information including mechanical parameters (such as Young's modulus and Poisson's ratio fields) and variables (e.g., stress and strain fields). It allows dealing with non-multiGaussian structures for the spatial structure of the material property realizations, thus allowing to reproduce the coalescence and connectivity among phases and existing crack patterns that often take place in composite materials, being these features crucial in order to obtain more reliable safety factors and fatigue life predictions. The methodology has been successfully applied for the characterization of a complex case study, where an uncertainty assessment has been carried out by means of multiple equally likely realizations.