A fuzzy‐stochastic model for transversely fiber reinforced plastics

Abstract

This work is directed to aleatoric and epistemic uncertainties in the framework of constitutive modeling, which are taken into account by stochastic and fuzzy analysis. The stochastic part of material parameters are expanded with the multivariate polynomial chaos expansion, where for epistemic uncertainty the polynomial chaos coefficients are defined as design variables, which are modeled as fuzzy sets. The resulting min-max optimization problem for the fuzzy analysis is approximated by α-level discretization. A numerical example for the hybrid fuzzy-stochastic analysis of material parameters is concerned with two different uncertain approximations to demonstrate the versatility of the proposed formulation.

A deep learning driven uncertain full‐field homogenization method

“…This work extends the method from [4] to complex microstructures. More precisely, uncertain three dimensional microstructures of spherical inclusions with uncertain material parameters are considered.…”

“…Since evaluations of quantities of interest directly from an established full-field homogenization methods via Monte Carlotype simulations (MC) are computationally expensive, surrogate models [6] like pseudospectral polynomial chaos expansion (PCE) [2] are used instead. In [4] a PCE based stochastic Galerkin method combined to the finite element method (FEM) to calculate uncertain effective properties of long fiber reinforced plastics is proposed.…”