A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics

Abstract

This work is focused on polymorphic uncertainties in the framework of constitutive modeling for transversely isotropic materials. To this end, we propose a hybrid fuzzy-stochastic model, where the stochastic part accounting for aleatory uncertainties of material parameters is expanded with the multivariate polynomial chaos expansion. In order to account for epistemic uncertainties, polynomial chaos coefficients are treated as fuzzy variables. The underlying minimum and maximum optimization problem for the fuzzy analysis is approximated by α-level discretization, resulting in a separation of minimum and maximum problems. To become more universal, so-called quantities of interest are employed, which allow a general formulation for the target problem. Numerical examples with fuzzy, fuzzy-stochastic, and hybrid fuzzy-stochastic input demonstrate the versatility of the proposed formulation.

Experimental Investigations of Carbon Fiber Reinforced Polymer Composites and Their Constituents to Determine Their Elastic Material Properties and Complementary Inhomogeneous Experiments with Local Strain Considerations

“…Due to the anisotropic nature and the large number of influencing factors, such as geometry variations and fiber content, it can be assumed that uncertainties will occur when determining the mechanical properties. These uncertainties in properties, some of which are determined here, have already been addressed in [14] for the macroscale and in [15] for the meso-scale. This is a further motivation of this work in order to determine the uncertainty on both scales and to be able to address it more closely.…”

An uncertainty model for the curing process of transversely fiber reinforced plastics

“…In this work, we focus on the fuzzy probability theory or fuzzy-stochastic described by fuzzy-random variables (FRVs). In this context, a polynomial chaos expansion (PCE) based fuzzy-stochastic analysis is modeled with PC coefficients as n s design variables [s 1 , ..., s ns ] T = s ∈ S within a design space S ⊂ R ns , which are modeled as fuzzy sets [1]. spectively, is shown in Fig.…”

“…Here, the fuzzy response at each selected α-level is obtained by solving a minimun-maximum problem. For a more detailed description, we refer to [1].…”