Fuzzy and stochastic approach applied to rubber like materials

Abstract In many engineering applications, a material behaviour, e.g. hyperelasticity, is described by appropriate constitutive models. These often lead to uncertainty due to heterogeneity of materials. As a key idea, materials are described by uncertain parameters, which may be modelled by different uncertainty approaches. In an experimental investigation, 40 specimens are used for parameter identification of an Ogden model for rubber like materials in order to quantify the uncertainty of the material parameters. Furthermore, a statistical analysis of the material parameters including their correlations is studied. The first part of this work is directed to epistemic uncertainty in the framework of constitutive models, which is taken into account by a fuzzy approach. An underlying min-max optimisation problem is approximated by α-level discretisation, where solutions are obtained with simple constraints. The second part of this work is directed to aleatoric uncertainty in the framework of constitutive models, which is taken into account by a stochastic approach, where hyperelastic stochastic material parameters are expanded with a multivariate polynomial chaos expansion. As a numerical example, a static problem for uniaxial tension of a rectangular plate is considered to demonstrate the versatility of the proposed fuzzy and stochastic approach.

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