A multivariate stochastic material model with correlated material parameters. Issue 1 (15th March 2018)

• Record Type: Journal Article
• Authors: Penner, Eduard; Caylak, Ismail; Mahnken, Rolf
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 17:Issue 1(2017)
• Page Start: 67
• Page End: 68
• Publication Date: 2018-03-15
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201710020
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: This paper concentrates on the aleatoric uncertainty of hyperelastic material models caused by material parameters which are characterized by random variables. To this end, the Polynomial Chaos Expansion (PCE) is applied to represent the random variables by a series of deterministic coefficients and random polynomials. To determine the corresponding PC coefficients and the polynomials of correlated stochastic material parameters we use the Cholesky decomposition and the Gram‐Schmidt algorithm. Based on experimental results and artificial data parameter identification of an Ogden material model for rubber is applied. As a numerical example we consider a static problem for uniaxial tension of the rectangular plate. This structure is investigated in order to represent the conditions for the experimental setup. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)