Journal Article

An Efficient Method for Material Characterisation of Hyperelastic Anisotropic Inhomogeneous Membranes Based on Inverse Finite-Element Analysis and an Element Partition Strategy

M. Kroon

in The Quarterly Journal of Mechanics and Applied Mathematics

Volume 63, issue 2, pages 201-225
Published in print May 2010 | ISSN: 0033-5614
Published online April 2010 | e-ISSN: 1464-3855 | DOI: https://dx.doi.org/10.1093/qjmam/hbq004
An Efficient Method for Material Characterisation of Hyperelastic Anisotropic Inhomogeneous Membranes Based on Inverse Finite-Element Analysis and an Element Partition Strategy

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An inverse method for estimating the distributions of the nonlinear elastic properties of inhomogeneous and anisotropic membranes is investigated. The material description of the membrane is based on a versatile constitutive model, including four material parameters: two initial stiffness values pertaining to the principal directions of the material, the angle between these principal directions and a reference coordinate system and a parameter related to the level of nonlinearity of the material. The estimation procedure consists of the following three steps: (i) perform experiments on the membranous structure whose properties are to be determined, (ii) define a corresponding finite-element (FE) model and (iii) minimise an error function (with respect to the unknown parameters) that quantifies the deviation between the numerical predictions and the experimental data. For this finite deformation problem, an FE framework for membranous structures exposed to a pressure boundary loading is outlined: the principle of virtual work, its linearisation and the related spatial discretisation. To achieve a robust parameter estimation, an element partition method is employed. In numerical examples, the proposed procedure is assessed by attempting to reproduce given random reference distributions of material fields in a reference membrane. The deviations between the estimated material parameter distributions and the related reference fields are within a few percent in most cases. The standard deviation for the resulting maximum principal stress was consistently below 1%.

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Subjects: Applied Mathematics ; Mathematical and Statistical Physics

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