Abstract

We propose using the Kelvin decomposition as a deformation projection tool to extend the linear elasticity formalism with fourth-order decomposition tensors in order to model nonlinear anisotropic hyperelastic behaviors in large deformation. We show how this decomposition makes it possible to generalize the Saint Venant–Kirchhoff model to a subclass of anisotropy. We also present a strategy to extend Ogden’s model to anisotropy. In the traditional Ogden approach, the eigenvalues of the strain tensor are used. We propose combining the Ogden model with the Kelvin decomposition in order to consider structural and stress-induced anisotropy.

An application is provided where the model parameters are optimized to fit both models on the experimental mechanical behavior of a textile reinforced elastomer. Results showed good accuracy between the experimental and modeled stress response.

Fourth-order projectors and the mathematical canvas make the analytical expression of the tangent elasticity tensor simpler. This method opens perspectives for easy implementation and modeling of linear and nonlinear anisotropic materials in finite element code.

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