Formulation for an Ogden-type hyperelastic analysis with hyper dual numbers and its performance evaluation

Abstract

A numerical calculation scheme for stress and its consistent tangent moduli with hyper-dual numbers(HDN) for Ogden-type hyperelastic material model was proposed. The main advantage of this scheme is that once the framework is coded, any Ogden-type hyperelastic material model can be implemented by only re-coding the strain energy density function. In this scheme, the new differentiation method for eigenvalue and eigenvector of the symmetric matrices with HDN were proposed. The proposed method can calculate the eigenvalue and eigenvector in non-real part analytically by using the eigenvalue and eigenvector in real part, in case that all eigenvalues in real part are not multiple root. We implemented the Neo-Hookean model and the Ogden model with the proposed scheme, to confirm the effectiveness and robustness of this method, and applied it to some examples. As the results, it was confirmed that the numerical results of the proposed method showed good agreement with analytical ones.