Implementation of an Ogden-type hyperelastic material model using complex-step derivative approximation

Abstract

This paper presents a novel methodology for implementing an Ogden-type hyperelastic material model with numerically computed consistent tangent moduli using complex-step derivative approximation (CSDA). In this formulation, numerical calculations of exact eigenvalues and eigenvectors of complex symmetric matrices are required to obtain the accurate consistent tangent moduli . For the request, the numerical calculations have convergence criteria which are defined in each of real and imaginary part independently. Finite element analyses using Ogden material model implemented with the present methodology are presented to show that the consistent tangent moduli are in good agreement with the analytic ones.