Efficient and Robust Method for Identifying Material Constant of Hyperelastic Material Model via Complex-step Derivative Approximation

Abstract

An efficient and robust method for deriving the stress-strain relationship of hyperelastic material model (HM-model) was proposed via complex-step derivative approximation. This method has a capability to calculate the stress-strain relationship with the same accuracy as the analytical solution by coding only the strain energy density function, being applied for the implementation of an identification program of material constants for HM-model using a Microsoft/Excel. The performance evaluation of HM-models (Yeoh and Ogden models) using this method revealed that all models could reproduce the results of the three types of material tests (uniaxial tensile (UT), pure shear (PS) and equibiaxial tensile (BT) tests) of carbon-black-filled SBR. Moreover, only the hyperelastic model composed of the first invariant of the right Cauchy-Green tensor could predict the PS and BT test results from the UT data. As a future prospect, we would like to proceed with studies on other rubber materials and HM models.