Abstract
Numerical approximation techniques of stress and consistent tangent moduli using complex-step derivative approximation (CSDA) are presented, and its applications to nonlinear hyperelastic models are demonstrated. The stress calculated by this technique does not suffer from inherent subtractive cancellations that limit the accuracy of finite difference approximations, such as the forward Euler method and so on. Therefore, the accuracy of output has as same as analytical one. In addition, once the proposed approximation method is coded in a subroutine, it can be used for other hyperelastic material models with no modification. The implementation and the accuracy of this approach are first demonstrated with a simple Mooney-Rivlin model. Subsequently, an anisotropic hyperelastic material model is applied to analyze the simple tensile test.
