In this study, we presented a numerically robust procedure to evaluate 4th order tangent moduli which are vital for acheiving quadratic convergence of global Newton-Raphson scheme.

In this study, the proposed method is verified for hyperelastic models alone. However, the same can be extended to other constitutive models.

The paper can be found at

Numerically approximated Cauchy integral (NACI) for implementation of constitutive models

10.1016/j.finel.2014.05.016

http://www.sciencedirect.com/science/article/pii/S0168874X14001061