Complex step derivative approximation for numerical evaluation of tangent moduli

• Complex step derivative approximation (CSDA) is used to evaluate consistent tangent moduli.
• Numerical sensitivity of CSDA to finite difference interval is investigated.
• Computational efficiency of CSDA is compared with other numerical procedures.
• CSDA is found to be numerically robust and computationally efficient.

In this paper the concept of complex step derivative approximation (CSDA) is revisited and its application in constitutive modeling of hyperelastic materials is presented. The performance of CSDA is demonstrated using simple examples. The idea of CSDA is then extended to numerically evaluate the second Piola–Kirchhoff stress tensor and tangent moduli for five popular hyperelastic constitutive models. The performance of CSDA is compared with the finite difference methods for the considered constitutive models. CSDA numerical scheme is observed to outperform other numerical differentiation schemes in terms of computational efficiency and sensitivity to the size of finite difference interval.