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tangent moduli

Numerical approximation of tangent moduli


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


Mario Juha's picture

Consistent linearized tangent moduli for hyperelastic materials... is it always a positive definite matrix?

In order to obtain numerical solution of problemsthat involves a hyperelastic material model, we use what is known as incremental/iterative solution techniques of Newthon's type. The basic idea is to contruct a discrete system of nonlinear equation, KU=F, and solving it using a Newton's method or a modified version of it. As we know, its lead to a systematic linearization of the internal force vector and by the chain rule to the linearization of the material model.

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