A Large Deformation Desai Flow Surface Implementation in Abaqus

Abstract

This research project aims to implement an elasto-plastic Neo-Hookean Alpha material with a Desai flow surface with hardening and softening in Abaqus via the Continuum Mechanics framework. This is done by first defining the elasto-plastic potato diagram and deriving the corresponding stress tensor definition and dissipation inequality. The elastic deformation gradient is needed in the definition of the stress tensor, which is found by using the Newton-Raphson procedure for the maximization of the dissipation inequality subjected to the plastic flow surface. The Neo-Hookean Alpha elastic material, the Desai plastic flow surface and the definition of the hardening and softening curve are given and are substituted in the stress tensor definition and the corresponding Newton-Raphson procedure, which finishes the derivation of the theory needed to implement this model. This model is implemented in both Abaqus and Python, where the latter is used for rapid prototyping of the model. The methodology of verifying both implementations is presented. The results of the verification of the implementations are given and show that the behaviour of both implementations is as expected and that both implementations correspond to each other; although there are a few small issues. In the end, these issues are discussed, and future recommendations are given to solve them.