Rate Sensitive Continuum Damage Models and Mesh Dependence in Finite Element Analyses
Paper in proceedings, 2013
The experiences from the orthogonal machining simulations show that the Johnson Cook dynamic failure model appears to exhibit a significant element size dependence.
Such pathological mesh dependence is a direct consequence of the utilization of local damage models unless some type of regularization is introduced. The current contribution is an investigation of the extent of the possible pathological mesh dependence and a comparison of the resulting behavior in the case of the Johnson Cook (JC) plasticity model being combined with two types of damage evolution. The first damage model is the Johnson Cook dynamic failure model where the development of the "damage" does not affect the response until the critical state is reached. The second is a continuum damage model based on work done by Cocks and Ashby, where, on the other hand, the damage variable is affecting the material response (and result in a softer development of stress vs. strain). Both the plasticity and the damage models considered in the formulation are rate dependent and the damage evolutions for both models are defined as a post-processing of the effective stress response. The investigation is conducted based on simulation of a series of 2D shear tests utilizing FE-representations, including elements with different sizes, of the plane strain plate with pearlite material properties. Furthermore, the crack propagation is described by the element deletion method. A one way of reducing the mesh dependence is to include a viscosity in the material law. Since the both damage models used in the investigation are rate dependent, different deformation rates have been used in order to reveal possible effects of the viscous regularization. The results show that, for both damage models, and with a realistic representation of the pearlite material properties, a similar extent of mesh dependence is obtained and that the viscous regularization effects are absent in the current investigation.