Martin Fagerström

Rate Sensitive Continuum Damage Models and Mesh Dependence in Finite Element Analyses

The experiences from orthogonal machining simulations show that the Johnson-Cook (JC) dynamic failure model exhibits significant element size dependence. Such mesh dependence is a direct consequence of the utilization of local damage models. The current contribution is an investigation of the extent of the possible pathological mesh dependence. A comparison of the resulting JC model behavior combined with two types of damage evolution is considered. The first damage model is the JC dynamic failure model, where the development of the “damage” does not affect the response until the critical state is reached. The second one is a continuum damage model, where the damage variable is affecting the material response continuously during the deformation. Both the plasticity and the damage models are rate dependent, and the damage evolutions for both models are defined as a postprocessing of the effective stress response. The investigation is conducted for a series of 2D shear tests utilizing different FE representations of the plane strain plate with pearlite material properties. The results show for both damage models, using realistic pearlite material parameters, that similar extent of the mesh dependence is obtained and that the possible viscous regularization effects are absent in the current investigation.

Finite Deformation Fracture Modelling of a Thermo-Mechanical Cohesive Zone

In the present contribution, the development of a thermo-mechanical cohesive zone model is discussed in the context of a strong discontinuity formulation according to the concept of partitions of unity [1]. On the basis of our previous work, [2, 3], and also the contributions, [4, 5], the deformation map is thereby defined in terms of mutually independent continuous and discontinuous portions of the displacement. As an extension, we also introduce a similar subdivision of the temperature field in one continuous and one discontinuous part, separated by the internal crack surface. As a result, we consider the weak formulation of the equation of motion and the energy equation as consisting of four coupled equations on the structure level. In the paper, we will focus on the conditions for onset as well as continued (coupled) discontinuity development within a thermo-hyperelastoplastic continuum with isotropic plastic hardening as well as thermally softening response. In the case of continued discontinuity development, a cohesive zone law is specified for the representation of the decay of the traction vector combined with heat flux across the interface zone. Apart from the crucial fracture modelling, we also discuss the numerical treatment and aspects of computational implementation of the proposed approaches. A couple of numerical examples that illustrate the capabilities of the proposed approach to the modelling of the thermo-mechanical cohesive zone are included.