Isotropic damage in viscoplastic flow conditions, FEM applications with practical examples

The damage mechanics is a very important branch of solid mechanics. Although it is still developing, it has already been applied to many engineering problems. Among many various types of damage models, which are commonly used, the main subject of this paper is the isotropic continuous damage in viscoplastic flow conditions. This paper include Information about the viscoplastic type of constitutive modelling, the presentation of mechanical representation of damage by the scalar variable D, effective stress concept, equations of the chosen isotropic damage model, the Chaboche viscoplastic constitutive model including damage effects and the identification procedure of damage material parameters with practical example. The chosen constitutive model is easy to apply to the finite element analysis. Using the MSC.Marc system, which great advantage is possibility ofa user subroutine application, the geometry nonlinear finite element analysis of plate and shell structures including damage is possible. This paper includes description of the applied program and user subroutines applied: UVSCPL - viscoplastic modelling (the standard MSC.Marc system supports the Chaboche model, but not in the damage variant) and UACTIV - deactivation of finite elements. The last part of the paper includes the practical numerical example of a clamped bar of 0.3 m long and 0.1x0.01 m cross-section size. In calculations the four-node thin-shell, divided into five layers, elements were used. dynamic, geometrically nonlinear analysis using Newmark integration algorithm has been performed. As the results, screen shots of displacements with maps of damage parameter for the bar infour time moments are presented.