CE 234 : Computational Inelasticity

This course will cover issues related to computational inelasticity in a variety of settings. A brief overview of 1-D plasticity with hardening in the small-deformation setting will be given. Proper algorithmic methods for approximating boundary value problems utilizing this constitutive relation will then be considered. Particular attention will be given to respecting the physical and theoretical properties of the continuum problem. Loading/unloading conditions will be covered in detail, as will be thermodynamic considerations as they pertain to algorithm design. Extensions of these methods to viscoplasticity will also be considered using the Perzyna and Duvaut-Lions regularizations. The 3-D formulation of classical rate-independent plasticity and viscoplasticity will also be covered. Included in this discussion will be a thermodynamic framework for such problems that has direct bearing on computational issues. Notations related to the maximum-dissipation hypothesis and stability will be presented. Based on the theoretical , algorithms will be considered that respect the properties of the time continuous equations. Closest-point projection and operator split methodologies will be examined. The remainder of the course will utilize these computational methodologies in large deformation inelasticity; both classical rate formulations and modern displacement based formulations will be examined. For large deformation problems in rate form, particular emphasis will be given to the development of algorithms that are incrementally objective. Displacement based formulations will be addressed by exploiting their formal mathematical relation to classical small-deformation plasticity in a setting that respects objectivity and thermodynamic properties of the continuum relations. Modern multiplicative formulations of finite strain plasticity will be studied in detail. Plasticity in coupled settings (i.e. thermoplasticity and plasticity of porous media) and their integration agorithms will also be discussed, as it will be damage theories and recent variational treatments involving relaxation, time permitting and depending of class interests.