Antiplane Shear Flows in Viscoplastic Solids Exhibiting Isotropic and Kinematic Hardening

The authors consider antiplane shearing motions of an incompressible visco-plastic solid. The particular constitutive equation employed assumes that the stress tensor has an “elastic” component and a component which can exhibit hysteresis. The model exhibits both “kinematic” and “isotropic” hardening. Our results consist of a set of energy type estimates for the resulting system, L2 contractivity estimates for the solution operator, and finally an analysis of the approach of our system to a “rate independent” model as a distinguished parameter describing our flow rule approaches zero. We also include some computational results for simple piecewise constant data. This research was partially supported by the Applied Mathematical Sciences Program, U.S. Department of Energy and the Mathematics and Computer Science Division, Army Research Office. This research was partially supported by the National Science Foundation. 1 DISCLAIMER This repon was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their cmployets, makes MY warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness. or usefulness of any information, apparatus, product, or process disclosed, or represents that its UK would not infringe privately owned rights. Reference herein to any specific commercial product, process, or SCMCC by trade name, trademark, manufacturer. or otherwise does not necessarily constitute or imply its endorsement, recornmendirtion, or favoring by the United States Government or any agency thereof. The views and opinions of authors exprrtsed herein do not neccssarily state or reflect thosc of the United States Government or any agency thereof. DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.