MURPHYS-HSFS-2014 - 7th International Workshop on Multi-Rate Processes & Hysteresis, 2nd International Workshop on Hysteresis and Slow-Fast Systems, April 7-11, 2014 - Abstract
Eleuteri, Michela
The aim of this talk is to address some thermodynamical models for fatigue accumulation in an oscillating elastoplastic Kirchhoff plate. Our main assumption will be that the fatigue accumulation rate is proportional to the dissipation rate. In the first part of the talk we will discuss the case when the temperature hystory is a priori given; in this simplified setting we are able to prove existence and uniqueness of the solution in the whole time interval before a singularity occurs (this is usually referred as material failure). In the last part of the presentation we will turn our attention to the full systems of momentum and energy balance equations coupled with a fatigue accumulation equation and we consider the usual viewpoint in engineering where the fatigue accumulation rate is assumed to be proportional just to the plastc part of the dissipation rate. In this manner shocks do not occur and in the case of periodic boundary conditions we are able to show that the solution exists globally. This is a joint project with J. Kopfova (Silesian University, Czech Republic) and Pavel Krejci (Academy of Sciences, Czech Republic)