Adrian Wielgos
supervisor: Krzysztof Chełmiński
The aim of the presentation is to briefly introduce the audience to my research topic which is an existence theory for plasticity theory models. In the first part I will show a general model of theory of plasticity. Then, I will note, why this model is not sufficient for some particular engineering applications and how it should be modified for such purposes. This will lead us to the class of models that I study in my research.
This class consists of models with equation of motion with nonlinear force term and inelastic constitutive law in form of differential inclusion of gradient-type. Moreover, I assume that studied body is made of viscoplastic material. Such models can be used to describe plastic deformation of charged, dielectric bodies in external electric field.
In the second part of the presentation I will put more emphasis on methods used in my research. First, I will show how I introduce simplified problems, which allow to find approximate solutions. Next, I will explain, why energy estimates are needed to show that approximate solutions converge to the solution to the base problem. Lastly, I will mention, in what sense the limit of approximate solutions satisfies the equations of studied model.
In the last part I will note, what parts of the theorems’ proofs are most problematic to deal with. I will show some of the sub-classes of models for which it is possible to avoid these problems.