Continuum Mechanics of defects in solids (and associated mathematical questions)
Organizer: Amit Acharya
We will discuss a continuum mechanics framework for 1 and 2 dimensional defects in elastic solids (e.g. dislocations, cracks, grain and phase boundaries, and g.disclinations – the ideas extend to corresponding defects in nematic and smectic liquid crystals as well). Such defects, if dealt within just (non)linear elasticity, often result in nasty singularities with non-integrable energies in finite bodies. Physically, one is also interested in the dissipative motion, and the mutual interaction of these defects, as well as with applied loads. The framework we will discuss covers a manageable setup to deal with such matters in a reasonable way. Results of finite element based computational proxy models of the nonlinear pde systems will be used to illustrate the ideas.