Variational methods for dissipative multifield problems in solid mechanics

Abstract

In many engineering applications, solid materials undergo processes that cause an irreversible change in their microstructure. Such dissipative phenomena usually have a multifield character which means that, besides the macro-deformation, also other physical fields such as temperature, species concentration or plastic and damage variables are involved. Practical applications include, for example, hot sheet metal forming, diffusion processes or brittle as well as ductile fracturing. The focus of this work is to develop a general and versatile modeling framework for dissipative multifield processes in solids undergoing large deformations. This framework is provided by incremental variational principles which fully describe the evolution of the system under consideration. Special attention is paid to the coupling of the involved physical fields in accordance with the fundamental laws of thermodynamics. The major contribution of this work is the development of new models and formulations for brittle and ductile fracturing in isotropic and anisotropic materials, diffusion in solids and the thermomechanics of gradient-extended continua including aspects of stability.