Variational methods for problems from plasticity theory and for generalized Newtonian fluids

In this monograph we develop a rigorous mathematical analysis of variational problems describing the equilibrium configuration for certain classes of solids and also for the stationary flow of some incompressible generalized Newtonian fluids. However, even if we restrict ourselves to the time-independent setting, it is not possible to include all aspects which might be of interest. So we made a selection which has been influenced by our scientific activities over the last years. In particular, we concentrate on variational problems from the deformation theory of plasticity and on fluid models whose stress-strain relation can be formulated in terms of a dissipative potential. The mathematical form of both problems is very close and may be reduced to the study of variational integrals with convex integrands depending only on the symmetric part of the gradient of the unknown vector-valued functions. In the applications these functions represent either displacement fields of a body or velocity fields of incompressible flows. (orig.)SIGLEAvailable from TIB Hannover: RA 7754(10,1) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman