Separately global solutions to rate-independent processes in large-strain inelasticity

Global Existence for Rate-Independent Gradient Plasticity at Finite Strain

We provide a global existence result for the time-continuous elastoplasticity problem using the energetic formulation. For this we show that the geometric nonlinearities via the multiplicative decomposition of the strain can be controlled via polyconvexity and a priori stress bounds in terms of the energy density. While temporal oscillations are controlled via the energy dissipation the spatial...

Global optimization numerical strategies for rate-independent processes

This paper presents an approach to numerical solution of problems posed in the framework of quasi-static rate-independent processes. As soon as a problem allows for an energetic formulation there are known methods of its time discretization by time incremental minimization problems, which demand for global optimization of a non-convex functional. Moreover the two-sided energy inequality, a nece...

Global Knowledge, Local Solutions: Interest Rate and Monetary Policy

Evolution of Rate–Independent Inelasticity with Microstructure using Relaxation and Young Measures

We use the energetic formulation for rate–independent inelasticity which is based in the dissipation distance on the internal state. From this the incremental problems inherit a variational form which can be used to derive suitable relaxations. As a result we obtain a similar energetic formulation on the set of Young measures which then describes the evolution of microstructure.

Balanced Viscosity (bv) Solutions to Infinite-dimensional Rate-independent Systems

Balanced Viscosity solutions to rate-independent systems arise as limits of regularized rate-independent flows by adding a superlinear vanishing-viscosity dissipation. We address the main issue of proving the existence of such limits for infinite-dimensional systems and of characterizing them by a couple of variational properties that combine a local stability condition and a balanced energy-di...