Variational calculus has been the basis of a variety of powerful methods in the ?eld of mechanics of materials for a long time. Examples range from numerical schemes like the ?nite element method to the determination of effective material properties via homogenization and multiscale approaches. In recent years, however, a broad range of novel applications of variational concepts has been developed. This c- prises the modeling of the evolution of internal variables in inelastic materials as well as the initiation and development of material patterns and microstructures. The IUTAM Symposium on Variational Concepts with Applications to the - chanics of Materials took place at the Ruhr-University of Bochum, Germany, on September 2226, 2008. The symposium was attended by 55 delegates from 10 countries. Altogether 31 lectures were presented. The objective of the symposium was to give an overview of the new dev- opments sketched above, to bring together leading experts in these ?elds, and to provide a forum for discussing recent advances and identifying open problems to work on in the future. The symposium focused on the developmentof new material models as well as the advancement of the corresponding computational techniques. Speci?c emphasis is put on the treatment of materials possessing an inherent - crostructure and thus exhibiting a behavior which fundamentally involves multiple scales. Among the topics addressed at the symposium were: 1. Energy-based modeling of material microstructures via envelopes of n- quasiconvex potentials and applications to plastic behavior and pha- transformations.

First Symposium on this topic State of the art research World leading expert contributors Includes supplementary material: sn.pub/extras

Klappentext
The symposium focused on novel applications of methods from the calculus of variations to the solid mechanics of materials, including the development of new material models as well as the advancement of the corresponding computational techniques. Specific emphasis was put on the treatment of materials posessing an inherent microstructure and thus exhibiting a behavior which fundamentally involves multiple scales. Among the topic treated in this volume are: Energy-based modeling of material microstructures; modeling of the evolution of material microstructures; micromechanical modeling of shape-memory alloys; variational multiscale methods and associated numerical procedures; and micromechanics of multifield and multiphysics problems.

Inhalt
Stability of Quasi-Static Crack Evolution through Dimensional Reduction.- FE2-Simulation of Microheterogeneous Steels Based on Statistically Similar RVEs.- Advancements in the Computational Calculus of Variations.- A Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena.- Application of Relaxation Methods in Materials Science: From the Macroscopic Response of Elastomers to Crystal Plasticity.- Variational Concepts with Applications to Microstructural Evolution.- A Micromechanical Model for Polycrystalline Shape Memory Alloys Formulation and Numerical Validation.- Solution-Precipitation Creep Modeling and Extended FE Implementation.- Time-Continuous Evolution of Microstructures in Finite Plasticity.- Models for Dynamic Fracture Based on Griffith's Criterion.- An Energetic Approach to Deformation Twinning.- Computational Homogenization of Confined Frictional Granular Matter.- Existence Theory for Finite-Strain Crystal Plasticity with Gradient Regularization.- Error Bounds for Space-Time Discretizations of a 3D Model for Shape-Memory Materials.- On the Implementation of Variational Constitutive Updates at Finite Strains.- Phase-Field Modeling of Nonlinear Material Behavior.- Polyconvex Energies for Trigonal, Tetragonal and Cubic Symmetry Groups.- Phase Transitions with Interfacial Energy: Interface Null Lagrangians, Polyconvexity, and Existence.- A Unified Variational Setting and Algorithmic Framework for Mono- and Polycrystalline Martensitic Phase Transformations.- Dissipative Systems in Contact with a Heat Bath: Application to Andrade Creep.