Mechanics of complex bodies: commentary on the unified modelling of material substructures

Basic issues of the general model-building framework of the mechanics of complex bodies are discussed. Attention is focused on the representation of the material elements, the conditions for the existence of ground states in conservative setting and the interpretation of the nature of the various balance laws occurring.Comment: 14 pages, in print on Theoretical and Applied Mechanics, 200

Ground states in complex bodies

A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappinngs and Cartesian currents. Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev maps and Cartesian currents describe the inner substructure of the material elements. Balance equations for irregular minimizers are derived. A contribution to the debate about the role of the balance of configurational actions follows. After describing a list of possible applications of the general results collected here, a concrete discussion of the existence of ground states in thermodynamically stable quasicrystals is presented at the end.Comment: 30 pages, in print on ESAIM-COC

Crystal plasticity: The Hamilton-Eshelby stress in terms of the metric in the intermediate configuration

The Hamilton-Eshelby stress is a basic ingredient in the description of the evolution of point, lines and bulk defects in solids. The link between the Hamilton-Eshelby stress and the derivative of the free energy with respect to the material metric in the plasticized intermediate configuration, in large strain regime, is shown here. The result is a modified version of Rosenfeld-Belinfante theorem in classical field theories. The origin of the appearance of the Hamilton-Eshelby stress (the non-inertial part of the energy-momentum tensor) in dissipative setting is also discussed by means of the concept of relative power