The role of canonical balance laws in the study of the progress of "defects" in microstructured materials

Abstract

A unified thermomechanical framework is presented for deformable materials endowed with a weakly non-local microstructure. In view of practical applications to fracture and the progress of discontinuity fronts (shock waves, phase-transition fronts) special attention is paid to the construction and immediate consequences of the canonical equations of balance of momentum and of energy at regular points and singular sets. This leads to obtaining the expression of driving forces and of the associated dissipation, if any. The recently formalized theory of inhomogeneity and configurational forces on the material manifold (so-called Eshelby mechanics) is the appropriate setting for this as: (i) it pertains to the loss of translational symmetry on the material manifold, (ii) it automatically captures all fields simultaneously, and (iii) it emphasizes gradient effects, here a most appropriate feature.