A generalized model of oriented continuum with defects

The aim of this paper is to present a general model of oriented continuum w ithin the frame of Newtonian-Eshelbian continuum mechanics to describe macr o- and microdeformations of solids taking into account the evolution of def ects as voids and cracks. Within a manifold-theoretical setting, position- and direction-dependent metric, deformation and strain measures are derived to describe macro- and micromotion of the body. A variational formulation is introduced leading to balance la ws, boundary and transversality conditi ons for macro- and microstresses of deformational as well as configurationa l type, where the latter have to be satisfied by the driving forces on macr o- and microdefects. A dissipation inequality for macro- and micromotion is derived via a suffic iency condition for the action integral. The Helmholtz free energy treated as the relevant thermodynamic potential is used to define thermo-inelastic stress-strain relations of incremental type. Far the macro-micro constituti ve equations associated phenomenological macro constitutive equations are d erived by introducing a second potential with corresponding evolution laws. Finally, the presented microtheory is applied to analyze the evolution of s hear bands in a rod under tension and the decrease of the load-deflection b ehaviour. Numerical results are given. A is shown that contrary to phenomen ological theories, where shear bands are determined as bifurcation from a h omogeneous state via the admittance of weak discontinuities on singular sur faces, conditions of this type are not needed within the presented micromod el of oriented continuum.