On geometry and continuum thermodynamics of movement of structural defects

A thermodynamic theory of the movement of point, line and surface defects is considered at finite deformations. This theory is based on the balance laws for crystal defects. The defects balance laws together with the well-known balance laws for the mass, momentum, moment of momentum, energy and entropy have been utilized to find the driving forces acting on crystal defects. Some of the derived formulae are well-known, e.g. Peach-Koehler formula, nevertheless, many new relations are obtained, e.g. for osmotic forces and for the energy flux due to the movement of crystal defects. The driving force acting on a grain boundary is found as a thermodynamic force needed to balance the jump in energy density across the moving discontinuity surface. Using the relations derived for driving forces the problem of the constitutive modelling of the crystal defect movement is considered. The elastic behaviour of materials with structural defects is determined by a constitutive equation imposed on the free energy density. This equation takes into account the elastic strain, crystal defect densities and temperature. The crystal plasticity is described by vector constitutive equations stated between the defects velocities and the respective driving forces.