Theorem on the kinetic energy in an elastic continuum with defects

Abstract

An expression of the theorem on the kinetic energy for an elastic continuum with dislocations is derived on the basis of the dynamical equations of a gauge model of the medium. This relation shows that the work performed by internal surface stresses in the volume is redistributed between the work performed by the effective stresses at the rates of the effective elastic distortions and plastic distortions. In phenomenological theories of plasticity the latter quantity, representing the rate of energy dissipation, governs the dissipative processes. An expression is obtained which relates the rate of energy dissipation with the self-energy density of the field of the defects and the energy flux of the defects.