Alan Needleman's KEYNOTE seminar "Discrete Defect Plasticity and Implications for Dissipation"

Alan_Needleman_ April_21_2022.pdf (pdf 142 kB)

Abstract. Inelastic deformation of solids is almost always, if not always, associated with the evolution of discrete defects. As the defect structure evolves, a portion of the mechanical energy expended in deforming the solid increases the stored elastic energy and a portion is dissipated. The partitioning between energy storage and dissipation plays a key role in a variety of mechanical processes including crack growth resistance, hysteresis in cyclic loading and the thermal softening behavior that promotes mechanical instabilities. The predictions of a mesoscale continuum mechanics framework for this partitioning will be discussed with attention restricted to discrete dislocation plasticity for crystalline solids and to shear transformation plasticity for amorphous solids. The dislocations are modeled as line defects and the shear transformation zones are modeled as Eshelby inclusions, along with kinetic equations for their evolution. The kinetic relations must satisfy the second law of thermodynamics which, in the context of a purely mechanical theory, requires that the dissipation rate is non-negative. Restrictions on kinetic relations for non-negative dissipation (a necessary but not sufficient condition) and of non-negative dissipation rate will be presented. The implications of the restrictions imposed by such kinetic relations will be discussed along with open questions.