Scale Independent Approach to Deformation and Fracture

Abstract

Deformation and fracture of solid-state materials is formulated comprehensively. Based on a fundamental physical principle known as gauge symmetry, this formalism is by nature scale independent and capable of describing all stages of deformation, from the elastic stage to fracture stage, on the same theoretical basis. The basic postulate of this theory is that in the plastic regime deformation is locally linear elastic. Dynamics in plasticity is formulated through consideration of the interaction among local elastic dynamics. It is analytically proved that in the elastic limit the present formalism reduces to the well-known continuum-mechanical formalism. Transitions from the elastic to plastic, and the plastic to fracturing regime are discussed based on the present formalism.