Past Event: Oden Institute Seminar

Line defect dynamics and solid mechanics -- Change in room, time

Amit Acharya, Professor, Carnegie Mellon University

Abstract

Line defects arise in a host of materials; dislocations, crack-tips, and grain/phase boundary junctions in crystalline and soft matter. Classical Continuum mechanics does not provide an adequate framework for treating them. The kinematics of line defect dynamics provides a unifying theme, augmenting the classical balance laws of continuum mechanics with a conservation law for topological charge carried by these lines. The resulting governing equations represent a new class of pattern-forming equations. Results at the atomic and tectonic scales from a pde-based, nonsingular theory of dislocation dynamics with inertia will be shown.The general ideas above will be used to formulate a continuum mechanical theory of fracture without singular fields. The primary contribution is the rationalization of the structure of a 'law of motion' for crack-tips, essentially as a kinematical consequence and involving topological characteristics. The thermodynamic driving force for crack-tip motion in solids of arbitrary constitution is a natural consequence of the model. Essential differences between crack and dislocation mechanics, while both represent displacement discontinuities, will be highlighted.