Fracture and singularities of the mass-density gradient field. (English) Zbl 1395.74080
Summary: A continuum mechanical theory of fracture without singular fields is proposed. 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. Questions of compatibility arising from the kinematics of the model are explored. The thermodynamic driving force for crack-tip motion in solids of arbitrary constitution is a natural consequence of the model. The governing equations represent a new class of pattern-forming equations.
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