We introduce a continuum model for mode III dynamic fracture that
consistently includes both macroscopic elasticity and a
microscopic mechanism for bond breaking. Our approach is based on
the highly successful phase-field methodology in use for solidification
and other interfacial pattern forming processes. We show how our formulation
avoids severe difficulties that plagued earlier attempts, in
particular how this model gives rise to asymptotically independent
crack surfaces behind the moving tip. Finally, we perform
preliminary simulations in 2d to demonstrate steady-state crack
motion in a strip geometry. More detailed simulations will probably require
adaptive mesh techniques as well as more careful attention to the stiffness
issues in the numerical integration.
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