Abstract
A nonlocal field theory of peridynamic type is applied to model the brittle fracture problem. The elastic fields obtained from the nonlocal model are shown to converge in the limit of vanishing non-locality to solutions of classic plane elastodynamics associated with a running crack. We carry out our analysis for a plate subject to mode one loading. The length of the crack is prescribed a priori and is an increasing function of time.
Highlights
Fracture can be viewed as a collective interaction across large and small length scales
Symmetric forces and boundary conditions are imposed, consistent with the assumption of a crack growing on a line and moving into the specimen
The time dependent domain is given by the domain surrounding the moving crack. This establishes a rigorous connection between the nonlocal fracture formulation using a peridynamic model derived from a double well potential and the wave equation posed on cracking domains given in [12]
Summary
Fracture can be viewed as a collective interaction across large and small length scales. With the application of enough stress or strain to a brittle material, atomistic scale bonds will break, leading to fracture of the macroscopic specimen. From a modeling perspective fracture should appear as an emergent phenomena generated by an underlying field theory eliminating the need for a supplemental kinetic relation describing crack growth. The displacement field inside the body for points x at time t is written u(x, t). Where H (x) is a neighborhood of x, ρ is the density, b is the body force density field, and f is a material-dependent constitutive law that represents the force density that a point y inside the neighborhood exerts on x as a result of the deformation field. The radius of the neighborhood is referred.
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