Nonlocal Elastodynamics and Fracture, by Prof. Robert Lipton

Описание: Title: Nonlocal Elastodynamics and Fracture

Speaker: Robert P. Lipton, Nicholson Professor
Department of Mathematics, Louisiana State University


Abstract: Fracture can be viewed as an emergent phenomenon. Here, local interactions between neighboring points result in global consequences like the emergence of fracture surfaces. Emergent phenomena can be modeled non-locally and examples include motion of flocks of birds modeled through the Cuker Smale model. A hallmark of fracture modeling using peridynamics is the numerical emergence of cracks through the use of nonlocal modeling and nonlinear constitutive laws. We provide a peridynamics model for calculating dynamic fracture. The force interaction is derived from a double well strain energy density function, resulting in a non-monotonic material model. The fracture set emerges from the model and is part of the dynamics. The material properties change in response to evolving internal forces eliminating the need for a separate phase field to model the fracture set. In the limit of zero nonlocal interaction, it is seen that the model reduces to a sharp crack evolution characterized by the classic Griffith free energy of brittle fracture with elastic deformation satisfying the linear elastic wave equation off the crack set. The nonlocal model is seen to encode the well-known kinetic relation of Linear Elastic Fracture Mechanics relating crack driving force to crack tip velocity. A rigorous connection between the nonlocal fracture theory and the wave equation posed on cracking domains given in Dal Maso and Toader is found.


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