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Recent developments in peridynamic mechanics

Banff International Research Station for Mathematical Innovation and Discovery

My presentation introduces the peridynamic model for predicting the initiation and evolution of complex fracture patterns. The model, a continuum variant of Newton's second law, uses integral rather than partial differential operators where the region of integration is over a domain. The force interaction is derived from a novel nonconvex strain energy density function, resulting in a nonmonotonic material model. The resulting equation of motion is proved to be mathematically well-posed. The model has the capacity to simulate nucleation and growth of multiple, mutually interacting dynamic fractures. In the limit of zero region of integration, the model reproduces the classic Griffith model of brittle fracture. The simplicity of the formulation avoids the need for supplemental kinetic relations that dictate crack growth or the need for an explicit damage evolution law.

Mathematics; Mechanics of deformable solids; Calculus of variations and optimal control; optimization; Material science

video/mp4

Author affiliation: Sandia National Laboratories

2017-02-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59688

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/