Nonlocal Strain Energy Density

Abstract

Continuum mechanics describes materials under stress using partial differential equations. However, this framework fails to model the behavior of discrete particles and discontinuities, such as crack propagation and fracturing. Over the past twenty years, the mathematical theory of Peridynamics has been developed to overcome the limitations of existing theories of continuous media. In Peridynamic models of materials under stress, the partial differential equations of continuum mechanics are replaced by integral equations, which can describe the interactions between material points nonlocally. Specifically, the strain energy density at a material point is determined by the deformed image of its neighborhood. This image is mapped by the deformation state tensor which combines with the Fréchet derivative of the strain energy density to associate force state vectors with each material bond. The resulting force state tensor describes the deformation gradient nonlocally. In this research project, we study the mathematical properties of the strain energy density under these nonlocal conditions. Our goal is to present on these mathematical properties to demonstrate the key differences between the continuum mechanics and nonlocal models of materials under stress.

Details

Session 2

3:00pm – 4:30pm

Grand Salon