Title: Connections between the non-local Peridynamic model of continuum mechanics and local Speaker: Olaf Weckner, Math Group, The Boeing Company, Bellevue, Washington Date/Time: Thursday, October 4, 2007, 2:00 pm Location: CSRI Building, Room 90 (Sandia NM) Brief Abstract: The peridynamic theory of continuum mechanics was proposed by S.A. Silling in 2000 in "Reformulation of elasticity theory for discontinuities and long-range forces", J. Mech. Phys. Solids 48. It is oriented towards deformations including spatial discontinuities, especially fractures. It has been successfully applied to a wide variety of inelastic problems such as the crushing of nanotubes, the propagation of phase-transformations or the formation of cracks in isotropic and anisotropic materials. However there are still a number of interesting open questions regarding the elastic response of a body, especially in comparison to the more traditional and widely accepted local formulations based on stress and strain tensors. It is important to address these fundamental questions in order to advance the understanding of this relatively new theory and also to improve its acceptance in the scientific community. In this talk I will therefore concentrate on the 1D and 3D elastic response within the linear peridynamic formulation which is governed by integro-differential equations for the components of the displacement field. Using Fourier transforms these equations can be solved analytically for a 1D infinite domain. This provides important insight into the fundamental differences between peridynamics and the classical formulation of continuum mechanics which relies on partial differential equations, in particular with respect to the propagation of elastic waves and the emergence of discontinuities. Finally the 3D equation of motion is shown to converge to the classical Navier equations of linear elasticity when the non-locality becomes small.CSRI POC: Stewart Silling, (505) 844-3973 |