Title: The peridynamic theory: comparison to classical continuum mechanics, numerical implementation, and applications at Boeing

Speaker: Olaf Weckner, The Boeing Math Group

Date/Time: Wednesday, March 7, 2007, 10:00am – 11:00am

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract: In this talk I intend to give an introduction to the Peridynamic theory of continuum mechanics (see Silling, S.A., 2000. Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48, 175-209 for an introduction). Using Fourier transforms the governing integro-differential equation (IDE) can be solved analytically for the simplified linear infinite 1D case. This provides important insight into the fundamental differences between this formulation and the classical formulation of continuum mechanics which relies on partial differential equations (PDE). In particular the propagation of elastic waves and the emergence of discontinuities are compared. The analytic solutions can also be used to evaluate different numerical approaches for the spatial discretization of the IDE such as Gauss-Hermite quadrature, composite midpoint rule and FEM. Finally I present some simulation results involving failure of composite materials which are of current interest at Boeing.

CSRI POC: Stewart Silling, (505) 844-3973