Concepts and Applications of Peridynamics
Friday, September 8, 2017
10AM – 11AM
The peridynamic theory of solid mechanics was originated as a reformulation of classical elasticity primarily motivated by the desire to replace the spatial derivatives in the governing equations with an integral functional that provides mathematical consistency with the nature of displacement discontinuities (e.g. cracks) in an otherwise continuously deforming body. Numerical simulations conducted with discrete peridynamic equations have demonstrated a unique capability to easily capture many interesting and challenging problems related to crack propagation, e.g. crack branching, oscillatory crack path instabilities in membranes, pervasive failure of brittle material, and complex fracture patterns in composite laminates. The early research in peridynamics focused on the theory’s attractiveness for modeling fracture, while utilizing simple constitutive models. However, peridynamics offers a rich kinematic description of deformation that is quite capable of very complex material modeling. The focus of this talk will be on the fundamental kinematic quantities that describe deformation in a peridynamic body, a rigorous and straightforward derivation of the peridynamic momentum equation, and a discussion of interesting applications and open topics.
John T. Foster is an associate professor in the Departments of Petroleum and Geosystems Engineering and Aerospace Engineering and Engineering Mechanics at the University of Texas at Austin. He received his BS and MS in mechanical engineering from Texas Tech University and PhD from Purdue University. From 2003-2011 he was a staff member at Sandia National Laboratories. He is a registered Professional Engineer in the State of Texas. During his career in research he has have been involved in many projects ranging from full scale projectile penetration field tests, to laboratory experiments using Kolsky bars, to modeling and simulation efforts using some of the world’s largest computers. His research interests are in experimental and computational mechanics and multi-scale modeling with applications to geomechanics, impact mechanics, fracture mechanics, and anomalous transport processes. Additionally, he has an interest in fundamental theoretical advancement of the peridynamic theory of solid mechanics. His teaching interests are in all areas of theoretical and computational mechanics.