Bio: Raul Radovitzky is the Raymond L. Bisplinghoff Professor of Aeronautics and Astronautics at the Massachusetts Institute of Technology. He also serves as the Associate Director of the MIT Institute for Soldier Nanotechnologies, where he also leads research efforts on Blast and Ballistic Protection. He received a Civil Engineer degree from the University of Buenos Aires in 1991, A S. M. in Applied Mathematics from Brown University in 1995 and a Ph.D. in Aeronautical Engineering from the California Institute of Technology in 1998. His research interests are in the development of numerical methods for multi-scale modeling of complex material response as well as in the formulation and implementation of algorithms for large-scale simulation of the dynamic response of materials to extreme loading conditions with emphasis on material and structural failure. The methods his group has developed have led to significant advances in our understanding of the physical effects of blast waves on the brain. This has helped to develop strategies to protect against Traumatic Brain Injury. Dr. Radovitzky is an Associate Fellow of the American Institute of Aeronautics and Astronautics and a member of the National Football League Head, Neck and Spine Injury Research Committee.

Extension of the peridynamic theory of solids for the simulation of materials under extreme loadings

The prediction of material and structural failure remains one of the most difficult challenges in structural and solid mechanics. Complexity emerges from the fundamental multiscale aspect of the mechanics of fracture, where the small-scale response is usually responsible for large-scale system damage and failure. In addition, significant algorithmic challenges remain, including the difficulty in representing fracture, some fundamental numerical convergence issues in the presence of material damage; and computational robustness and scalability enabling large-scale simulations.
In this presentation, I will describe our efforts on the investigation of the theory of peridynamics and its numerical implementation, as a promising alternative approach for simulating extreme material response. Peridynamics is a relatively new, nonlocal formulation of continuum mechanics based on integral equations. It includes a physical length scale and naturally supports the presence of discontinuities in the solution field. As part of our work in this area, we have proposed an extended formulation of the state theory of peridynamics addressing some fundamental issues present in the original theory. Specifically, we have found that unphysical energy modes that do not contribute to the strain energy are allowed in the original formulation, which, in turn, are responsible for the numerical instabilities commonly observed in peridynamic particle discretizations. In order to address this issue, we introduce an extension of the constitutive correspondence framework based on bond-level nonlinear strain measures of the Seth-Hill type, in direct analogy to local measures of deformation in continuum mechanics. We show that the numerical instabilities are eliminated when the numerical discretization is based on the extended theory.
In addition, we have explored different approaches for incorporating material damage and fracture within the context of peridynamics formulations. I will describe one approach based on continuum damage models and another one particularly suited for brittle fracture.
The algorithms resulting from a particle discretizations of the proposed extended peridynamics framework have been implemented in our research code ΣMIT. I will provide examples illustrating the key numerical properties of the method. In addition, I will show numerical results that demonstrate the ability of the method to capture experimentally observed ballistic limit curves for ductile materials, as well as realistic fracture patterns in brittle materials subjected to projectile impact loadings.

Prof. Radovitzky is being hosted by Prof. Garikipati (Mechanical Engineering). If you would like to meet with him, please send an email to [email protected]