Raul Radovitzky, Professor, Department of Aeronautics and Astronautics, and Associate Director of the Institute for Soldier Nanotechnologies, MIT, will present a talk: “Extension of the Peridynamic Theory of Solids for the Simulation of Materials under Extreme Loadings.”
Abstract: 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 frame-work 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.