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

Abstract

The simulation of materials exposed to extreme loads, as is relevant in many areas of engineering, including protection materials, impact damage in turbine engines and high velocity impact in space, remains one of the key challenges in the field of computational mechanics. Despite significant advances, a fully robust and generally applicable computational framework for simulating the response of materials under a wide range of dynamic loading conditions is still lacking and the search for improved approaches continues. Existing methods suffer from a litany of limitations and drawbacks, including difficulty representing fracture, robustness issues, difficulty scaling to a large number of processors, excessive computational expense, and fundamental convergence issues for problems involving material damage. In this thesis, we conduct a thorough investigation into 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 the work for this thesis, we uncover fundamental limitations in existing constitutive formulations of the peridynamic theory, and propose solutions to these limitations which furnish an extended constitutive theory of peridynamic for large deformations of continua. It is shown that these issues are responsible for numerical instabilities commonly observed in peridynamic particle discretizations. Specifically, unphysical deformation modes which allow for matter interpenetration, without contributing to the strain energy, are shown to exist in the original formulation. In order to address this issue, we introduce an extension of the constitutive correspondence framework based on bond-level nonlinear strain measures. It is found that numerical instabilities are suppressed by the extended theory. In addition, we address the issue of incorporating damage and fracture, as is required for modeling materials subjected to intense loads. In particular, two novel approaches for modeling damage and fracture within peridynamics are proposed. One is based on classical continuum damage models, while the other is specifically suited for brittle fracture response. A robust, scalable computational framework based on these extensions to the peridynamic theory is developed, and numerical examples are provided which demonstrate the ability to capture experimentally observed ballistic limit curves for ductile materials, as well as realistic fracture patterns in brittle materials subjected to projectile impact loadings.