An approach to modeling extreme loading of structures using peridynamics

Abstract

We address extreme loading of structures using peridynamics. The peridynamic model is a theory of continuum mechanics that is formulated in terms of integro-differential equations without spatial derivatives. It is a nonlocal theory whose equations remain valid regardless of fractures or other discontinuities that may emerge in a body due to loading. We review peridynamic theory and its implementation in the EMU computer code. We consider extreme loadings on reinforced concrete structures by impacts from massive objects. Peridynamic theory has been extended to model composite materials, fluids, and explosives. We discuss recent developments in peridynamic theory, including modeling gases as peridynamic materials and the detonation model in EMU. We then consider explosive loading of concrete structures. This work supports the conclusion that peridynamic theory is a physically reasonable and viable approach to modeling extreme loading of structures.

Impact fracture analysis enhanced by contact of peridynamic and finite element formulations

“…However, there is no analytical solution to Equations (27) and (28). To solve numerically, a few iterations of the least-squares projection are used to generate an initial guess as [52].…”

“…Silling and Lehoucq [27] presented the development of the peridynamic theory of solid mechanics. Demmie and Silling [28] reviewed the developments in peridynamics and conducted simulations of extreme loading on concrete structures using peridynamics. Xu et al [29] [30] applied peridynamics to model damage and failure in composites.…”

Parallel programming of a peridynamics code coupled with finite element method

“…Liu and Hong (2012b) also presented a parallel implementation of peridynamics for execution on graphics processing units. Demmie and Silling (2007) investigated extreme loadings on reinforced concrete structures caused by airplane impact with parallel peridynamics code using MPI. Kilic andMadenci (2009), Kilic (2008) predicted the progressive failure under thermal loadings using OpenMP.…”

Meshless modeling framework for fiber reinforced concrete structures

“…The original form of the peridynamic theory, bond-based peridynamics (BBPD), includes a central pair-wise force function to describe the interactions between material particles [18,19]. The bond-based peridynamics have been primarily used for a fracture analysis of plain and reinforced concrete under quasi-static loading [20,21] as well as impact loading [19,22,23]. However, the simplification of central pair-wise force limits its application to isotropic, linear, and microelastic materials as the Poissons ratio must be 1/4 [24][25][26].…”