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Peridynamics with LAMMPS : a user guide

Parks, Michael L.; Plimpton, Steven J.; Silling, Stewart A.; Lehoucq, Richard B.

Peridynamics is a nonlocal extension of classical continuum mechanics. The discrete peridynamic model has the same computational structure as a molecular dynamics model. This document provides a brief overview of the peridynamic model of a continuum, then discusses how the peridynamic model is discretized within LAMMPS. An example problem is also included.

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TYPE SAND Report YEAR 2011
OSTIDOI

Statistical mechanical foundation of the peridynamic nonlocal continuum theory: Energy and momentum conservation laws

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Lehoucq, Richard B.; Sears, Mark P.

The purpose of this paper is to derive the energy and momentum conservation laws of the peridynamic nonlocal continuum theory using the principles of classical statistical mechanics. The peridynamic laws allow the consideration of discontinuous motion, or deformation, by relying on integral operators. These operators sum forces and power expenditures separated by a finite distance and so represent nonlocal interaction. The integral operators replace the differential divergence operators conventionally used, thereby obviating special treatment at points of discontinuity. The derivation presented employs a general multibody interatomic potential, avoiding the standard assumption of a pairwise decomposition. The integral operators are also expressed in terms of a stress tensor and heat flux vector under the assumption that these fields are differentiable, demonstrating that the classical continuum energy and momentum conservation laws are consequences of the more general peridynamic laws. An important conclusion is that nonlocal interaction is intrinsic to continuum conservation laws when derived using the principles of statistical mechanics. © 2011 American Physical Society.

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TYPE Conference YEAR 2011
ScopusOSTI

Energy balance in peridynamics

Silling, Stewart A.; Lehoucq, Richard B.

The peridynamic model of solid mechanics treats internal forces within a continuum through interactions across finite distances. These forces are determined through a constitutive model that, in the case of an elastic material, permits the strain energy density at a point to depend on the collective deformation of all the material within some finite distance of it. The forces between points are evaluated from the Frechet derivative of this strain energy density with respect to the deformation map. The resulting equation of motion is an integro-differential equation written in terms of these interparticle forces, rather than the traditional stress tensor field. Recent work on peridynamics has elucidated the energy balance in the presence of these long-range forces. We have derived the appropriate analogue of stress power, called absorbed power, that leads to a satisfactory definition of internal energy. This internal energy is additive, allowing us to meaningfully define an internal energy density field in the body. An expression for the local first law of thermodynamics within peridynamics combines this mechanical component, the absorbed power, with heat transport. The global statement of the energy balance over a subregion can be expressed in a form in which the mechanical and thermal terms contain only interactions between the interior of the subregion and the exterior, in a form anticipated by Noll in 1955. The local form of this first law within peridynamics, coupled with the second law as expressed in the Clausius-Duhem inequality, is amenable to the Coleman-Noll procedure for deriving restrictions on the constitutive model for thermomechanical response. Using an idea suggested by Fried in the context of systems of discrete particles, this procedure leads to a dissipation inequality for peridynamics that has a surprising form. It also leads to a thermodynamically consistent way to treat damage within the theory, shedding light on how damage, including the nucleation and advance of cracks, should be incorporated into a constitutive model.

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TYPE Conference YEAR 2010
OSTI
Results 76–100 of 163
Results 76–100 of 163