Implementing peridynamics within a molecular dynamics code

By Michael L. Parks, R. Lehoucq, S. Plimpton, Stewart A. Silling. Computer Physics Communications, 2007

351 citations recorded by the source corpus.

Peridynamics (PD) is a continuum theory that employs a nonlocal model to describe material properties. In this context, nonlocal means that continuum points separated by a finite distance may exert force upon each other. A meshless method results when PD is discretized with material behavior approximated as a collection of interacting particles. This paper describes how PD can be implemented within a molecular dynamics (MD) framework, and provides details of an efficient implementation. This adds a computational mechanics capability to an MD code, enabling simulations at mesoscopic or even macroscopic length and time scales.

Subfields: Civil and Structural Engineering, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/371202d39679a27bd3c09c4da0a50c786cdb4a12

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Citations in the corpus

Meshfree Methods: Progress Made after 20 Years (2017, neutral): “…reassociate connectivity for penetration and fragment-impact problems (Johnson et al. 1996; Li et al. 2012, 2013; Libersky et al. 1997; Ma et al. 2009; Parks et al. 2008; Rabczuk and Belytschko 2007; Rabczuk and Eibl 2003; Rabczuk et al. 2004; Randles and Libersky 1996; Ren and Li 2010; Silling…”
A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities (2012, background): “The mechanical peridynamic theory ([78], [82]) has been successfully applied to model brittle fracture ([79], [80], [62], [71]), rupture of membranes and nanofiber networks ([81], [10]), spallation [95], damage in composite materials and polycrystalline ceramics ([96], [5]), phase transformations [3”
A computational library for multiscale modeling of material failure (2013, methodology): “Moreover, PERMIX has a full interface to the LAMMPS Library that includes Peridynamics [121,122,99] and the SPH method [56,73] in addition to its comprehensive MD library.”
Dynamic problems for metamaterials: Review of existing models and ideas for further research (2014, methodology): “In the other words, S represents the non-local behaviour both in time and space, like in the viscoelasticity or non-local elasticity (Eringen, Edelen, 1972; Haseganu, Steigmann, 1996; Parks et al., 2008; Lehoucq, Silling, 2008).”
Peridynamic Theory of Solid Mechanics (2010, methodology): “Solution of the peridynamic continuum equations within the LAMMPS molecular dynamics code is described in [56].”
An extended constitutive correspondence formulation of peridynamics based on nonlinear bond-strain measures (2014, background): “A key feature of peridynamics is the ability to naturally describe discontinuities such as cracks [2, 3, 4, 5, 6, 7] and phase transition boundaries [8] within a single continuum framework.”
Impact Mechanics and High-Energy Absorbing Materials: Review (2008, background): “Fragmentation due to impact on a thin brittle target is also modeled successfully in Silling and Askari (2005), Wei (2005), and Parks et al. (2008).”
A peridynamic material model for the analysis of dynamic crack propagation in orthotropic media (2014, background): “In this theory, each infinitesimal unit of the continuum, called particle, interacts with other particles located in its neighbourhood through forces, similar to the molecular dynamics theory (Parks et al. 2008; Parks et al. 2010).”
ON THE ROLE OF THE INFLUENCE FUNCTION IN THE PERIDYNAMIC THEORY (2011, methodology): “Similar mesh-dependent crack growth was observed in Parks et al. (2008) for small values of the horizon δ.”