Specifying a nonlocal material model requires more information than is needed for the same material in the local theory. A nonlocal model, because it contains a length scale for interactions between material points, requires the characterization of how these interactions depend on the distance between points. This dependence on distance cannot generally be determined by ordinary laboratory material property tests.To gain insight into how the nonlocal force interactions can be specified for a real material, molecular dynamics can be applied with the help of a new coarse graining method. The coarse graining method starts with a precise definition of the upscaled degrees of freedom, which are the mean displacements at a point weighted by a smoothing function. As a consequence of Newton’s second law applied to the individual atoms, the smoothed displacements are shown to follow the peridynamic form of the linear momentum balance. The interactions between the coarse grained displacements are obtained by applying the smoothing functions to the interatomic potentials.By deforming the molecular dynamics model according to a prescribed set of boundary conditions, the interaction forces are determined as a function of the relative displacements of the coarse grained material points. These coarse grained bond forces automatically include a dependence on the bond length, providing, in effect, a direct way to compute nonlocality. The peridynamic horizon is obtained from the bond forces, since they eventually decay to zero outside some cutoff distance for the coarse grained interactions. The coarse grained bond forces are useful in calibrating an assumed peridynamic material model.As an example, a single sheet of graphene at finite temperature is modeled with molecular dynamics using the Tersoff potential. The coarse graining method is applied to the molecular dynamics grid subjected to two deformations: uniaxial strain and isotropic extension. The resulting bond forces are then used to calibrate a peridynamic continuum material model. In this case, the assumed continuum model is ordinary state-based. The model is nonlinear in its bond strain dependence and includes a maximum in the bond force as large strains are applied. For strains beyond this maximum, the model enters an elastically unstable regime reflecting the onset of material failure.A bond breakage criterion can be obtained by computing the surface energy of newly created fractures in the molecular dynamics grid. This surface energy consists of the increase in the potential energy in the interatomic potential due to the missing atoms along the new free surface. This surface energy, which is assumed to equal the critical energy release rate, is easily translated into a critical bond strain for the coarse grained peridynamic model.The calibrated material model for graphene sheets is applied to the simulation of an experiment (Lee et al., 2008) in which a graphene sheet is deflected up to the point of failure by an atomic force microscope probe. The curve of the reaction force on the probe versus deflection obtained by a peridynamic simulation is compared against the experimental data, including the occurrence of failure and post-failure damage.

Calibrating a Peridynamic Material Model With Molecular Dynamics

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

Supporting the need among researchers worldwide for additional online and multimedia content, ASME now offers the ASME Conference Video Collection. This platform will collect and provide long-term access to conference presentation videos, encompassing all technology areas within ASME's technical conference and events program. About 30,000-40,000 engineers across all mechanical engineering and related disciplines participate in ASME conferences each year. This includes authors of approximately 6,000 to 8,000 technical papers published by ASME, the majority of whom also submit video presentations for our virtual conferences. The video collection will be available as an add-on to existing product packages or as a separate subscription.