A harmonic/anharmonic energy partition method for lattice statics computations

Abstract

A method of lattice statics analysis is developed. Consideration of anharmonic effects is reslricted to finite regions surrounding lattice defecls. All displacements of the nysral are expressed as the effect of unknown forces applied to a perfect harmonic lattice of infinite extent.Displacements are related m the unknown applied forces by means of the Green function of the perfect harmonic lactice. so that equilibrating forces need only be applied to the anharmonic region. The unknown forces are determined so as to maximize the complementary energy of the crjsral, which yields a lower bound to the potential energy. The method daes not require the explicit enforcement of equilibrium or compatibility conditions acmss the boundary beween the harmonic and anharmonic regions. The performance of the method is assessed on the basis of selected numerical examples. The rate of convergence of the method with increasing domain size is found to be cubic. This is one or two orders of magnitude faster than rigid boundary methods based on the harmonic and continuum solutions. respectively.

Discrete dislocations in graphene

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A multifield model for blocky materials based on multiscale description

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Long-term dynamic stability of discrete dislocations in graphene at finite temperature

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