The role of the patch test in 2D atomistic-to-continuum coupling methods

Abstract

For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy--Born nonlinear elasticity, this paper adresses the question whether patch test consistency (or, absence of ghost forces) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction, (iii) volumetric scaling of the interface correction, and (iv) connectedness of the atomistic region. The extent to which these assumptions are necessary is discussed in detail.

Version 2: correction of some minor mistakes, added discussion of multiple connected atomistic region, minor improvements of style

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Cited by in corpus (7)

• Consistent Energy-based Atomistic/Continuum Coupling for Two-body Potentials in Three Dimensions
• Atomistic/Continuum Blending with Ghost Force Correction
• Analysis of an Energy-based Atomistic/Continuum Coupling Approximation of a Vacancy in the 2D Triangular Lattice
• Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces: a 2D model problem
• Linear Stationary Iterative Methods for the Force-based Quasicontinuum Approximation
• Analysis of Blended Atomistic/Continuum Hybrid Methods
• Atomistic-to-Continuum Coupling Approximation of a One-Dimensional Toy Model for Density Functional Theory