THE ROLE OF THE PATCH TEST IN 2D ATOMISTIC-TO-CONTINUUM COUPLING METHODS ∗
THE ROLE OF THE PATCH TEST IN 2D ATOMISTIC-TO-CONTINUUM COUPLING METHODS ∗
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DOI：
10.1051/m2an/2012005
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发表时间：
2011-01
期刊：
影响因子：
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通讯作者：
C. Ortner
中科院分区：
文献类型：
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作者：
C. Ortner
对于一般的原子-连续耦合方法，将多体原子间势与柯西非线性弹性力学的P_1有限元离散相耦合，本文讨论了斑块检验一致性(或无鬼力)是否意味着一阶误差估计的问题。在两个维度上，在下列附加的技术假设下，这确实是正确的：(I)能量一致性条件，(Ii)界面修正的局部性，(Iii)界面修正的体积标度，和(Iv)原子区的连通性。详细讨论了这些假设的必要性程度。
For a general class of atomistic-to-continuum coupling methods, coupling multi-body inter- atomic 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.