On the passage from atomistic systems to nonlinear elasticity theory for general multi-body potentials with p-growth
On the passage from atomistic systems to nonlinear elasticity theory for general multi-body potentials with p-growth
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关于具有 p 增长的一般多体势从原子系统到非线性弹性理论的转变
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
B. Schmidt
中科院分区：
文献类型：
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作者：
J. Braun;B. Schmidt
当原子间距离趋于零时，我们严格推导了非线性弹性理论领域中原子模型的连续极限。特别是，我们在连续介质理论中获得了作用于变形梯度的积分函数，该函数取决于潜在的原子相互作用势和晶格几何形状。我们的理论适用的相互作用势是多晶格上的一般有限范围模型，特别是还可以解释多极相互作用和键角相关贡献。此外，我们讨论了柯西玻恩规则的适用性。我们的极限能量密度类由一般拟凸函数组成，符合柯西玻恩规则的线性化极限能量类由不受柯西关系限制的一般二次形式组成。
We derive continuum limits of atomistic models in the realm of nonlinear elasticity theory rigorously as the interatomic distances tend to zero. In particular we obtain an integral functional acting on the deformation gradient in the continuum theory which depends on the underlying atomistic interaction potentials and the lattice geometry. The interaction potentials to which our theory applies are general finite range models on multilattices which in particular can also account for multi-pole interactions and bond-angle dependent contributions. Furthermore, we discuss the applicability of the Cauchy-Born rule. Our class of limiting energy densities consists of general quasiconvex functions and the class of linearized limiting energies consistent with the Cauchy-Born rule consists of general quadratic forms not restricted by the Cauchy relations.