Connecting Atomistic and Continuous Models of Elastodynamics
Connecting Atomistic and Continuous Models of Elastodynamics
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连接弹性动力学的原子模型和连续模型
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
J. Braun
中科院分区：
文献类型：
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作者：
J. Braun
我们证明了原子弹性动力学方程在有界区域上的解的长时间存在性，以及当原子间距离趋于零时，它们收敛到连续非线性弹性动力学的解。这里，连续介质能量密度由柯西-玻恩规则给出。考虑的模型允许一般有限范围的相互作用。为了控制大变形的稳定性，我们还证明了一个新的原子Gårding不等式。
We prove the long-time existence of solutions for the equations of atomistic elastodynamics on a bounded domain with time-dependent boundary values as well as their convergence to a solution of continuum nonlinear elastodynamics as the interatomic distances tend to zero. Here, the continuum energy density is given by the Cauchy–Born rule. The models considered allow for general finite range interactions. To control the stability of large deformations we also prove a new atomistic Gårding inequality.