Boundary layer energies for nonconvex discrete systems
Boundary layer energies for nonconvex discrete systems
复制标题
非凸离散系统的边界层能量
DOI：
10.1142/s0218202511005210
复制
发表时间：
2011
影响因子：
3.5
通讯作者：
C. Zanini
中科院分区：
文献类型：
--
作者：
L. Scardia;A. Schlömerkemper;C. Zanini
在这项工作中，我们考虑了一个一维原子链，它通过Lennard-Jones型的最近和次近邻相互作用相互作用。我们施加了狄利克雷边界条件，并规定了链的第二个和最后一个原子的变形。这相当于规定了离散设置边界处的斜率。我们计算了零阶和一阶的Γ-limits，其中后者导致边界层对能量的贡献的发生。这些贡献取决于链是否在边界附近表现出弹性或是否存在裂缝。这又取决于给定的边界数据。我们还分析了裂缝的位置依赖于规定的离散斜率。
In this work we consider a one-dimensional chain of atoms which interact through nearest and next-to-nearest neighbour interactions of Lennard–Jones type. We impose Dirichlet boundary conditions and in addition prescribe the deformation of the second and last but one atoms of the chain. This corresponds to prescribing the slope at the boundary of the discrete setting. We compute the Γ-limits of zero and first order, where the latter leads to the occurrence of boundary layer contributions to the energy. These contributions depend on whether the chain behaves elastically close to the boundary or whether there is a crack. This in turn depends on the given boundary data. We also analyse the location of fracture in dependence on the prescribed discrete slopes.