论文标题
常规三角晶格中的离散模型的粗晶模型
Coarse-graining of a discrete model for edge dislocations in the regular triangular lattice
论文作者
论文摘要
我们考虑了平面弹性的离散模型，其中粒子在参考配置中坐在常规三角晶格上，并通过最近的邻居成对电位相互作用，键模为线性化弹性弹簧。在此框架内，我们引入了塑料滑道，其围绕每个三角形的离散循环检测到边缘位错的可能存在。 我们提供了$γ$ - 融合分析，因为晶格间距趋于零，即在能量状态中边缘诱导的弹性能量，与对应于有限数量的几何必需位错相对应。
We consider a discrete model of planar elasticity where the particles, in the reference configuration, sit on a regular triangular lattice and interact through nearest neighbor pairwise potentials, with bonds modeled as linearized elastic springs. Within this framework we introduce plastic slip fields, whose discrete circulation around each triangle detects the possible presence of an edge dislocation. We provide a $Γ$-convergence analysis, as the lattice spacing tends to zero, of the elastic energy induced by edge dislocations in the energy regime corresponding to a finite number of geometrically necessary dislocations.
