缺陷扩展的一维周期模型及其与某些连续介质模型的关系
A One-Dimensional Peridynamic Model of Defect Propagation and its Relation to Certain Other Continuum Models
摘要：
固体的周向模型不涉及位移场的空间梯度，因此非常适合于研究缺陷的传播。在这里，基于键的周波理论被用来研究平衡和稳定的传播的晶格缺陷-一个扭结-在一个维度。当扭结通过时，材料局部地从一种状态转变为另一种状态。如果所施加的力小于计算出的某个临界值，则扭结处于平衡状态，并且如果所施加的力超过该临界值，则扭结扩展。给出的动力学关系作为所施加的力的函数的传播速度也来自。此外，它表明，某些微分方程为基础的模型的连续的动力学解是相同的那些提供的微模函数选择适当的周波模型。导出了等效周波模型的微模量函数的计算公式，并举例说明。这种能力，以取代微分方程为基础的模型与peridadic一个可能证明是有用的，当数值研究更复杂的问题，如涉及多个和相互作用的缺陷。
英文摘要：
The peridynamic model of a solid does not involve spatial gradients of the displacement field and is therefore well suited for studying defect propagation. Here, bond-based peridynamic theory is used to study the equilibrium and steady propagation of a lattice defect -- a kink -- in one dimension. The material transforms locally, from one state to another, as the kink passes through. The kink is in equilibrium if the applied force is less than a certain critical value that is calculated, and propagates if it exceeds that value. The kinetic relation giving the propagation speed as a function of the applied force is also derived. In addition, it is shown that the dynamical solutions of certain differential-equation-based models of a continuum are the same as those of the peridynamic model provided the micromodulus function is chosen suitably. A formula for calculating the micromodulus function of the equivalent peridynamic model is derived and illustrated. This ability to replace a differential-equation-based model with a peridynamic one may prove useful when numerically studying more complicated problems such as those involving multiple and interacting defects.
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