具有周期性微结构的一维弹性材料的周向影响函数
Deriving peridynamic influence functions for one-dimensional elastic materials with periodic microstructure
摘要：
围动态材料模型中的影响函数对弹性波的动态行为有很大影响，反过来又会极大地影响断裂传播和材料失效的动态模拟。通常情况下，在周波模型中使用的影响函数是根据其数值特性选择的，而不考虑物理因素。在这项工作中，我们提出了一种方法来推导周期性微结构材料的一维初/边值问题的周期性影响函数。从微尺度下的线性局部弹性动力学运动方程出发，首先用多项式近似微结构位移，然后导出宏观位移的均匀化非局部动力学运动方程，该方程可以很容易地转化为具有离散影响函数的线性周期运动方程。离散影响函数的形状和局部化完全取决于微结构的力学性能和长度尺度。通过与高分辨率的微结构有限元模型和具有线性衰减影响函数的标准线性周波模型的比较，我们证明了从微结构考虑导出的影响函数在预测随时间变化的位移和波动动力学方面更准确。
英文摘要：
The influence function in peridynamic material models has a large effect on the dynamic behavior of elastic waves and in turn can greatly effect dynamic simulations of fracture propagation and material failure. Typically, the influence functions that are used in peridynamic models are selected for their numerical properties without regard to physical considerations. In this work, we present a method of deriving the peridynamic influence function for a one-dimensional initial/boundary value problem in a material with periodic microstructure. Starting with the linear local elastodynamic equation of motion in the microscale, we first use polynomial anzatzes to approximate microstructural displacements and then derive the homogenized nonlocal dynamic equation of motion for the macroscopic displacements; which, is easily reformulated as linear peridyamic equation with a discrete influence function. The shape and localization of the discrete influence function is completely determined by microstructural mechanical properties and length scales. By comparison with a highly resolved microstructural finite element model and the standard linear peridynamic model with a linearly decaying influence function, we demonstrate that the influence function derived from microstructural considerations is more accurate in predicting time dependent displacements and wave dynamics.
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