Multiscale Dynamics of Heterogeneous Media in the Peridynamic Formulation
Multiscale Dynamics of Heterogeneous Media in the Peridynamic Formulation
复制标题
近场动力学公式中异质介质的多尺度动力学
DOI：
10.1007/s10659-010-9291-4
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发表时间：
2012
影响因子：
2
通讯作者：
["Bacim Alali
中科院分区：
文献类型：
--
作者：
["Bacim Alali
提出了一种使用近场动力学公式给出的非局部连续介质模型研究异质介质动力学的方法。这里提出的方法提供了对宏观动力学建模的能力，同时解析微观结构长度尺度上的动力学。该方法的核心是一个新颖的两尺度演化方程。该方程的重新调整后的解可以为近场动力学材料内部的实际变形提供强有力的近似。两个尺度的演化可以分为跟踪异质性长度尺度动态的微观部分和跟踪体积平均（均质）动态的宏观部分。微观和宏观动力学之间的相互作用由演化方程的耦合系统给出。方程表明，介质内部均匀变形产生的力通过历史相关本构关系与均匀变形相关。
A methodology is presented for investigating the dynamics of heterogeneous media using the nonlocal continuum model given by the peridynamic formulation. The approach presented here provides the ability to model the macroscopic dynamics while at the same time resolving the dynamics at the length scales of the microstructure. Central to the methodology is a novel two-scale evolution equation. The rescaled solution of this equation is shown to provide a strong approximation to the actual deformation inside the peridynamic material. The two scale evolution can be split into a microscopic component tracking the dynamics at the length scale of the heterogeneities and a macroscopic component tracking the volume averaged (homogenized) dynamics. The interplay between the microscopic and macroscopic dynamics is given by a coupled system of evolution equations. The equations show that the forces generated by the homogenized deformation inside the medium are related to the homogenized deformation through a history dependent constitutive relation.