Asymptotic Analysis of a Coupled System of Nonlocal Equations with Oscillatory Coefficients
Asymptotic Analysis of a Coupled System of Nonlocal Equations with Oscillatory Coefficients
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DOI：
10.1137/19m1288085
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发表时间：
2019-09
期刊：
影响因子：
--
通讯作者：
J. Scott;T. Mengesha
中科院分区：
文献类型：
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作者：
J. Scott;T. Mengesha
本文研究了具有振动系数的强耦合积分方程组解的渐近性态。该系统的方程是由一个peridadic模型的变形的非均匀介质，另外占短程力的动机。我们认为消失的非局部性限制在相同的长度尺度上的异质性，并表明该系统的有效行为的特点是耦合系统的局部方程是椭圆的意义上的Legendre-Hadamard。这个有效的系统的特点是由一个四阶张量，与柯西弹性张量，出现在经典的线性化弹性平衡方程的共享属性。
In this paper we study the asymptotic behavior of solutions to systems of strongly coupled integral equations with oscillatory coefficients. The system of equations is motivated by a peridynamic model of the deformation of heterogeneous media that additionally accounts for short-range forces. We consider the vanishing nonlocality limit on the same length scale as the heterogeneity and show that the system's effective behavior is characterized by a coupled system of local equations that are elliptic in the sense of Legendre-Hadamard. This effective system is characterized by a fourth-order tensor that shares properties with Cauchy elasticity tensors that appear in the classical equilibrium equations for linearized elasticity.