Multiscale Modeling &Simulation, Volume 18, Issue 4, Page 1462-1488, January 2020.
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.

中文翻译：

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具有振动系数的非局部方程组的渐近分析。

《多尺度建模与仿真》，第18卷，第4期，第1462-1488页，2020
年1月。在本文中，我们研究了具有振动系数的强耦合积分方程组的解的渐近行为。方程组由异质介质变形的周向动力学模型驱动，该模型还考虑了短程力。我们考虑了与异质性在相同长度范围上消失的非局部极限，并表明该系统的有效行为的特征是在勒让德-哈达玛的意义上是椭圆的局部方程的耦合系统。这个有效的系统的特征在于四阶张量与柯西弹性张量共享属性，柯西弹性张量出现在线性弹性的经典平衡方程中。