本文研究统计非均匀两相弹性离散结构的力学问题。特别地，遵循（Luciano和Willis，Journal of the Mechanics and Physics of Solids 53，1505-1522，2005）中提出的方法，针对具有由二阶空间统计量化的异质性分布的离散系统开发了Hashin-Shtrikman-Willis类型的能量边界和估计。三个数值算例表明，所得到的势能系综平均值的表达式是完全明确的，计算上是可行的，没有可调参数。此外，与参考蒙特卡罗模拟的比较证实了一个显着的改进，在精度方面的方法，完全基于一阶统计。
英文摘要：
In this paper, we study the mechanics of statistically non-uniform two-phase elastic discrete structures. In particular, following the methodology proposed in (Luciano and Willis, Journal of the Mechanics and Physics of Solids 53, 1505-1522, 2005), energetic bounds and estimates of the Hashin-Shtrikman-Willis type are developed for discrete systems with a heterogeneity distribution quantified by second-order spatial statistics. As illustrated by three numerical case studies, the resulting expressions for the ensemble average of the potential energy are fully explicit, computationally feasible and free of adjustable parameters. Moreover, the comparison with reference Monte-Carlo simulations confirms a notable improvement in accuracy with respect to approaches based solely on the first-order statistics.
Can Strain or Anion Interchange Make an Unstable Structure Stable? Energetics, Lattice Dynamics and Strain-Tunable Band Gaps of Lithium Chalcohalide Antiperovskites (Li$_{3}$$BA$) and their Anion Interchange Variants (Li$_{3}$$AB$)
Evidence for Distributed Fault Energetics and Their Impact on Deformation in a Chemically Complex Alloy
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；The University of Osaka（大阪大学）；Shanghai University（上海大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Argonne National Laboratory（阿贡国家实验室）；University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）；Monash University（蒙纳士大学）
Intertwined spin-charge stripe order and polar lattice distortion in La$_{3}$Ni$_{2}$O$_{7}$
Key Laboratory of Materials Physics, Institute of Solid State Physics, HFIPS, Chinese Academy of Sciences（中国科学院合肥物质科学研究院固体物理研究所材料物理重点实验室）；Science Island Branch of Graduate School, University of Science and Technology of China（中国科学技术大学研究生院科学岛分院）；Anhui Province Key Laboratory of Low-Energy Quantum Materials and Devices, High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences（中国科学院合肥物质科学研究院强磁场实验室安徽省低能量子材料与器件重点实验室）
