Solid solutions are of critical importance to many technological applications. While continuum frameworks have been developed and invoked in the past for studying behavior of solid solutions, recent studies point to the importance of image stresses in finite systems, and in particular, suggest that the homogenized self-stress field of the solutes, which enter the chemical potential in the prevalent continuum models, should be excluded in a correct treatment. The present work is concerned with the study of a solute atmosphere in the vicinity of a void in two-dimensional elasticity wherein the solute atmosphere is treated as a distribution of solute rods extended indefinitely normal to the plane of analysis. A statistical mechanics framework is adopted based on the Gibbs canonical ensemble, and the well-established path-independent integrals of solid mechanics are used for examining configurational forces on the void induced by the presence of a solute atmosphere. Numerical Monte Carlo simulations fully accounting for the interaction energy between the solute rods are used for calculation of the ensemble averages of the energy release rates associated with void translation and expansion, and semi-analytical solutions are further developed in the limit of dilute solute concentrations and large temperatures. Effect of interaction between the stress fields of a solute atmosphere and an external loading on the configurational forces is also investigated through both numerical and analytical calculations. It is shown that the interaction between the image stress field of a given concentration of solute rods and the stress field of an equi-biaxial loading results in an added contribution to the energy release rate of void expansion which does not fade away even when the solid dimensions grow indefinitely. Numerical simulations are further used to examine the effect of loading-induced solute redistribution on the energetic driving force for void expansion.

固体解决方案对于许多技术应用至关重要。虽然过去已经开发并调用了连续体框架来研究固溶体的行为，但最近的研究指出了有限系统中图像应力的重要性，特别是指出了进入溶液中的溶质的均质自应力场。流行的连续模型中的化学势应在正确的治疗中排除。本工作涉及二维弹性中空隙附近的溶质气氛的研究，其中溶质气氛被视为无限长地垂直于分析平面延伸的溶质棒的分布。根据吉布斯（Gibbs）规范合奏采用了统计力学框架，并使用成熟的固体力学独立于路径的积分来检查溶质气氛的存在在空隙上引起的构型力。完全考虑了溶质棒之间相互作用能的数值蒙特卡洛模拟用于计算与空隙平移和膨胀相关的能量释放速率的整体平均值，并且在稀溶质浓度和极限范围内进一步开发了半解析解。高温。还通过数值和解析计算研究了溶质气氛的应力场与外部载荷之间的相互作用对构型力的影响。结果表明，给定浓度的溶质棒的图像应力场与等双轴载荷的应力场之间的相互作用导致了对空隙膨胀的能量释放速率的额外贡献，即使在固体状态下，它也不会消失尺寸无限增长。数值模拟还用于检查载荷引起的溶质再分配对空隙膨胀的能量驱动力的影响。