The paper presents a rigorous analysis of the singularities of elastic fields near a dislocation loop in a body of arbitrary material symmetry that extends over the entire three-space. Explicit asymptotic formulas are given for the stress, strain and the incompatible distortion near the curved dislocation. These formulas are used to analyze the main object of the paper, the renormalized energy. The core-cutoff method is used to introduce that notion: first, a core in the form of a curved tube along the dislocation loop is removed; then, the energy of the complement is determined (= the core-cutoff energy). As in the case of a straight dislocation, the core-cutoff energy has a singularity that is proportional to the logarithm of the core radius. The renormalized energy is the limit, as the radius tends to 0, of the core-cutoff energy minus the singular logarithmic part. The main result of the paper are novel formulas for the coefficient of logarithmic singularity (the ‘prelogarithmic energy factor’) and for the renormalized energy.

该论文对延伸到整个三空间的任意材料对称体中位错环附近弹性场的奇异性进行了严格分析。给出了弯曲位错附近的应力、应变和不相容畸变的显式渐近公式。这些公式用于分析论文的主要对象，即重整化能量。核心切割方法用于引入该概念：首先，沿着位错环去除弯曲管形式的核心; 然后，确定补体的能量（=核心截止能量）。与直位错的情况一样，核心截止能量具有与核心半径的对数成正比的奇点。重整化能量是极限，因为半径趋于0，核心截止能量减去奇异对数部分。该论文的主要结果是对数奇点系数（“前对数能量因子”）和重整化能量的新公式。