In this paper, the cohesive fracture is revisited as an energy minimization problem. The energy functional is rigorously derived based on a pair of integral transformations and a novel directional energy decomposition method. The resulting description of the regularized crack is perfectly suitable for cohesive fracture. A well-defined crack direction is associated with each material point. The resulting constitutive relation shows that a damage-induced material orthotropy within the regularized crack is introduced in this theory, which is suitable for cohesive fracture. The proposed method can implement an arbitrarily given mixed-mode cohesive law. The tensile and shear fracture modes are covered in a unified manner and controlled by the tensile-to-shear strength ratio. These theoretical results are presented with detailed proofs and verified numerically by some representative examples involving tension, shear, and compression.

在本文中，内聚断裂被重新审视为能量最小化问题。能量泛函是基于一对积分变换和一种新颖的定向能量分解方法严格推导的。规则化裂纹的最终描述非常适合内聚断裂。明确定义的裂纹方向与每个材料点相关联。得到的本构关系表明，该理论引入了正则化裂纹内的损伤诱发材料正交各向异性，适用于内聚断裂。所提出的方法可以实现任意给定的混合模式内聚律。拉伸和剪切断裂模式以统一的方式覆盖并由拉伸-剪切强度比控制。