A cohesive phase-field model of ductile fracture in a finite-deformation setting is presented. The model is based on a free-energy function in which both elastic and plastic work contributions are coupled to damage. Using a strictly variational framework, the field evolution equations, damage kinetics, and flow rule are jointly derived from a scalar least-action principle. Particular emphasis is placed on the use of a rational function for the stress degradation that maintains a fixed effective strength with decreasing regularization length. The model is employed to examine crack growth in pure mode-I problems through the generation of crack growth resistance (J-R) curves. In contrast to alternative models, the current formulation gives rise to J-R curves that are insensitive to the regularization length. Numerical evidence suggests convergence of local fields with respect to diminishing regularization length as well.

提出了有限变形环境中韧性断裂的内聚相场模型。该模型基于自由能函数，其中弹性功和塑性功都与损伤耦合。使用严格的变分框架，场演化方程、损伤动力学和流动规则是从标量最小作用原理共同推导出来的。特别强调使用应力退化的有理函数，该函数保持固定的有效强度，随着强度的降低而降低。正则化长度。该模型用于通过生成裂纹扩展阻力 (JR) 曲线来检查纯模式 I 问题中的裂纹扩展。与替代模型相比，当前的公式产生了对正则化长度不敏感的 JR 曲线。数值证据表明，随着正则化长度的减少，局部场也会收敛。