Standard phase-field fracture methods are rooted in brittle fracture theory and therefore do not inherently prescribe a material strength for crack nucleation, while also struggling to capture cohesive fracture behaviour. Recent eigenstrain-based formulations overcome both limitations by introducing fracture eigenstrains that decouple the strength surface from the fracture energy, but their implementation has so far relied on direct energy-minimization frameworks rather than standard finite-element procedures. In this work, we exploit the fact that the eigenstrains require no spatial gradients and reformulate the eigenstrain evolution as a local constitutive model, analogous to those used in plasticity, that is resolved at each integration point. As a result, the cohesive phase-field requires no additional global degrees of freedom beyond those of a standard phase-field formulation and can be readily integrated into existing finite-element codes. Two strength criteria are considered: a non-smooth criterion with independent tensile and shear strengths, and a smooth Drucker-Prager-like criterion that captures pressure-dependent strengthening under compression. Consistent tangent operators are derived for both criteria, ensuring robust convergence of the global Newton-Raphson solver. The framework is validated against three benchmark problems: a plate with a hole under tension and compression, a single-edge notched plate under shear, and a notched plate under dynamic loading. The results demonstrate mesh-independent and phase-field length-scale-independent behaviour, confirm that the fracture energy governs the transition between brittle and cohesive regimes, and show that complex phenomena such as crack branching under dynamic loading are naturally captured. All source codes are openly available.

翻译：标准相场断裂方法根植于脆性断裂理论，因此本质上无法预设材料强度以描述裂纹成核，同时也难以捕捉内聚断裂行为。近年来基于特征应变的公式通过引入断裂特征应变，成功解耦了强度面与断裂能，从而克服了上述双重限制。然而，其实现迄今仍依赖于直接能量最小化框架，而非标准有限元流程。本文利用特征应变无需空间梯度的特性，将特征应变演化重新表述为局部本构模型（类似于塑性力学中的处理方法），并在每个积分点处求解。因此，内聚相场模型除标准相场公式所需的全局自由度外无需额外自由度，可便捷地集成至现有有限元代码中。本研究考虑了两种强度准则：一种是非光滑准则（具有独立的拉伸与剪切强度），另一种是光滑的德鲁克-普拉格型准则（能捕捉压缩下与压力相关的强化效应）。为两种准则推导出一致的切线算子，确保全局牛顿-拉夫逊求解器具有稳健收敛性。通过三个基准算例验证该框架：含孔平板受拉与受压、单边缺口板剪切、以及缺口板动态加载。结果表明该框架具有网格无关性与相场长度尺度无关性，证实断裂能主导脆性与内聚断裂模式间的转变，并表明动态加载下裂纹分叉等复杂现象可自然捕捉。所有源代码均公开提供。