Peridynamics formulates the balance of linear momentum as an integro-differential equation, making it naturally suited for fracture modeling without special treatment of discontinuities. The bond-associated correspondence formulation provides a highly accurate peridynamic framework by computing bond-wise deformation gradients that are free of zero-energy modes and yield accurate results even near boundaries. However, the traditional fracture approach based on irreversible bond deletion can compromise this formulation, as the progressive removal of bonds degrades the nonlocal approximation of the deformation gradient and can lead to numerical instabilities. In this work, a novel phase-field peridynamics approach is introduced that avoids these instabilities. Instead of deleting bonds, the energetic contribution of each bond is continuously degraded through a bond phase-field parameter, while a separate kinematic degradation function preserves the accuracy of the nonlocal deformation gradient approximation. The normalization constant ensuring thermodynamic consistency with Griffith's fracture theory is derived analytically for general spherical kernel functions as a ratio of two one-dimensional integrals. Numerical examples including mode I and mode II fracture, the boundary tension test with different kernel functions and horizon ratios, and the Kalthoff-Winkler experiment demonstrate the stability, accuracy, and consistency of the proposed approach.

翻译：近场动力学将线性动量平衡表述为积分-微分方程，使其无需对不连续性进行特殊处理即可自然适用于断裂建模。键关联对应公式通过计算无零能模态且即使在边界附近也能获得精确结果的键向变形梯度，提供了高精度的近场动力学框架。然而，基于不可逆键断裂的传统断裂方法可能损害该公式，因为键的逐步移除会降低变形梯度的非局部近似精度，并可能导致数值不稳定。本文提出了一种新颖的相场近场动力学方法以避免这些不稳定性。该方法不删除键，而是通过键向相场参数持续降低每个键的能量贡献，同时通过独立的运动学退化函数保持非局部变形梯度近似的精度。确保与格里菲斯断裂理论热力学一致性的归一化常数，对于一般球对称核函数被解析推导为两个一维积分之比。包括I型和II型断裂、使用不同核函数和水平比的边界拉伸试验以及卡尔托夫-温克勒实验在内的数值算例，证明了所提方法的稳定性、准确性和一致性。