A history-dependent cohesive zone model is considered in the linear elasticity framework with the cohesive stresses governed by the fracture condition formulated in terms of a nonlinear Abel-type integral operator. A possibility for the cohesive stresses to possess a weak singularity has been examined by utilizing asymptotic modeling approach. It has been shown that the balance of the leading-term asymptotic representations in the model equations is possible for nonsingular cohesive stresses only.

中文翻译：

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奇异的非线性历史相关的内聚区模型：可能吗？

在线性弹性框架中考虑了基于历史的内聚区模型，内聚应力由断裂条件控制，该断裂条件由非线性Abel型积分算子表示。通过使用渐近建模方法，研究了内聚应力具有弱奇异性的可能性。已经表明，模型方程式中前导渐近表示的平衡仅对于非奇异的内聚应力是可能的。