An equivalent indentation method is developed for the external crack problem with a Dugdale cohesive zone in the both axisymmetric and two-dimensional (2D) cases. This is achieved based on the principle of superposition by decomposing the original problem into two simple boundary value problems, with one considering action of a constant traction within the cohesive zone, and the other corresponding to indentation by a rigid concave punch. Closed-form expressions are derived for the distributions of displacement and traction on the crack interface, which are consistent with the classical results in fracture mechanics. Results show that the interfacial traction distributions in the axisymmetric and 2D cases share the similar mathematical forms except for different coordinate parameters. Finite element analysis is performed to validate the obtained analytical solutions. The proposed method relies solely on a few contact solutions on the surface irrespective of a general elasticity solution in the whole body, and it may find applications in the external crack analysis and adhesive contact model involving functionally graded elastic solids or piezoelectric materials.

中文翻译：

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具有 Dugdale 粘性带的外部裂纹的等效压痕法

在轴对称和二维 (2D) 情况下，针对具有 Dugdale 内聚区的外部裂纹问题开发了等效压痕方法。这是基于叠加原理通过将原始问题分解为两个简单的边值问题来实现的，一个考虑内聚区内恒定牵引力的作用，另一个对应于刚性凹冲头的压痕。推导出裂纹界面位移和牵引力分布的闭式表达式，与断裂力学经典结果一致。结果表明，除了坐标参数不同外，轴对称和二维情况下的界​​面牵引分布具有相似的数学形式。进行有限元分析以验证获得的解析解。所提出的方法仅依赖于表面上的一些接触解，而不管全身的一般弹性解，它可能会在涉及功能梯度弹性固体或压电材料的外部裂纹分析和粘附接触模型中找到应用。