Cracks with quasibrittle behavior are extremely common in engineering structures. The modeling of cohesive cracks involves strong nonlinearity in the contact, material, and complex transition between contact and cohesive forces. In this article, we propose a novel contact algorithm for cohesive cracks in the framework of the extended finite element method. A cohesive‐contact constitutive model is introduced to characterize the complex mechanical behavior of the fracture process zone. To avoid the stress oscillations and ill‐conditioned system matrix that often occur in the conventional contact approach, the proposed algorithm employs a special dual Lagrange multiplier to impose the contact constraint. This Lagrange multiplier is constructed by means of the area‐weighted average and biorthogonality conditions at the element level. The system matrix can be condensed into a positive definite matrix with an unchanged size at a very low computational cost. In addition, we illustrate solving the cohesive crack contact problem using a novel iteration strategy. Several numerical experiments are performed to illustrate the efficiency and high‐quality results of our method in contact analysis of cohesive cracks.

中文翻译：

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扩展有限元法中粘性裂纹的接触算法

具有准脆性行为的裂纹在工程结构中极为常见。粘性裂纹的建模涉及接触，材料以及接触力和内聚力之间复杂过渡的强烈非线性。在本文中，我们在扩展有限元方法的框架内提出了一种新的粘性裂纹接触算法。引入内聚接触本构模型来表征断裂过程区的复杂力学行为。为了避免传统接触方法中经常发生的应力振荡和病态系统矩阵，建议的算法采用特殊的对偶拉格朗日乘数来施加接触约束。该拉格朗日乘数是通过元素级别的面积加权平均值和双正交条件构造的。系统矩阵可以以非常低的计算成本浓缩为大小不变的正定矩阵。另外，我们说明了使用一种新颖的迭代策略来解决粘性裂纹接触问题。进行了一些数值实验，以说明我们的方法在粘性裂纹接触分析中的效率和高质量结果。