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Stabilization of the extended finite element method for stiff embedded interfaces and inclusions
International Journal for Numerical Methods in Engineering ( IF 2.9 ) Pub Date : 2021-09-20 , DOI: 10.1002/nme.6834
Recep Emre Erkmen 1 , Daniel Dias‐da‐Costa 2
Affiliation  

This article investigates the performance of the XFEM for stiff embedded interfaces and inclusions. It is known that the XFEM may lead to ill-conditioned stiffness matrices and oscillations in the interface traction field, the severity of which depends on the underlying basis functions, as well as on the orientation of the interface. The jumps at the discontinuity are shown to contain quadratic bubble residuals that can introduce oscillatory behavior. Those residuals are worsened by the ill-conditioning of the system with very stiff interfaces. A variationally consistent method is proposed to overcome the oscillatory behavior and ill-conditioning, in which the assumed strain method is developed to directly eliminate bubble residuals and deploy Legendre polynomials and explore their orthogonality properties to improve the conditioning of the stiffness matrices. Numerical examples illustrate the efficiency and generality of the proposed approach at both element and structural levels. The new approach is shown to be robust for imposing Dirichlet type boundary conditions at the crack interface, such as crack closure and initially rigid cohesive laws. The effects of numerical oscillations on the prediction of effective properties of composites in XFEM-based computational homogenization procedures are also discussed.

中文翻译:

刚性嵌入界面和夹杂物的扩展有限元方法的稳定性

本文研究了 XFEM 对刚性嵌入界面和夹杂物的性能。众所周知,XFEM 可能会导致界面牵引场中的病态刚度矩阵和振荡,其严重程度取决于基础基函数以及界面的方向。显示不连续点处的跳跃包含可引入振荡行为的二次气泡残差。这些残差因具有非常僵硬界面的系统的病态而恶化。提出了一种变相一致的方法来克服振荡行为和病态,其中开发了假设应变方法以直接消除气泡残差并部署勒让德多项式并探索它们的正交性以改善刚度矩阵的条件。数值例子说明了所提出的方法在元素和结构级别的效率和通用性。新方法对于在裂纹界面处施加狄利克雷型边界条件(例如裂纹闭合和初始刚性内聚定律)是稳健的。还讨论了数值振荡对基于 XFEM 的计算均匀化程序中复合材料有效性能预测的影响。新方法对于在裂纹界面处施加狄利克雷型边界条件(例如裂纹闭合和初始刚性内聚定律)是稳健的。还讨论了数值振荡对基于 XFEM 的计算均匀化程序中复合材料有效性能预测的影响。新方法对于在裂纹界面处施加狄利克雷型边界条件(例如裂纹闭合和初始刚性内聚定律)是稳健的。还讨论了数值振荡对基于 XFEM 的计算均匀化程序中复合材料有效性能预测的影响。
更新日期:2021-11-29
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