Abstract

In the recent years, isogeometric analysis (IGA) has found wide application in modeling different types of discontinuities produced by cracks, contact surfaces and bi-material interfaces. This technique eliminates the geometry discretization errors associated with the representation of complex geometries. The present paper employs the extended isogeometric analysis (XIGA) and the coupled finite element-isogeometric analysis (FE-IGA) to model large elasto-plastic deformations in bi-material engineering components. XIGA models all types of discontinuities independent of the grid chosen for analysis. Instead, the standard displacement-based approximation is enriched with additional enrichment functions to include the effects of these discontinuities in the formulation. In the coupled FE-IGA technique, IGA is used in the weak portion of the domain to eliminate the problems of mesh distortion and conventional finite element method is used in the stronger portion where mesh distortions do not occur. The transition elements are employed to couple the finite element and isogeometric portions of the domain. Finally, several numerical problems are solved by XIGA and coupled FE-IGA techniques to illustrate the applicability, efficiency and accuracy of the proposed techniques in modeling large elasto-plastic deformations in bi-material specimens. The results obtained in the present study are compared with finite element solutions which have been taken as the reference solution for the given problems.

摘要

近年来，等几何分析（IGA）在模拟由裂缝、接触面和双材料界面产生的不同类型的不连续性方面得到了广泛的应用。该技术消除了与复杂几何表示相关的几何离散化误差。本文采用扩展等几何分析 (XIGA) 和耦合有限元等几何分析 (FE-IGA) 来模拟双材料工程部件中的大弹塑性变形。XIGA 对所有类型的不连续性进行建模，与选择用于分析的网格无关。相反，标准的基于位移的近似增加了额外的丰富函数，以将这些不连续性的影响包含在公式中。在耦合 FE-IGA 技术中，IGA用于域的薄弱部分以消除网格变形的问题，而传统的有限元方法用于不发生网格变形的强部分。过渡元素用于耦合域的有限元和等几何部分。最后，通过 XIGA 和耦合 FE-IGA 技术解决了几个数值问题，以说明所提出的技术在模拟双材料试样中的大弹塑性变形时的适用性、效率和准确性。本研究中获得的结果与作为给定问题的参考解决方案的有限元解决方案进行了比较。过渡元素用于耦合域的有限元和等几何部分。最后，通过 XIGA 和耦合 FE-IGA 技术解决了几个数值问题，以说明所提出的技术在模拟双材料试样中的大弹塑性变形时的适用性、效率和准确性。本研究中获得的结果与作为给定问题的参考解决方案的有限元解决方案进行了比较。过渡元素用于耦合域的有限元和等几何部分。最后，通过 XIGA 和耦合 FE-IGA 技术解决了几个数值问题，以说明所提出的技术在模拟双材料试样中的大弹塑性变形时的适用性、效率和准确性。本研究中获得的结果与作为给定问题的参考解决方案的有限元解决方案进行了比较。