Multidimensional Space Method for Geometrically Nonlinear Problems under Total Lagrangian Formulation Based on the Extended Finite-Element Method
Publication: Journal of Engineering Mechanics
Volume 143, Issue 7
Abstract
For the standard extended finite-element method (XFEM), the degrees of freedom (DOFs) at nodes around the surfaces and tips of cracks are enriched to represent the discontinuity and the singularity of cracks. However, for the incremental approach, the XFEM encounters some troubles as the total number of DOFs increases with the crack growth. This leads to difficulties of the matrix algorithm. In this paper, a multidimensional space method for geometrically nonlinear problems under the total Lagrangian formulation is presented to simulate the crack growth and coalescence. The multidimensional space method is developed from the XFEM. The core concept is that the two-dimensional domain containing cracks is placed into the 12-dimensional space. Each node has DOFs in the domain containing cracks. The total Lagrangian formulation is applied to analyze the two-dimensional (2D) geometrically nonlinear problems, especially for large deformation. Moreover, three numerical experiments are presented to verify the efficiency and robustness of the proposed method.
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Acknowledgments
The work is supported by the National Natural Science Foundation of China (Nos. 51325903, 51679017), project 973 (Grant No. 2014CB046903), the Natural Science Foundation Project of CQ CSTC (No. CSTC, cstc2013kjrc-ljrccj0001), and the research fund of the Doctoral Program of Higher Education of China (No. 20130191110037).
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 7 • July 2017
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©2017 American Society of Civil Engineers.
History
Received: Oct 11, 2015
Accepted: Nov 23, 2016
Published ahead of print: Feb 26, 2017
Published online: Feb 27, 2017
Published in print: Jul 1, 2017
Discussion open until: Jul 27, 2017
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