Enriched degree of freedom locking in crack analysis using the extended finite element method

• Published in: Advances in mechanical engineering 2019-06, Vol.11 (6), p.168781401985979
• Main Authors: Kim, Han-Soo, Kim, Geon-Hyeong
• Format: Article
• Language: English
• Subjects: Crack propagation; Cracks; Degrees of freedom; Enrichment; Finite element analysis; Finite element method; Locking; Mathematical analysis; Nonlinear programming; Reinforced concrete; Stress concentration; Stress distribution; Three dimensional analysis
• ISSN: 1687-8132; 1687-8140; 1687-8140
• DOI: 10.1177/1687814019859793

In this article, the enriched degree of freedom locking that can occur in a crack analysis with the extended finite element method is described. The discontinuous displacement field formulated by the enriched degree of freedom in the extended finite element method does not activate due to the enriched degree of freedom locking. Using the phantom node method, the occurrence of locking when two adjacent elements are simultaneously cracked in a loading step was verified. Two adjacent cracks can be determined to have developed simultaneously when an analysis model reveals a relatively uniform stress distribution on two adjacent elements. Numerical examples of a simply tensioned bar and a reinforced concrete beam are presented to demonstrate the erroneous analysis result due to the enriched degree of freedom locking. As a simple method to circumvent the enriched degree of freedom locking, the tensile strength of the neighboring elements was slightly increased in the numerical examples, and the effectiveness of the method was demonstrated. The proposed method is simple and easy for practicing engineers, and it can be easily applied to the three-dimensional crack propagation analysis.