Numerical simulation for T-stress for complex multiple branching and intersecting cracks based on continuous-discontinuous cellular automaton. (April 2022)

• Record Type: Journal Article
• Authors: Yan, Fei; Yang, Hao-Ran; Jiang, Quan; Li, Shao-Jun; Xu, Ding-Ping; Tang, Zhi-Dan
• Is Part Of: Theoretical and applied fracture mechanics. Volume 118(2022)
• Publication Date: 2022-04
• Subjects: Intersecting cracks -- Branching cracks -- Continuous-discontinuous cellular automaton -- T-stress -- Displacement correction method; Fracture mechanics -- Periodicals; 620.1126
• DOI: 10.1016/j.tafmec.2021.103234
• Languages: English
• ISSNs: 0167-8442

Abstract

Highlights: A new enrichment scheme is proposed to reflect the influences both singular term and nonsingular constant term of T-stress. A mixed uniformly varying function and a modified enriched scheme for blending cells are developed. Mathematic descriptions for strong discontinuities of intersecting and branching cracks are developed for both opening cracks and close cracks. A comprehensive cellular automaton model considering T-stress is constructed. Abstract: In this work, a discontinuous cellular automaton combined non-singular stress term of T-stress is developed for multiple cracks problems. In order to reflect the influence both singular term of SIFs and nonsingular constant term of T-stress, a new enriched shape function based on crack tip near-field asymptotic functions is proposed, which can simultaneously describe singular and non-singular stress around crack tip. Aimed at non-convergence and internal discontinuity for blending cells, a modified formulation for mathematic description of cellular automaton approximation is employed, in which a mixed uniformly varying function is employed. Besides, mathematic descriptions for strong discontinuities of intersecting and branching cracks are developed in this paper, both opening crack surfaces and close crack surfaces are given in detail respectively. Finally, a comprehensive cellular automaton model considering T-stress is constructed, which includes cell, neighborhood, updating rules and so on. Some numerical examples are given to illustrate that the present method is efficient and accurate, and it can be widely used for some practical engineering.