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Stress concentration in two-dimensional lattices with imperfections

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Abstract

Based on the principle of superposition and a newly developed stripe method, an analytical equivalent model is proposed to calculate the stress fields in two imperfect planar isotropic lattices: the regular triangular lattice and the Kagome lattice, both containing single bar defects. Finite element simulations are used to validate the model predictions. According to the degree of the imperfection, four types of defects: vacancy defect, weak defect, strong defect, and rigid inclusion are classified and the induced local stress fields are analyzed. The stress concentration factor (SCF) caused by the imperfection is analytically obtained, and the influence of the imperfection degree, loading condition, and relative density on the SCF is quantified. Based on the equivalent model, the interaction of dual defects with the thickness of elastic boundary layer in the two lattices is also estimated. In the presence of a vacancy defect, the distinct deformation mechanism results in only a small knock-down in the strength of a triangular lattice but a substantial strength knock-down of a Kagome lattice. Both lattices exhibit no obvious sensitivity to the presence of a rigid inclusion. It is indicated that compared with the corresponding Kagome lattice, the triangular lattice containing a single missing bar possesses a considerable better strength performance. In addition, the analytical results of imperfection interaction demonstrate that the influence of imperfections on stress field calculations and strength analysis is important for the triangular lattice.

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Authors and Affiliations

  1. Department of Engineering Mechanics, AML, Tsinghua University, 100084, Beijing, People’s Republic of China

    Xiaodong Cui, Yihui Zhang & Daining Fang

  2. Laboratoire de Mécanique et Technologie (LMT-Cachan), ENS-Cachan/CNRS-UMR8535/Université Paris 6, 61 Avenue du Président Wilson, 94235, Cachan Cedex, France

    Han Zhao

  3. MOE Key Laboratory for Strength and Vibration, School of Aerospace, Xi’an Jiaotong University, 710049, Xi’an, People’s Republic of China

    Tian Jian Lu

  4. LTCS, College of Engineering, Peking University, 100084, Beijing, People’s Republic of China

    Daining Fang

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  1. Xiaodong Cui
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  2. Yihui Zhang
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  3. Han Zhao
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  4. Tian Jian Lu
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  5. Daining Fang
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Correspondence to Daining Fang.

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Cui, X., Zhang, Y., Zhao, H. et al. Stress concentration in two-dimensional lattices with imperfections. Acta Mech 216, 105–122 (2011). https://doi.org/10.1007/s00707-010-0354-1

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  • DOI: https://doi.org/10.1007/s00707-010-0354-1

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