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Unified elastoplastic finite difference and its application

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Abstract

Two elastoplastic constitutive models based on the unified strength theory (UST) are established and implemented in an explicit finite difference code, fast Lagrangian analysis of continua (FLAC/FLAC3D), which includes an associated/non-associated flow rule, strain-hardening/softening, and solutions of singularities. Those two constitutive models are appropriate for metallic and strength-different (SD) materials, respectively. Two verification examples are used to compare the computation results and test data using the two-dimensional finite difference code FLAC and the finite element code ANSYS, and the two constitutive models proposed in this paper are verified. Two application examples, the large deformation of a prismatic bar and the strain-softening behavior of soft rock under a complex stress state, are analyzed using the three-dimensional code FLAC3D. The two new elastoplastic constitutive models proposed in this paper can be used in bearing capacity evaluation or stability analysis of structures built of metallic or SD materials. The effect of the intermediate principal stress on metallic or SD material structures under complex stress states, including large deformation, three-dimensional and non-association problems, can be analyzed easily using the two constitutive models proposed in this paper.

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Authors and Affiliations

  1. School of Civil Engineering and Architecture, Xi’an University of Technology, 5 South Jinhua Road, Xi’an, 710048, P. R. China

    Zong-yuan Ma  (马宗源) & Fa-ning Dang  (党发宁)

  2. Department of Civil Engineering, Xi’an Jiaotong University, 28 Xianning West Road, Xi’an, 710049, P. R. China

    Hong-jian Liao  (廖红建)

Authors
  1. Zong-yuan Ma  (马宗源)
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  2. Hong-jian Liao  (廖红建)
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  3. Fa-ning Dang  (党发宁)
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Correspondence to Zong-yuan Ma  (马宗源).

Additional information

Project supported by the National Natural Science Foundation of China (No. 41172276) and the Central Financial Funds for the Development of Characteristic Key Disciplines in Local Universities (Nos. 106-00X101 and 106-5X1205)

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Ma, Zy., Liao, Hj. & Dang, Fn. Unified elastoplastic finite difference and its application. Appl. Math. Mech.-Engl. Ed. 34, 457–474 (2013). https://doi.org/10.1007/s10483-013-1683-7

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  • DOI: https://doi.org/10.1007/s10483-013-1683-7

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Chinese Library Classification

2010 Mathematics Subject Classification

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