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A second order cone complementarity approach for the numerical solution of elastoplasticity problems

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Abstract

In this paper we present a new approach for solving elastoplastic problems as second order cone complementarity problems (SOCCPs). Specially, two classes of elastoplastic problems, i.e. the J 2 plasticity problems with combined linear kinematic and isotropic hardening laws and the Drucker-Prager plasticity problems with associative or non-associative flow rules, are taken as the examples to illustrate the main idea of our new approach. In the new approach, firstly, the classical elastoplastic constitutive equations are equivalently reformulated as second order cone complementarity conditions. Secondly, by employing the finite element method and treating the nodal displacements and the plasticity multiplier vectors of Gaussian integration points as the unknown variables, we obtain a standard SOCCP formulation for the elastoplasticity analysis, which enables the using of general SOCCP solvers developed in the field of mathematical programming be directly available in the field of computational plasticity. Finally, a semi-smooth Newton algorithm is suggested to solve the obtained SOCCPs. Numerical results of several classical plasticity benchmark problems confirm the effectiveness and robustness of the SOCCP approach.

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Authors and Affiliations

  1. School of Mathematical Sciences, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian Universityof Technology, Dalian, 116024, China

    L. L. Zhang

  2. Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian Universityof Technology, Dalian, 116024, China

    J. Y. Li & H. W. Zhang

  3. School of Mechanical Engineering, Tianjin University of Science & Technology, Tianjin, 300222, China

    J. Y. Li

  4. Department of Applied Mathematics, South China University of Technology, Guangzhou, 510641, China

    S. H. Pan

Authors
  1. L. L. Zhang
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  2. J. Y. Li
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  3. H. W. Zhang
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  4. S. H. Pan
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Correspondence to J. Y. Li.

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Zhang, L.L., Li, J.Y., Zhang, H.W. et al. A second order cone complementarity approach for the numerical solution of elastoplasticity problems. Comput Mech 51, 1–18 (2013). https://doi.org/10.1007/s00466-012-0698-6

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  • DOI: https://doi.org/10.1007/s00466-012-0698-6

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