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A mixed finite element and mesh-free method using linear complementarity theory for gradient plasticity

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Abstract

A mixed finite element (FE) and mesh-free (MF) method for gradient-dependent plasticity using linear complementarity theory is presented. The assumed displacement field is interpolated in terms of its discrete values defined at the nodal points of the FE mesh with the FE shape functions, whereas the assumed plastic multiplier field required to express its Laplacian is interpolated in terms of its discrete values defined at the integration points of the FE mesh with the MF interpolation functions. A standard form of linear complementarity problem is constructed by combining the weak form of momentum conservation equation and pointwise enforcements of both non-local constitutive equation and non-local yield criterion. The discrete values of the plastic multiplier are taken as the only primary unknowns to be determined. The numerical results demonstrate the validity of the proposed method in the simulation of the strain localization phenomenon due to strain softening.

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Authors and Affiliations

  1. The State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Junbo Zhang & Xikui Li

  2. School of Civil Engineering, Dalian University of Technology, Dalian, 116024, China

    Junbo Zhang

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  1. Junbo Zhang
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  2. Xikui Li
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Correspondence to Xikui Li.

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Zhang, J., Li, X. A mixed finite element and mesh-free method using linear complementarity theory for gradient plasticity. Comput Mech 47, 171–185 (2011). https://doi.org/10.1007/s00466-010-0527-8

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  • DOI: https://doi.org/10.1007/s00466-010-0527-8

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