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A stabilized complementarity formulation for nonlinear analysis of 3D bimodular materials

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Abstract

Bi-modulus materials with different mechanical responses in tension and compression are often found in civil, composite, and biological engineering. Numerical analysis of bimodular materials is strongly nonlinear and convergence is usually a problem for traditional iterative schemes. This paper aims to develop a stabilized computational method for nonlinear analysis of 3D bimodular materials. Based on the parametric variational principle, a unified constitutive equation of 3D bimodular materials is proposed, which allows the eight principal stress states to be indicated by three parametric variables introduced in the principal stress directions. The original problem is transformed into a standard linear complementarity problem (LCP) by the parametric virtual work principle and a quadratic programming algorithm is developed by solving the LCP with the classic Lemke’s algorithm. Update of elasticity and stiffness matrices is avoided and, thus, the proposed algorithm shows an excellent convergence behavior compared with traditional iterative schemes. Numerical examples show that the proposed method is valid and can accurately analyze mechanical responses of 3D bimodular materials. Also, stability of the algorithm is greatly improved.

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Acknowledgments

The project was supported by the National Natural Science Foundation of China (Grants 11232003, 91315302, 11502035) and the Open Research Foundation (Grant GZ1404) of State Key Laboratory of Structural Analysis for Industrial Equipment at Dalian University of Technology.

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Authors and Affiliations

  1. Department of Engineering Mechanics, College of Aerospace Engineering, Chongqing University, Chongqing, 400030, China

    L. Zhang, J. Wu & B. Yan

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

    L. Zhang & H. W. Zhang

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  1. L. Zhang
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  2. H. W. Zhang
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  3. J. Wu
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  4. B. Yan
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Correspondence to L. Zhang.

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Zhang, L., Zhang, H.W., Wu, J. et al. A stabilized complementarity formulation for nonlinear analysis of 3D bimodular materials. Acta Mech. Sin. 32, 481–490 (2016). https://doi.org/10.1007/s10409-015-0517-3

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  • DOI: https://doi.org/10.1007/s10409-015-0517-3

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