4.5 Article

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

Journal

ACTA MECHANICA SINICA
Volume 32, Issue 3, Pages 481-490

Publisher

SPRINGER HEIDELBERG
DOI: 10.1007/s10409-015-0517-3

Keywords

Bimodular materials; Non-smooth stress-strain relationship; Parametric variational principle; Complementarity

Funding

  1. National Natural Science Foundation of China [11232003, 91315302, 11502035]
  2. Open Research Foundation of State Key Laboratory of Structural Analysis for Industrial Equipment at Dalian University of Technology [GZ1404]

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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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