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Comparative study of contact problems solution based on the Penalty and Lagrange multiplier

Research Area: Uncategorized Year: 2011
Type of Publication: In Proceedings Keywords: Contact Problem, Penalty Method, Lagrange Method
  • Vulovic, Snezana
  • Grujovic, Nenad
  • Zivkovic, Miroslav
  • Slavkovic, Radovan
Editor: TCCM 2011
Book title: Trends & Challenges in Computational Mechanics, A Conference in honor of Peter Wriggers' 60th birthday
Organization: TCCM 2011 Month: September
ISBN: : 978-88-96477-22-9
In the paper a model for contact problem with friction, based on the penalty and Lagrange multiplier method, was described. As the configuration of two bodies coming into the contact is not a priori known, contact represents a nonlinear problem even when the continuum behaves as a linear elastic material. Presented approach, based on a Coulomb’s frictional law, elasto-plastic tangential slip decomposition, and consistent linearization, results in quadratic rates of convergence with the Newton-Raphson iteration. Due to the intrinsic similarity between friction and the classical elasto-plasticity, the constitutive model for friction can be constructed following the same formalism as in classical elasto-plasticity. Using penalty method calculation time is less but results are strongly dependent on choice for a value of a penalty factor. The Lagrange multiplier method leads to exact solution but with more iterations and significant extension of a number of degrees of freedom i.e. equations and thus computational efficiency. The both models have been implemented into a version of the computational finite element program PAK.