B and F Projection Methods for Nearly Incompressible Linear and Nonlinear Elasticity ... · 2011....
61
¯ B and ¯ F Projection Methods for Nearly Incompressible Linear and Nonlinear Elasticity and Plasticity using Higher-order NURBS Elements T. Elguedj 1 ,Y. Bazilevs 1 ,V.M. Calo 1 ,T.J.R. Hughes 2 Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th street, 1 University Station C0200, Austin, TX 78712-0027, USA Abstract This paper presents projection methods to treat the incompressibility constraint in small and large deformation elasticity and plasticity within the framework of Isogeometric Analysis. After reviewing some fundamentals of isogeometric analysis, we investigate the use of higher-order Non-Uniform Rational B-Splines (NURBS) within the ¯ B projection method. The higher-continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results. A new nonlinear ¯ F projection method, based on a modified minimum potential energy principle and inspired by the ¯ B method is proposed for the large-deformation case. It leads to a symmetric formulation for which the consistent linearized operator for fully nonlinear elasticity is derived and used in a Newton-Raphson iterative procedure. The performance of the methods is assessed on several numerical examples, and results obtained are shown to compare favorably with other published techniques. Key words: Isogeometric Analysis; NURBS; Volumetric locking; Nonlinear Elasticity; Plasticity; Incompressibility; B-bar method; F-bar method. 1 Postdoctoral Fellow 2 Professor of Aerospace Engineering and Engineering Mechanics, Computational and Applied Mathematics Chair III Preprint submitted to Comput. Methods Appl. Mech. Engrg 28 August 2007
