B-bar and F-bar projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements

Thomas Elguedj (1, 2) , Yuri Bazilevs (3) , Victor M. Calo (3) , Thomas J.R. Hughes (3)

1 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
2 MIMESIS - Mécanique Multiéchelle pour les solides
3 ICES - Institute for Computational Engineering and Sciences [Austin]

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-bar 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-bar projection method, based on a modified minimum potential energy principle and inspired by the B-bar 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.

Mots clés: Isogeometric analysis; NURBS; Volumetric locking; F-bar method; B-bar method; Incompressibility; Non-linear elasticity; Plasticity

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Thomas Elguedj, Yuri Bazilevs, Victor M. Calo, Thomas J.R. Hughes. B-bar and F-bar projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements. Computer Methods in Applied Mechanics and Engineering, 2008, 197 (33-40), pp.2732-2762. ⟨10.1016/j.cma.2008.01.012⟩. ⟨hal-00457010⟩