F-bar projection method for finite deformation elasticity and plasticity using NURBS based isogeometric analysis

This paper presents projection methods to treat the incompressibility constraint in large deformation elasticity and plasticity within the framework of Isogeometric Analysis. The continuity property of higher-order Non-Uniform Rational B-Splines (NURBS) is explored in nearly incompressible applications and shown to produce accurate and robust results. A new nonlinear \(\mathop F\limits^ - \) projection method, based on a modified minimum potential energy principle and inspired by the \(\mathop B\limits^ - \) 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.