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\(\overline {\text B}\) and \(\overline {\text F}\) projection methods for nearly incompressible linear and nonlinear elasticity and plasticity using higher-order NURBS elements. (English) Zbl 1194.74518
Summary: 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 \(\overline {\text B}\) 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 non-linear \(\overline {\text F}\) projection method, based on a modified minimum potential energy principle and inspired by the \(\overline {\text B}\) method is proposed for the large-deformation case. It leads to a symmetric formulation for which the consistent linearized operator for fully non-linear 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.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74B20 Nonlinear elasticity
74B05 Classical linear elasticity
Software:
HYPLAS; LS-DYNA
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