An axisymmetrical B-spline model for the non-linear free inflation of rubberlike membranes

Erwan Verron (1) , Gilles Marckmann (1)

1 GeM - Institut de Recherche en Génie Civil et Mécanique

A new B-spline interpolation model for the free inflation of axisymmetric rubberlike membranes is presented in this paper. The membrane coordinates are interpolated by cubic B-splines and the treatment of the spline boundary conditions is highlighted. Both circular and cylindrical cases are considered. The formulation of the element is detailed and formulas for the tangent operator are presented. In order to solve the non-linear system of equations, the Newton-Raphson algorithm is sucessfully associated with the arc-length method. Some numerical examples are presented to validate our approach and to exhibit convergence properties of the method.

Domaines: Mécanique des matériaux [physics.class-ph]

Erwan Verron, Gilles Marckmann. An axisymmetrical B-spline model for the non-linear free inflation of rubberlike membranes. Computer Methods in Applied Mechanics and Engineering, 2001, 190 (46-47), pp.6271-6289. ⟨10.1016/S0045-7825(01)00227-4⟩. ⟨hal-01004983⟩