Three-dimensional non-linear buckling of thick-walled elastic tubes under pressure

Abstract

This paper is concerned with numerical simulations of three-dimensional finite deformation of a thick-walled circular elastic tube subject to internal or external pressure and zero displacement on its ends. We formulate the system of equations that can accommodate large strain and displacement for the incompressible isotropic neo-Hookean material. The fully non-linear governing equations are solved using the C++ based object-oriented finite element library libMesh. A Lagrangian mesh is used to discretize the governing equations, and a weighted residual Galerkin method and Newton iteration solver are used in the numerical scheme. To overcome the sensitivity of the fully non-linear system to small changes in the iterations, the analytical form of the Jacobian matrix is derived, which ensures a fast and better numerical convergence than using a numerically approximated Jacobian matrix.Results are presented for different parameters in terms of wall thickness/radius ratio, and length/radius ratio, as well as internal/external pressure. Validation of the model is achieved by the excellent agreement with the results obtained using the commercial package Abaqus. Comparison is also made with the previous work on axisymmetric version of the same system (Zhu et al., 2008 [34]; Zhu et al. 2010 [43]), and interesting fully three-dimensional post-buckling deformations are highlighted. The success of the current approach paves the way for fluid–structure interaction studies with potential application to collapsible tube flows and modeling of complex physiological systems.