Buckling and postbuckling of concentric cylindrical tubes under external pressure

The problem considered involves a structure composed of two concentric and bonded tubes subjected to external and uniform pressure. Compression tests are conducted using structures formed by a thin-walled internal rubber tube and a thick-walled external foam tube. Experimental results are plotted under the form of a bifurcation diagram representing the inner cross-sectional area of the thin tube as a function of pressure. The buckling pressure P_b and the contact pressure P_co are determined from this non linear diagram. A numerical computation by the Finite Element Method (FEM) is used in order to calculate the Euler buckling pressure P_b and the results are compared with experimental data. It is shown that the buckling pressure and the associated buckling mode n, strongly depend upon the elastic and geometrical parameters of both the tubes. The experimental and numerical investigations are also extended to postbuckling behaviour. The contact between the opposite sides of the inner wall is occured with a buckling mode index n = 2, 3. This contact phenomenon is given rise to the discontinuity of a previous diagram and was characterized by the contact pressure P_co.