3.2.14 Cylinder under internal pressure

Product: ABAQUS/Standard  

This problem is one of the best-known simple examples of elastic-plastic behavior and has been discussed extensively (see Prager and Hodge, 1951). It consists of a cylinder made of elastic-plastic material, subjected to internal pressure, under plane strain conditions. In this case the example is used as an elementary verification of the finite-strain, elastic-plastic capability in ABAQUS. For this purpose a large change in the cylinder's inner radius (a factor of three) is prescribed. Both axisymmetric and plane strain models are used to verify both of these kinematic formulations.

Problem description

Loading

The cylinder is expanded by applying internal pressure. Following initial yielding, the cylinder reaches a limit state, after which the pressure decreases rapidly as the cylinder expands. This load-displacement behavior is unstable (softening) and, therefore, requires use of the modified Riks algorithm for solution under load control. Another approach, followed here, is to load the cylinder by prescribing the radial displacement at the innermost nodes. The pressure is then computed from the reaction forces conjugate to these prescribed radial displacements. (Snap-through buckling analysis of circular arches, Section 1.2.1 of the ABAQUS Example Problems Manual, and Snap-through of a shallow, cylindrical roof under a point load, Section 1.1.6, among others, illustrate the use of the modified Riks algorithm.)

The cylinder is expanded to three times its initial radius in a small number of increments. This requires very large strain increments and would probably be too large for a more complicated problem that involves shear and rotation as well as direct straining. However, large strain increments are suitable for this simple case.

Results and discussion

Input files

Reference

Figures

Figure 3.2.14–1 Thick cylinder under internal pressure.

Figure 3.2.14–2 Internal pressure versus inside radius, axisymmetric models.

Figure 3.2.14–3 Stress at  1.5 versus inside radius, axisymmetric models.

Figure 3.2.14–4 Internal pressure versus inside radius, plane strain models.

Figure 3.2.14–5 Stress at 1.5 versus inside radius, plane strain models.