On the Analytical Solution and Mechanism for the Cusp Formation in a Nonlinear Elastic Cylinder or Tube subject to Compression

Project: Research

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Stabilities and instabilities are important topics in finite elasticity and structures. In this project, the cusp instability shall be studied. Such an instability was also found in the experiments on a sufficiently short thick-walled elastic tube subject to compression, which is known as the Willis instability phenomenon. Once a cusp is formed, there is a high concentration of energy around it and the material could be damaged. Unfortunately, no analytical study has been made on this kind of instability. Actually, even when the post-buckling state has a smooth profile, it is difficult to get the analytical solution. Here, a novel approach shall be developed involving compound series-asymptotic expansions to deduce the analytical solution for the cusp profile in an elastic cylinder under compression and to reveal the physical mechanism of its formation. The results are expected to be extended to the study of an elastic tube, and then satisfactory mathematical and physical explanations can be offered to the Willis instability phenomenon.


Project number9041102
Grant typeGRF
Effective start/end date1/10/064/06/10