General tube law for collapsible thin and thick-wall tubes

Modeling the complex deformations of cylindrical tubes under external pressure is of interest in engineering and physiological applications. The highly non-linear post-buckling behavior of cross-section of the tube during collapse attracted researchers for years. Major efforts were concentrated on studying the behavior of thin-wall tubes. Unfortunately, the knowledge on post-buckling of thick-wall tubes is still incomplete, although many experimental and several theoretical studies have been performed. In this study we systematically studied the effect of the wall thickness on post-buckling behavior of the tube. For this purpose, we utilized a computational model for evaluation of the real geometry of the deformed cross-sectional area due to negative transmural (internal minus external) pressure. We also developed an experimental method to validate the computational results. Based on the computed cross-sections of tubes with different wall thicknesses, we developed a general tube law that accounts for thin or thick wall tubes and fits the numerical data of computed cross-sectional areas versus transmural pressures.