Application of Finite Elastic Theory to the Deformation of Cylindrical Tubes

Abstract

In Part I three types of symmetrical deformations of thin cylindrical rubber tubes are discussed. In the first type a rubber tube is deformed into another circular cylindrical tube of different length and diameter by simultaneous inflation and extension of the tube. This deformation is useful in determining the mechanical properties of tube-like material and it was found that Rivlin-Saunder form of strain-energy fitted a particular latex rubber used in our experiments. The second and third types of deformation are a tube deformed by a longitudinal stretching or an increase in internal pressure to a curved surface of revolution. A number of numerical examples were worked out with a view toward designing experiments to determine mechanical properties of short cylindrical tubes. In Part II experimental studies on the overall mechanical properties of large blood vessels are presented. Two Lagrangian stresses and two extension ratios are used to describe the stress and strain states of the vessels subjected to symmetrical deformations. The interested deformation range is about ten to twenty percent in the neighborhood of the natural state. Tests consisted of (1) a longitudinal stretching while the diameter of the vessels was maintained, (2) a lateral distension with the length of the vessels unchanged, and (3) repeated stretching of the vessels at low frequency. The first two tests show that the stress-strain law of the vessels tested is highly nonlinear and the vessels behave more rigidly in the longitudinal direction than in the lateral direction. The last test shows that the vessels are more likely to behave as a plastic elastic metal and a higher tangential modulus was observed for the vessels stretched at a smaller oscillation amplitude.