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Within the context of finite deformation elasticity theory the problem ofdeforming an open sector of a thick-walled circular cylindrical tube into acomplete circular cylindrical tube is analyzed. The analysis provides a meansof estimating the radial and circumferential residual stress present in anintact tube, which is a problem of particular concern in dealing with themechanical response of arteries. The initial sector is assumed to be unstressedand the stress distribution resulting from the closure of the sector is thencalculated in the absence of loads on the cylindrical surfaces. Conditions onthe form of the elastic strain-energy function required for existence anduniqueness of the deformed configuration are then examined. Finally, stabilityof the resulting finite deformation is analyzed using the theory of incrementaldeformations superimposed on the finite deformation, implemented in terms ofthe Stroh formulation. The main results are that convexity of the strain energyas a function of a certain deformation variable ensures existence anduniqueness of the residually-stressed intact tube, and that bifurcation canoccur in the closing of thick, widely opened sectors, depending on the valuesof geometrical and physical parameters. The results are illustrated forparticular choices of these parameters, based on data available in thebiomechanics literature.

On deforming a sector of a circular cylindrical tube into an intact tube: existence, uniqueness, and stability