Cosserat Elasticity of Helically Wound Cylinders

• Published in: Journal of elasticity Vol. 155; no. 1-5; pp. 205 - 220
• Main Authors: McAvoy, R. C., Steigmann, D. J.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.07.2024; Springer Nature B.V
• Subjects: Biomechanics; Classical and Continuum Physics; Classical Mechanics; Continuous fiber composites; Deformation analysis; Deformation effects; Elastic deformation; Elasticity; Engineering; Helices; Kinematics; Materials Science; Mathematical Applications in the Physical Sciences; Theoretical and Applied Mechanics; Cosserat elasticity; 74A60; Fiber-reinforced solids; 74A05; Helically wound cylinder; 74B20; 74A30
• ISSN: 0374-3535; 1573-2681
• DOI: 10.1007/s10659-022-09934-z

We present a model of the equilibrium response of a pressurized circular cylindrical elastic tube, reinforced by two families of continuously distributed spatial rods arranged as right- and left-handed helices. The framework underlying our analysis is a modified version of Cosserat elasticity in which the basic kinematic descriptors are a single deformation field and two rotation fields, one for each fiber family, subject to the constraint that the fibers convect with the deformation as material curves. The effect of the intrinsic and torsional stiffnesses of the fibers on the overall force-extension response of the cylinder is quantified.