Torsion Instability of Anisotropic Cylindrical Tissues with Growth

Growth shapes soft tissues not only through mass addition or volume expansion but also through deformation instabilities and consequent morphological evolution. In this paper, we probe the torsion instability of an anisotropically growing tube with fiber reinforcement, which mimics many tubular organs in animals or plants. We derive the Stroh formulation for the incremental boundary value problem and numerically solve it using the surface impedance method. A linear stability analysis is conducted to investigate the critical condition for the onset of wrinkling. The thresholds of helical wrinkling are calculated in terms of growth ratio and external load. The effect of fibers on the critical state under axial stretching is examined. It is found that the tangential growth tends to enhance the critical torsion angle but has a weak influence on the critical longitudinal mode of wrinkling, which, however, can be remarkably affected by the axial growth. Our study can help understand the formation of helical morphologies in biological materials and provide cues for engineering desired structures or devices.