Three-dimensional morphological wrinkling of cylindrical soft tissues

Abstract

Investigations of the growth-induced deformations of soft biological tissues may help understand the underlying mechanical mechanisms of their morphogenesis and provide clues for diagnosing some diseases. In the framework of continuum mechanics, we establish a three-dimensional model to analyze the instabilities of cylindrical soft tissues induced by volumetric growth. The different three-dimensional wrinkling patterns under either free or fixed boundary conditions at the outer surface are considered. It is found that Euler buckling, axially symmetrical wrinkling, and checkerboard wrinkling may occur under the traction-free boundary conditions, while axisymmetric pattern and checkerboard pattern often appear under the fixed boundary conditions. Phase diagrams are constructed to predict the morphologies in terms of the geometrical and material parameters of the system. Besides, a pseudo-dynamic numerical method is invoked to simulate the postbuckling evolutions of the wrinkling patterns.