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From:
“Surface wrinkling of mucosa induced by volumetric growth: Theory, simulation and experiment” by Xi-Qiao Feng and Huajian Gao, J. Mech. Phys. Solids, January 2011
ABSTRACT: Mechanics of living tissues focusing on the relationships between growth, morphology and function is not only of theoretical interest but can also be useful for diagnosis of certain diseases. In this paper, we model the surface wrinkling morphology of mucosa, the moist tissue that commonly lines organs and cavities throughout the body, induced by either physiological or pathological volumetric growth. A theoretical framework of finite deformation is adopted to analyze the deformation of a cylindrical cavity covered by mucosal and submucosal layers. It is shown that compressive residual stresses induced by the confined growth of mucosa can destabilize the tissue into various surface wrinkling patterns. A linear stability analysis of the critical condition and characteristic buckling patterns indicates that the wrinkling mode is sensitive to the thicknesses of the mucosal and submucosal layers, as well as the properties of the tissues. The thinner the mucosal layer and the lower its elastic modulus, the shorter the buckling wavelength. A series of finite element simulations are performed to validate the theoretical predictions and to study local wrinkling or non-uniform patterns associated with inhomogeneous growth. Our postbuckling analysis shows that the surface pattern may evolve towards a period-doubling morphology due to continuous growth of mucosa or submucosa beyond the critical state. Finally, the theoretical predictions and numerical simulations are compared to experimental observations.
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