On skin growth using hyperelastic membrane model

The aim of this paper is to formulate and numerically model the phenomenon of growth in skin under mechanical loading. The main feature and innovation of the current research is that it considers the skin as a membrane that follows the constitutive equations of hyperelastic materials. At first, the kinematics of membranes under large deformations is formulated, and the relevant basic tensors are introduced. Afterward, the formulation of growth mechanics and its special state for membranes are presented. Next, in order to numerically solve the governing equations, a Total Lagrangian nonlinear finite element formulation is developed. Finally, two examples for the growth and large deformation of the skin in the form of a flat membrane with three geometries, square, circular and rectangular, and also in a non-flat state with initial curvature in the form of a cylindrical section under internal pressure are studied. Although the model presented in this work is much simpler than the previous studies, the results obtained here are consistent with the results in the literature. Moreover, the numerical calculations and the amount of memory space required are significantly reduced by the current formulation, so that the number of membrane elements used in the current modeling is less than one and a half percent of the number of three-dimensional elements that have been used in previous researches. Furthermore, the mass ratio resulting from skin growth is also calculated for different cross-sectional areas. The results show that the mass of skin under growth in the considered examples is more than three times the mass of skin before growth.