On viscoelastic deformation of growing skin in reconstructive surgery

Skin is a living organ which can grow in a specific situation. In some cases, a defect like a wound or congenital nevus can bother the patients. Accordingly, the defect needs to be repaired with adjacent skin, and the growth phenomenon will be necessary in these conditions. Some studies have been done to model the growth of skin; however, none of them considered the viscoelastic property which is an inherent characteristic of the skin. Therefore, the main goal of this paper is to develop a nonlinear viscoelastic formulation for growing skin. The formulation is derived in such a way that the pure growth phenomenon can be recovered when the effect of viscoelasticity is ignored. Moreover, to deal with highly nonlinear formulation, a nonlinear finite element formulation in Total Lagrangian framework is developed. Furthermore, implicit trapezoidal time integration method is employed for evolution equations obtained from viscoelastic and growth contributions. Finally, some examples are provided to investigate the performance of the developed formulation and the good results compared to those available in the literature are obtained.