Wrinkling of Plane Isotropic Biological Membranes

Abstract

The problem of the wrinkling of plane isotropic membranes characterized by a Fung type constitutive model in biaxial tension has been formulated and solved within the framework of finite strain hyperelasticity. The formulation follows the approach of Pipkin [Pipkin, A.C., 1986, IMA J. Appl. Math., 36, pp. 85–99; 1994, ibid., 52, pp. 297–308], and the out of plane geometric nonlinearities are treated as constitutive nonlinearities through a modification of the elastic potential. The wrinkling criteria are based on the natural contraction of a membrane in simple tension. Both the natural contraction and the modified elastic potential are defined in closed form. The model has been implemented in a finite element code and the numerical solution validated using study cases with analytical solution. Applications are presented that simulate the response of stretched membranes, where distinct regions of behavior (taut, wrinkled, and slack or inactive) develop during loading, and a simple procedure of reconstructive surgery, characterized by the excision of a circular portion of the skin and the suture of the wound edges, where the wrinkling of the skin causes the extrusion of the edges (dog-ear formation).