Different computational approaches in the modeling of wrinkling of biological membranes

Abstract

In [1],[2], the authors examined the problem of the wrinkling of plane isotropic biological membranes following the approach of Pipkin [3] and treating the out of plane geometric nonlinearities as constitutive nonlinearities through a modification of the elastic potential. The problem has been solved within the framework of finite strain hyperelasticity for a material characterized by a Fung type constitutive law in biaxial tension. All assumptions of classical Tension Field theory emerge as a result of such formulation. The model formulated in [1,2] is able to identify the distinct regions of behavior that characterize the response of stretched membranes: taut (biaxial tension), wrinkled (uniaxial tension) and slack (inactive). However, the assumption of zero bending stiffness does not allow for detailed predictions of the deformation fields of real membranes where wrinkles with finite magnitude and wavelength develop. This aspect of the problem has been highlighted by Cerda [4] where the limits of the Tension Field Theory [5] in the description of the wrinkling phenomenon have been discussed referring to the problem of a stretched annular membrane.