Redistribution of stress due to a circular hole in a nonlinear anisotropic membrane

Many clinical procedures introduce holes into thin tissues that are typically under multiaxial stresses and finite strains. Such incisions change the stresses and strains from their homeostatic values, which may induce cells to alter their orientation and cytoskeletal organization as well as to migrate, proliferate, change their synthesis of matrix, or even to enter the cell death cycle. To correlate such changes in cellular activity with changes in the mechanics, we need solutions for the native and the perturbed boundary value problems. Such problems will often be complex and require a finite element solution; weak solutions should be evaluated independently, however, at least for special cases. Herein, we present a numerical solution of the governing nonlinear ordinary differential equation for the special case of stress redistribution due to the introduction of a circular hole into a finitely deformed, Fung-type, circular membrane that exhibits a cylindrical orthotropy. Among other results, we show that the anisotropy plays an increasingly greater role as the size of the hole becomes smaller, which is of course a goal of minimally invasive procedures.