Effect of initial imperfections of struts on the mechanical behavior of tensegrity structures

Tensegrity has been widely accepted as a conceptual model for cell mechanics. Tensegrity models developed to study cell mechanical behavior have never considered the initial imperfection of the struts. However, the curved shapes of microtubules in living cells and the nonlinear cell mechanical behavior lend support to the necessity of introducing initial imperfections to cell tensegrity. Here we use a simple three-member tensegrity structure to investigate the mechanical behavior of tensegrity structures with initial imperfections. Our analytical results demonstrated that the stiffness of the tensegrity structure will be reduced significantly with even small initial imperfections. Further, a strong nonlinearity arises with increased initial imperfection both in terms of the maximum deformation of the strut as well as the stiffness behavior of the tensegrity. Finite element simulations of tensegrity structures with 2 struts and 3 struts show great consistency with the analytical solution. The initial imperfection method provides an intuitive way to introduce nonlinearity to cellular mechanical behavior. It has major implications in understanding load bearing capacity and force distribution in cytoskeleton.