Numerical Modeling of Force-Stiffness Response of Cross-Linked Actin Networks Using Tensegrity Systems

A three-dimensional tensegrity structure is used as a computational model for cross-linked actin networks. The postbuckling behavior of the members under compression is considered and the constitutive relation of the postbuckling members is modeled as a second-order polynomial. A numerical scheme incorporating the equivalent constitution of the postbuckling members is used to predict the structural response of the tensegrity model under compression loads. The numerical simulation shows that the stiffness of the tensegrity structure nonlinearly increases before member buckling and abruptly decreases to a lower level as soon as members buckle. This result qualitatively mimics the experimentally observed stiffness to compression stress response of cross-linked actin networks. In order to take member length variety into account, a large number of simulations with the length of buckling members varying in the given range are also carried out. It is found that the mean response of the simulations using different buckling member length exhibits more resemblance to the experimental observation.