Length-dependent wave propagation and directionality in microtubule-based metamaterials based on the consistent couple stress theory

Abstract

The vital role of microtubule networks in crucial cell processes such as cell division and organization of the cell components have encouraged researchers to investigate their properties to a wider extent. However, it has been shown that mechanical properties of microtubules are length-dependent. Therefore, classical continuum theories are incapable of reaching a comprehensive mechanical model for predicting their behavior and higher-order theories are required. Present manuscript aims to investigate the length-dependent wave propagation in microtubule-based periodic lattices of various topologies. To that aim, the consistent couple stress theory is utilized to take the size-dependency into account. Furthermore, the governing equations of motion for the periodic chains of microtubules are solved adopting the finite element method. Results prove that the length-dependency of the behavior of microtubules can affect the wave propagation and filtering capabilities of microtubule-based metamaterials; therefore, size effects need to be considered in modeling the dynamic properties of microtubule-based chains. Moreover, the results obtained by the consistent couple stress theory is compared to the predictions of the modified couple stress theory as well as the classic continuum theory. It is found that higher stiffness predicted by the consistent couple stress theory can lead to a significant change in the wave propagation characteristics of microtubule-based periodic lattices.