Orientation-dependent mechanical properties of planar microtubule-based bio-nanometamaterials

Abstract

Microtubules are protein-based filaments that carry out essential biological roles of eukaryotic cells. They play, in vivo, critical roles in a wide variety of physical situations such as maintaining cell shape, supporting cellular motions, and playing significant roles in both intracellular transport and cellular division. To perform some of these functions, microtubules may need to form different topologies in various orientations. Therefore, the need to introduce different structures of microtubules arises. Orientation-dependent architected structures are a type of periodic architected materials that can exhibit various mechanical properties in different orientations. In the present study, several periodic architectures of various topologies are investigated numerically, and their mechanical properties (elastic modulus, Poisson’s ratio, and natural frequencies) are analyzed in different spatial orientations. For this purpose, the representative volume elements are constructed by considering unit cells of different models aligned in different spatial angles, and their elastic moduli and Poisson’s ratios are obtained by the finite element method. Then the finite element equation of motion for the given structures are solved to find their six natural frequencies. Besides, Bloch’s theorem is implemented to study wave propagation and compare the bandgap widths of the structures in different orientations. It is found that while the elastic properties of some architected structures may increase as the orientation angle increases from zero, for some others, a reduction in the elastic moduli can be observed as the angle rises. Further, it is seen that some structures may exhibit positive (and high) values of Poisson’s ratio in some angles, while for a different orientation, these values turn out to be negative. Also, the effects of orientation angle on the natural frequencies and stop-band performance are observed to be significant in some topologies and negligible in some others. A better understanding of the behavior of architected structures in different orientations may provide new ways to design and manufacture various structures with enhanced and tunable mechanical properties.