Study On Theoretical Models Of One-and Two-dimensional Chiral Materials

Bone,wood,tendrils and other chiral biological materials possess intricated chiral microstructures such as helical microfibers at the subcellular level and even at multiple structural levels.Chiral microstructure can not only control smartly the growth morphologies and color of biological materials,but also determine the physical and mechanical properties and even the biological functions to a large extent.The chiral microstructure imparts the chiral symmetry properties to the material properties,which are mainly manifested by the coupling of physical fields such as mechanics-electricity,light-electricity and the stretch-twist,bend-shear coupling deformations.At present,it is not clear enough and even lack of basic mechanical model to describe the mechanical behaviors of chiral materials.In this paper,one-dimensional and two-dimensional theoretical models of chiral material are established,and then the bending and vibration behaviors of chiral material are investigated.Affected by the material chirality,chiral materials usually has three more degrees of freedom compared to those of normal elastic materials.Based on the noncentrosymmetric micropolar elasticity theory and Hamilton principle,the Timoshenko beam model and plate model of chiral material are established using the variational method.Based on the equations of motion,the static bending and free vibration of chiral beam and plate are studied.The effects of chiral parameters and the length to height ratio on deflection,rotation and natural frequency of the beam and plate under different boundary conditions are investigated.It is found that the material chirality has significant effects on the mechanical behaviors of beam and plate.Based on the elastic rod model of chiral materials,the spatial shape equations of the long and thin biological filaments such as DNA,flagellar filaments and tendrils are derived,and the deformation characteristics of the helical biological filaments are analyzed.The effects of chiral parameters,uniaxial tension and the material radius on the deformation of the chiral rod are investigated.The works of this thesis are helpful to understand and describe the related mechanical behavior of chiral materials and can be used as a basic model to characterize the basic mechanical properties of chiral materials.In addition,it also helps to design and fabricate devices made of chiral material.