Mechanical Model And Analysis Of Quasi One-dimensional And Two-dimensional Chiral Materials

Different with general engineering materials, chiral materials havenoncentrosymmetrical properties, such as the extension-torsion couplingand some special optical, electrical, thermal and mechanical properties,so that this material has a good application prospect. Chirality and chiralphenomenons attract more and more attention of many fields in recentyears. Study on the mechanical properties and behaviors of chiralmaterials is significant to the theoretical researches and practicalapplications for understanding the growth and assembly of chiralmaterials, the creation of chiral nano devices, and the design andbiomimetic of multi-level chiral materials. This paper focuses on themechanical model of quasi one-dimensional and two-dimensional chiralmaterials.A generalized Cosserat chiral rod model is constructed by utilizingthe nonlinear constitutive relationships of chiral rods within theframework of generalized Cosserat theory of rods. The three-dimensionalcomplicate calculation can be avoided by appling the chiral rod model asthe equivalent one-dimensional model of helical structures. Theparameters of the chiral rod model can be determined through the resultsof springs’ tension tests, and the model can be used to describe elasticbehaviors of helical inclusions.Based on the constructed chiral rod model, the stability of chiral rodis analyzed. The work studies the stability problems of chiral rod loadedwith axial compression and torsion, and gives the instability critical loadand strains after instability. The work also analyzes the influences of thechiral level and cross-section radius on the instability critical load. Theresults shows that, under the axial tension and torsion, theextension-torsion coupling and the shear-flexure coupling have an important influence on the stability of chiral rods and make the instabilitycritical load increase or decrease. The smaller the radius of chiral rod is,the more likely to be instability chiral rod is, and the smaller the criticalload is.As for two-dimensional chiral materials, the work introduces themetric used in the incompatible covariant elasticity into the straingradient elasticity, and constructs a chiral plate model of two-dimensionalmetric strain gradient elasticity. Then the chiral plate model is used toanalyze the tension behaviors of chiral thin plate.The models in this paper can effectively describe the mechanicalbehaviors of quasi one-dimensional and two-dimensional chiral materials,and contribute to the characterization of mechanical properties of suchmaterials.