Geometric nonlinearity in nanoscale helical coils

The mechanical properties of nanoscale helical structures have become the subjects of great research interest lately. These helical structures include natural helices like the α-helical polypeptide and man-made helices such as nanosprings or nanocoils. Based on a common belief that a nanoscale helical structure would behave like a spring, much attention is devoted to obtaining its spring-constant, or stiffness. For nanocoils, however, whether a single stiffness value exists is questionable. Very often, a nanospring structure experiences a large deformation with respect to its dimension, and its coil radius decreases when it is in tension and increases when in compression. According to the classical equation by Ancker and Goodier, the stiffness of a coil is inversely proportional to the coil radius to the third order. Thus, a single stiffness value does not exist for nanosprings: the stiffness should increase when it is in tension and decrease when in compression. To investigate the mechanical characteristics of nanoscale helical coils undergoing large deformations, nonlinear finite element analysis (both elastic and plastic) modeling was performed. Nanocoils behave linearly with single stiffness values only when their deformation, either extension or shortening, is very small. When the deformation is large, nanocoils will exhibit stiffening behavior in tension and softening behavior in compression. The stiffening and softening behavior of the nanocoils is mainly attributed to the geometric nonlinearity, which is caused by the change in the geometric configuration of the nanocoils. Geometric nonlinearity is elastic in nature, and the deformation in the nanocoils will disappear when the applied load is removed. It differs from material nonlinearity, with which plastic permanent deformation will develop in the nanocoils.