Nonlinear elasticity equations for nanostructure in doublet mechanics

Doublet mechanics (DM) is one of the higher order gradient continuum theories may be regarded as a special case of the Cosserat theory and then can be derived from three dimensional elasticity theory via variational method. Here, for the first time, nonlinear DM theory is directly obtained from the local equations and boundary conditions of the three dimensional theory explicitly incorporates scale effects. To obtain the fundamental elasticity equations in nonlinear DM, the granular media is considered as an assembly of equal spheres undergoing large elongational, shearing and torsional deformations between the particles. These deformations can be expanded in a convergent Taylor series about the nodal point. Through a variational formulation, the microstress equations of motion are obtained, together with natural boundary conditions and the transition from the microstresses to the macrostresses. To show the accuracy and capability of this method, two example problem are given and the results obtained herein are compared with the available results and good agreement is observed. It is notable that the results generated herein are new and may be served as a benchmark for future works.

کلیدواژه ها:

Doublet mechanics ، nonlinear equation of motion ، variational method