Non-classic multi scale analysis of 2D-manipulation with AFM based on modified couple stress theory

• We developed the multi scale method based on the modified couple stress theory.
• Size effect is investigated for dynamic behavior of manipulation by AFM.
• Results indicated that the classic model predicts greater deflection of tip.
• Separation time span anticipated by non-classic is shorter than classic model.

This paper develops a multi scale method based on the equations of non-classic continuum mechanics. For this purpose, a new synthesis is developed based on modified couple stress theory for the size effect improvement in dynamic behavior of nano-manipulation with an Atomic Force Microscope (AFM). Considering the Euler–Bernoulli beam model for the cantilever and the tip of AFM, the governing dynamic equations of Macro Field (MF) are obtained. Subsequently, the multi-scale algorithm is utilized to combine the equations of MF with the equations of Nano Field (NF)-governed by molecular dynamics. The Generalized Differential Quadrature (GDQ) method as a semi-analytical procedure is used to solve governing equations of the MF. The numerical results revealed that there is a remarkable difference between classic and non-classic models to predict the travelled distance of nano-particle in the manipulation process. The RMS diagrams illustrate that the classic model predict greater deformation for the AFM tip. In contrast, the deformation of the particle is greater in non-classic model. In addition, due to the increase in the stiffness of the structure in non-classic model, the separation time span anticipated by non-classic model is shorter than one in the classic model.

An AFM structure is composed of cantilever with micro dimension which is used to manipulate a particle in nano dimension. The size effect is one of the most important factors in micro- and nano-scale modeling. This paper has aimed the investigation of manipulation behavior of AFM with focusing on the multi-scale method a combination of large-scale equations with MD equations based on modified couple stress theory.Figure optionsDownload as PowerPoint slide