Rolling behavior of a micro-cylinder in adhesional contact

Understanding the rolling behavior of a micro-object is essential to establish the techniques of micro-manipulation and micro-assembly by mechanical means. Using a combined theoretical/computational approach, we studied the critical conditions of rolling resistance of an elastic cylindrical micro-object in adhesional contact with a rigid surface. Closed-form dimensionless expressions for the critical rolling moment, the initial rolling contact area, and the initial rolling angle were extracted after a systematic parametric study using finite element method (FEM) simulations. The total energy of this system is defined as the sum of three terms: the elastic energy stored in the deformed micro-cylinder, the interfacial energy within the contact area, and the mechanical potential energy that depends on the external moment applied to the cylindrical micro-object. A careful examination of the energy balance of the system surprisingly revealed that the rolling resistance per unit cylindrical length can be simply expressed by "work of adhesion times cylindrical radius" independent of the Young's modulus. In addition, extending a linear elastic fracture mechanics based approach in the literature, we obtained the exact closed-form asymptotic solutions for the critical conditions for initial rolling; these asymptotic solutions were found in excellent agreement with the full-field FEM results.