Abstract
A numerical method for axisymmetric adhesive contact of elastic bodies is proposed. It allows computing the size of the contact spot, the force of interaction as well as the contact pressure distribution unrestricted to any particular form of the initial gap between the bodies. Therefore, compared to the existing analytical theories, it is a more versatile research tool that can be used to study such phenomena as adhesive strength of conjugate bodies and stability loss induced energy dissipation in oscillating contact. A variational principle that can be used to construct an approximate solution is proposed. The derived nonlinear equations of the discretized mini-max problem determine the unknown radius of the circular contact spot and the nodal values of the thought-for contact pressure. Unlike other numerical methods where contact domain is updated by subtracting or adding separate boundary elements of finite size, the proposed approach enables gradual continuous variation of the contact area. The arc-length method was implemented in the numerical routine in order to solve for the unstable sections of the adhesive interaction process. Besides the distance and force variables, the increment of the contact area is included in the control for the sake of convergence. The numerical error of the approximate method with respect to the known analytical solutions is evaluated. Linear convergence with mesh refinement in computed force and contact area is observed. Extension of the proposed approach for arbitrary three-dimensional shape of the contacting bodies is planned for the future. This is required to study the impact of the random surface roughness on their adhesive properties.
Highlights
The phenomenon of adhesion occurs due to the action of molecular forces when the surfaces of solids come close within their range
The most fundamental approach consists in representing the microscopic structure of the bodies and modeling both the elastic behavior and contact interaction by means of molecular mechanics [4]
It is proposed to develop it based on the existing boundary element methods, using in particular generalized minimum principle for adhesive contact and its formulations proposed in [15]
Summary
The phenomenon of adhesion occurs due to the action of molecular forces when the surfaces of solids come close within their range. Similar analytical solutions are possible for cases with different geometries such as the contact of a paraboloid with an axisymmetric wavy surface [2]. Another well-known approach suggested by Derjaguin, Muller and Toporov [3] assumes the occurrence of attraction in a vicinity just beyond the contact area where the separation between bodies remains within a certain threshold. The advantage of this model is that it accounts explicitly for the finite range of molecular forces. Numerical methods of analysis are required to predict adhesive behavior in case of arbitrary geometry or more sophisticated physical models of surface interaction
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