Continuum Modeling Of Adhesive Interaction Based On Interatomic Potentials
Adhesion between solid bodies plays a prominent role in a wide variety of situations ranging from tribological applications to dust coagulation initiating the formation of planets. It can be due to various reasons like capillary, electrostatic, van der Waals, and hydrophobic forces. Among these, adhesion due to van der Waals force| which has its origin in permanent or instantaneous electric dipoles present in all atoms and molecules|is of special significance as it is present in all cases. Computational studies on adhesion due to van der Waals force commonly assume it as a surface force due to its short effective range, which is about a few tens of nanometers, in comparison to the length-scales commonly encountered. However, such restrictions are often violated in various important problems. For example, the characteristic dimensions of asperities| which are the smallest roughness elements interacting to cause friction and wear| are usually of nanometer length-scale. In addition, the assumptions inherent in development of surface force model are exact only when the deformations are small. In all such situations, the van der Waals force must be assumed as distributed over the volume. In this work, a computational model is developed by incorporating van der Waals force and short-range repulsion (steric repulsion or Pauli repulsion) as body forces distributed over the volume in a large deformation, static/transient, finite element framework. First the development of the general formulation is discussed, and then it is specialized for various considerations like handling symmetry and interaction between an elastic body and a rigid half-space, which offer significant computational advantages over the general formulation. The applicability of the model is illustrated by using a number of benchmark and practical problems. The comparison of the analysis results and well-established analytical models are provided, which validates our method. As a specific example, the smooth change of interaction force from a thin-rod model to a at-plate model on increasing the cross-sectional areas of two interacting elastic rods is demonstrated. The impact of elastic bodies in presence adhesion, and the associated energy loss is an important concern in studies regarding the origin of friction. Therefore, adhesive impact of elastic rods and spheres is studied using our formulation. Emphasis of the study is on finding the apparent energy loss during impact, which represents the part of energy lost to elastic stress waves remaining in the body after the impact, and hence not available for rebound motion. In case of impact of elastic rods on a rigid half-space, it is shown that the apparent energy loss is a unique function of the tensile strain energy developed in the rod due to van der Waals attraction. A one-dimensional model is developed for this case to determine the energy loss based on the specified problem parameters, which can be used to predict practically relevant phenomena like capture. In case of impact of elastic spheres, which is often correlated with asperity interactions, the energy loss is found to be significant only if adhesion-induced instabilities occur. The behavior shown by rods and spheres are probably at the two extremes with regards to energy loss during impact of elastic bodies in presence of adhesion. Practical use of the formulation is demonstrated by applying it to the study of amplitude variation and phase shifts in tapping-mode atomic force microscopy. Specifically, the advantage of operating the AFM cantilever just below its natural frequency as compared to operating it just above the natural frequency is demonstrated. Bistable behavior, which is the coexistence of two stable vibration modes under exactly same operating conditions, is shown to be severe when the driving frequency is higher than the natural frequency of AFM cantilever even in the absence of adhesion, which can result in spurious contrast-reversal artifacts during imaging. The hysteresis loop associated with the bistable behavior may lead to erroneous conclusions regarding presence of adhesion. Since this model overcomes the limitations of lumped parameter models and the computational models based on surface force approximation, the results can be used for much more realistic interpretation of experimental data. Computational framework developed in this study achieves the capability for analysis of adhesive contact problems directly from van der Waals interaction and steric repulsion. Such a model can be used for revisiting the fundamental problems in contact mechanics, as well as for providing better insights into experimental observations.
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