Hysteresis in Approach-Retraction Frictional Contacts with Geometric and Material Nonlinearity

Abstract:

Classical linear contact mechanics, formulated with small strain and displacement assumption, struggles to accurately describe experiments involving rubbers and elastomers. Indeed, under high loads, these materials undergo large deformations and exhibit constitutive behaviors that deviate from a linear relationship between stress and strain. In such cases, it is essential to move beyond linear elasticity to account for nonlinearity caused by large deformations and displacements. Despite efforts to develop numerical tools capable of incorporating these non-linearities in contact problems, our understanding of their impact on contact mechanical responses remains limited. In this study, we investigate the basic case of normal contact between a wavy rigid indenter and a flat, deformable substrate. We examine the influence of geometric non-linearities, arising from large deformations and displacements, alongside material non-linearities, under both frictionless and frictional interfacial conditions. To this end, we developed a finite element model, and we compared its predictions with those of Westergaard’s fully linear theoretical model. The results indicate that even in frictionless contact scenarios, non-linearities produce a mechanical response that differs significantly from predictions based on linear theory. This discrepancy becomes more pronounced as the aspect ratio of the wavy indenter increases, thereby invalidating the small-displacement assumption inherent in linear models. Moreover, the presence of friction, coupled with geometric non-linearities, induces contact hysteresis during loading and unloading cycles a phenomenon often attributed to other interfacial behaviors such as adhesion and plasticity.

• Periodical: Materials Science Forum (Volume 1151)
• Pages: 109-115
• DOI: https://doi.org/10.4028/p-e9rARn
• Online since: June 2025
• Authors: Marco Ceglie, Guido Violano, Luciano Afferrante, Nicola Menga*
• Keywords: Finite Element Method, Friction, Hyperelasticity, Hysteresis, Large Deformations, Nonlinear Contact Mechanics

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