Abstract
When an elastomer approaches or retracts from an adhesive indenter, the elastomer’s surface can suddenly become unstable and reshape itself quasi-discontinuously, e.g., when small-scale asperities jump into or snap out of contact. Such dynamics lead to a hysteresis between approach and retraction. In this study, we quantify numerically and analytically the ensuing unavoidable energy loss for rigid indenters with flat, Hertzian and randomly rough profiles. The range of adhesion turns out to be central, in particular during the rarely modeled approach to contact. For example, negligible traction on approach but quite noticeable adhesion for nominal plane contacts hinges on the use of short-range adhesion. Central attention is paid to the design of cohesive-zone models for the efficient simulation of dynamical processes. Our study includes a Griffith’s type analysis for the energy lost during fracture and regeneration of a flat interface. It reveals that the leading-order corrections of the energy loss are due to the finite-range adhesion scale at best, with the third root of the linear mesh size, while leading-order errors in the pull-off force disappear linearly.
Highlights
As we find in preliminary simulations of adhesive, randomly rough surfaces, these cohesive zone models (CZMs) can be similar to the Morse potential, as they can be well described by a difference between two exponentially decaying functions
The three main aims of this paper were (i) to provide a comprehensible theoretical framework describing the formation and failure of an adhesive, periodically repeated interface under constant normal stress and the subsequent energy hysteresis, (ii) to deduce generally applicable rules for the construction of cohesive zone models from the theoretical framework, and (iii) to apply the schemes obtained for the contact between two ideally flat surfaces to uneven surfaces
A particular focus of our work was the much overlooked approach to contact and the question at what separation an initially flat elastomer approaching a substrate with short but finite-range adhesion becomes unstable to the formation of surface undulations
Summary
A popular method to avoid singularities and to reduce the stiffness of adhesive contact problem is to use so-called cohesive zone models (CZMs) [4,5,6] They describe, usually in analytical form, how the traction depends on the local separation between two surfaces. We propose a rule for how to select the mesh size for a given CZM, and more importantly, we provide a recipe for how to redesign it such that it provides accurate force-displacement dependencies if the mesh size cannot be made arbitrarily small Towards this end, we focus on the case of a smooth flat elastomer in contact with a rigid, flat, smooth indenter with adhesive interaction as the most basic model.
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