Journal
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 160, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2022.104781
Keywords
Adhesion and adhesives; Hysteresis; Elastic material; Contact mechanics; Crack propagation and arrest
Funding
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germanys Excellence Strategy [EXC-2193/1 - 390951807]
- European Research Council [StG-757343]
- DFG [INST 39/1099-1 FUGG, INST 39/963-1 FUGG]
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This study focuses on the adhesion hysteresis of soft elastic spheres with low roughness or weak heterogeneity, introducing a crack-perturbation model to describe the indentation process and contact shapes.
The crack-perturbation model accurately predicts contact shapes and hysteresis force-penetration curves, offering a more efficient computational approach compared to traditional methods.
Adhesion hysteresis can be caused by elastic instabilities that are triggered by surface roughness or chemical heterogeneity. However, the role of these instabilities in adhesion hysteresis remains poorly understood because we lack theoretical and numerical models accounting for realistic roughness. Our work focuses on the adhesion of soft elastic spheres with low roughness or weak heterogeneity, where the indentation process can be described as a Griffith-like propagation of a nearly circular external crack. We discuss how to describe the contact of spheres with chemical heterogeneity that leads to fluctuations in the local work of adhesion. We introduce a variational first-order crack-perturbation model and validate our approach using boundary-element simulations. The crack-perturbation model faithfully predicts contact shapes and hysteretic force-penetration curves, provided that the contact perimeter remains close to a circle and the contact area is simply connected. Computationally, the crack-perturbation model is orders of magnitude more efficient than the corresponding boundary element formulation, allowing for realistic heterogeneity fields.
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