Energy Criterion for Attachment and Detachment in Viscoelastic Adhesive Contacts

Adhesion plays a crucial role across a wide range of natural systems and technological applications. High adhesion is typically observed in contacts involving highly deformable materials, which are generally viscoelastic in nature. Although some of the key concepts explored in this work—such as the application of energy-based criteria to viscoelastic adhesive contacts—have been addressed in earlier studies, including the seminal work by Greenwood and Johnson, these approaches relied on considerably more complex analytical methods. In this paper, we build on those foundational insights and present a significantly simplified and more accessible formulation by employing the Method of Dimensionality Reduction (MDR). We propose that the processes of adhesive crack propagation and viscoelastic material relaxation occur on well-separated timescales, which allows the use of a Griffith-like energy balance criterion even in viscoelastic systems. This MDR-based energetic approach not only provides conceptual clarity but also enables the straightforward analytical treatment of a wide range of practical problems, including arbitrary loading scenarios. The theory naturally explains the different effective works of adhesion during attachment and detachment and offers a unified, first-principles framework for analyzing and designing soft adhesive systems.

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