New Mathematical Framework Unifies Sliding and Rolling Friction in Viscoelastic Materials
Researchers have derived a class of viscoelasto-kinematic equations that model both sliding and rolling friction in viscoelastic bodies using a system of partial differential equations. The framework combines linear viscoelastic rheologies with nonlinear dynamic friction models, treating bristle-like interface elements as the fundamental unit of analysis. The work suggests that sliding and rolling contact—traditionally studied separately—share closely related underlying dynamics, potentially simplifying future modeling efforts.
A preprint submitted to arXiv by Dr. Luigi Romano presents a unified theoretical framework for modeling frictional contact between viscoelastic bodies under both sliding and rolling conditions. The approach couples linear viscoelastic material descriptions with established nonlinear dynamic friction models, yielding a system of partial differential equations (PDEs) that govern frictional force evolution, bristle deformations, and internal state variables at the contact interface. A key mathematical result is that linear viscoelasticity preserves the hyperbolic character of the PDE systems already known from rolling contact theory, providing a rigorous structural foundation for the model. Representative examples of both sliding and rolling contact are analyzed, revealing that the two regimes—often treated as fundamentally distinct phenomena—can exhibit closely related dynamics within this formulation. The framework is intended to be broadly applicable across a wide class of viscoelastic frictional systems, with potential relevance to tire mechanics, soft robotics, biomechanics, and other engineering domains. The paper spans 33 pages with 8 figures and has been submitted for peer-reviewed journal publication.
What's missing
As a preprint, this work has not yet undergone peer review, so the validity of the mathematical derivations and the physical assumptions (e.g., the bristle-element idealization, linearity of viscoelastic rheology) remain to be independently assessed. The paper does not appear to include experimental validation of the proposed models against empirical friction data, leaving open the question of quantitative accuracy in real-world applications. The range of viscoelastic materials and contact geometries for which the framework remains tractable is also not fully characterized.
What different sources said
- arXiv physicsCenter
Dynamic sliding and rolling friction models for linear viscoelastic contact pairs
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