Scientific Article

A thermal elasto-plastic friction model for bowed-string simulation

¹ SARC, School of Electronics, Electrical Engineering, and Computer Science, Queen’s University Belfast, Cloreen Park BT5 9HN Belfast, UK
² Department of Music Acoustics (IWK), University of Music and Performing Arts Vienna, Anton von Webern Platz, Vienna 1030, Austria

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 16 February 2026
Accepted: 21 April 2026

Abstract

Over the past five decades, the understanding of the stick-slip behaviour of bowed-string instruments has advanced through a combination of experimental work and physical modelling. A major breakthrough occurred with the discovery of the role that thermal effects play in bow-string friction, and the incorporation of these into models has led to significantly improved simulations. However, the best models to date still struggle to accurately co-predict the steady-state and transient behaviour across the musically relevant bowing parameter ranges. To contribute to addressing this long-standing problem, a new friction force formulation is proposed that incorporates both elasto-plastic pre-sliding and thermal effects, as such bridging two existing modelling approaches. Validation is carried out by comparing measured bridge force signals to those obtained via simulation using a modally-expanded bowed-string model featuring torsional motion and a finite-width bow. The results obtained with a specific steady bow velocity indicate that the friction parameters can be set such that the model accurately predicts the minimum and maximum bowing forces that sustain Helmholtz motion across a range of bow-bridge distances, while several further measures also largely align with the experimental findings.