Existence of long‐time solutions to dynamic problems of viscoelasticity with rate‐and‐state friction

• Published in: Zeitschrift für angewandte Mathematik und Mechanik Vol. 99; no. 11
• Main Author: Pipping, Elias
• Format: Journal Article
• Language: English
• Published: Weinheim Wiley Subscription Services, Inc 01.11.2019
• Subjects: 35Q74; 74L10; 74M10; ageing law; Friction; Mathematical analysis; quasivariational evolutionary inequality; rate‐and‐state friction; State variable; surface friction; Viscoelasticity
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201800263

We establish existence of global solutions to a dynamic problem of bilateral contact between a rigid surface and a viscoelastic body, subject to rate‐and‐state friction. The term rate‐and‐state friction describes friction laws where the friction is rate‐dependent and depends on an additional internal state variable defined on the contact surface. Our mathematical conditions rule out certain slip laws, but do cover the ageing law, and thus at least one of the rate‐and‐state friction laws commonly used in the geoscience. We establish existence of global solutions to a dynamic problem of bilateral contact between a rigid surface and a viscoelastic body, subject to rate‐and‐state friction. The term rate‐and‐state friction describes friction laws where the friction is rate‐dependent and depends on an additional internal state variable defined on the contact surface. Our mathematical conditions rule out certain slip laws, but do cover the ageing law, and thus at least one of the rate‐and‐state friction laws commonly used in the geoscience.