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Existence of long‐time solutions to dynamic problems of viscoelasticity with rate‐and‐state friction
Author(s) -
Pipping Elias
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800263
Subject(s) - viscoelasticity , slip (aerodynamics) , cover (algebra) , state (computer science) , state variable , mechanics , law , mathematics , materials science , classical mechanics , thermodynamics , engineering , physics , mechanical engineering , composite material , algorithm , political science
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.