Slip instability and state variable friction laws

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Abstract
The dependence of the friction force on slip history is described by an experimentally motivated constitutive law where the friction force is dependent on slip rate and state variables. The state variables are defined macroscopically by evolution equations for their rates of change in terms of their present values and slip rate. Experiments may strongly suggest that one state variable is adequate or prove that one is inadequate. Analysis of steady slip governed by a single state variable in a spring and (massless) slider predict oscillations at a critical spring stiffness k = kcrit. The critical stiffness kcrit is given by a simple formula and steady slip is stable for k > kcrit and unstable for k < kcrit. State variable friction laws may superficially appear as a simple slip rate dependence, slip distance dependence, or time dependent static friction, depending on experiment and testing machinery. Truly complicated motion is possible in a spring‐slider model if more than one state variable is used. Further consequences of state variable friction laws can include creep waves and apparent rate independence for some phenomena.