Friction constitutive law with rate and state dependences
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A general formula for the Dieterich-Ruina friction constitutive law with rate and state (n-state variables,n=1, 2,...) dependences has been obtained and discussed under the assumption that the slip acceleration a varies ion a linearly with the slip displacement δ, namelya = a0 + α(δ-δ0). Wherea0, δ0 are initial constants, α is the acceleration rate and constant.a0 and α may be arbitrary constants (positive, negative or zero).
The extreme value of frictional resistance and the existence condition of the extreme value, which are very important and govern to some degree the motion process of a frictionally slipping mechanical system, have been analyzed. A critical value λc which is the measure of the velocity weakening and velocity strengthening of the mechanical system, and its properties and the relationship to the extreme problem have been studied. Again, according to the critical value λc, the concepts of light or strong velocity weakening (or strengthening) are introduced.
A possibly new phenomenon that frictional resistance may vary in some kind of decayed oscillation is found. Finally, the condition for the smallest frictional resistance for a slipping mechanical system with nonuniform acceleration has been obtained.
Key wordsFiction constitutive law accelerating slip
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