ISSN:
1089-7550
Source:
AIP Digital Archive
Topics:
Physics
Notes:
The possibility of describing transient phenomena associated with flow and consolidation of solids, such as stress relaxation or physical aging, in terms of a kinetic mechanism comprising spontaneous and induced events is discussed. The starting point is the differential equation dn(overdot)/dt=−an(overdot)[1−(b/a)n(overdot)], with n denoting the number of relaxed entities and n(overdot)=dn/dt (a,b are constants, t is time), yielding an n(overdot)(t) function reminiscent of a Bose–Einstein distribution. The corresponding n(t) relation describes the linear variation of n with log t, and the exponential dependence of n(overdot) on n, as often found experimentally. Replacing n(overdot) in the starting equation by the relative rate n(overdot)/n yields a power-law-type n(overdot)(n) dependence. A further modification, where the induction term n(overdot)/n is not linear but raised to a power (approximately-greater-than)1, finally produces a generalized version of the stretched exponential. When interpreted formally in terms of a spectrum of relaxation times τ, all three equations produce response functions with discrete τ distributions, provided a≠0.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.351998
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