On K-BKZ and other viscoelastic models as continuum generalizations of the classical spring-dashpot models |
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Authors: | A Narain |
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Institution: | (1) Department of Mechanical Engineering and Engineering Mechanics, Michigan Technological University, 49931 Houghton, Mich., USA |
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Abstract: | An alternate constitutive formulation for visco-elastic materials, with particular emphasis on macromolecular viscoelastic fluids, is presented by generalizing Maxwell's idealized separation of elastic and relaxation mechanisms. The notion ofrelative rate of change of elastic stress is identified, abstracted, and formulated with the help of the established theory of finitely elastic isotropic materials. This given a local rate-type constitutive relation for an elastic mechanism in a simple material.For the simplest class of viscoelastic polymer melts, the notion of rate of change of elastic stress and its damped accumulation is identified and formulated. Under conditions of moderate strain rates, this scheme implies the reliable K-BKZ model for a class of polymer melts. An obvious extension generalizes the remaining classical spring-dashpot models.
I
Set of second-order tensors.A I is identified with a 3 × 3 matrix in a Cartesian co-ordinate system
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I
sym
Set of symmetric second order tensors
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Q
Orthogonal tensor, i.e.Q
T=Q
–1.
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Symbol for the value of the functional
H:X I
sym, whereX is the set of piecewise continuous and differentiable strain historiesF
to
: t
0,t] I Other functionals, unless otherwise specified, should be interpreted in a similar manner. |
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Keywords: | Elastic stress instantaneous elasticity configurational relaxation material alignment strain-dependent elasticity modulus K-BKZ model |
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