Building arrangement by Maxwell model
Schematic comparison of mechanical models by lever scales with dissimilar
type integrals for relaxation modulus G(t) as a function of relaxation time λ or time t.
The strongest element g1 or widest load w1 relates the longest and most effective chains.
(a) Maxwell model of spring-dashpot arrangements for weight loads illustrating G(t).
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Maxwell model is normally described by a spring and dashpot arrangement.
Generalized Maxwell model is illustrated by parallel arrangement of spring-dashpot elements and a
stress force of relaxation modulus. We can illustrate the same by a lever scale, were on the left
side are those spring-dashpot elements and respectively on the right side are relaxation moduli
elements presented by loads in the wireframe. The loads on the bar are named as a function of time t
i
and respectively elements by relaxation time λ
i steps.
As the lever is all the time in balance, we can neglect the distance to the turning point of the
bar and model is linear in mathematical sense.
Nonlinear correction.
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In the case we add infinity amount of these spring-dashpot elements, we still cannot model the nonlinear
behaviour of polymers. One solution could be additional some kind integrated circuit component (chip)
illustrating correction function f
i(t). In the arrangement is still needed some information for complicated
non-linear corrections. This is an impossible task mechanically and even mathematically to get general procedure.