If we stepwise increase the stresses, as demonstrated in Fig.6.9, the strain can be
estimated from a linear summation of the individual responses to the stresses,
eðtÞ¼s 1 Jðtt 0 Þþs 2 Jðtt 1 Þþs 3 Jðtt 2 Þþ:::::: (6.14)This behavior follows the so-called Boltzmann superposition principle
(Boltzmann 1874 ).
The ideal elasticity can be modeled as a Hookean spring, as demonstrated in
Fig.6.10,
s¼Ee (6.15)While the ideal viscous behavior can be modeled as a Newtonian dashpot, as
also demonstrated in Fig.6.10,
s¼
de
dt(6.16)
Fig. 6.9 Illustration of Boltzmann superposition principle for the strain response linearly
integrated with the stepwise increase of stresses
Fig. 6.10 Illustration of a series connection of the Maxwell model and the Kelvin model for the
four-element model to describe the viscoelastic creep behaviors of polymers
6.2 Relaxation of Polymer Deformation 101