166
4 Visco-Elasticity
σ
σ
e m
v m
E m 1
η m 1
E m m
η m m
E m M
η m M
Fig. 4.47 Specific Generalized-Maxwell model
and (ii) a viscous dashpot (see the sketc.h of the specific Generalized-Maxwell model
in Fig. 4.47).
The basic kinematic assumption of the mth Maxwell element is the additive
decomposition of the total strain into the elastic strain e m (representing the elongation of the mth elastic spring) and the viscous strain v m (representing the elongation
of the mth viscous dashpot), i.e.
= e m + v m for m = 1, . . . , M.
(4.186)
Note that the set of viscous strains { v 1 , . . . , v m , . . . , v M } denote the M elements contained in the set of internal variables α = { v 1 , . . . , v m , . . . , v M } for the
Generalized-Maxwell model.
4.5.1 Standard-Linear-Solid Maxwell Model: Formulation
The specific Generalized-Maxwell model, displayed in Fig. 4.47, consists of a parallel
arrangement of M specific Maxwell elements each (m = 1, . . . , M) consisting of a
serial arrangement of (i) a linear elastic spring with stiffness E m m and (ii) a linear
viscous dashpot with viscosity η m m .