1.2 Compositions of Rheological Models
11
σ
σ
σ
σ
σ
σ
1
2
Fig. 1.9 Serial-parallel arrangements of ERMs. These are denoted the slider-[spring+dashpot],
the slider-[dashpot+slider], and the slider-[slider+spring] model, respectively
primary ERM and the stress σ 2 of the serial-CRM (the stresses in the two serial
secondary ERM coincide σ 2.1 = σ 2.2 ), whereas the strain of the resulting parallelserial-CRM coincides with the strain 1 in the primary ERM and the resulting strain
2 in the serial-CRM (the summation of the strains 2.1 and 2.2 in the two serial
secondary ERMs)
σ = σ 1 + σ 2 and = 1 = 2
with
2 = 2.1 + 2.2 and σ 2 = σ 2.1 = σ 2.2 .
(1.9)
Possible parallel-serial combined arrangements of the three ERMs from Fig. 1.1 are
showcased in Figs. 1.11, 1.12, and 1.13. Out of these, the catalogue contains an
account on the Generalized Maxwell SLS model.
For a parallel arrangement of a primary ERM, say ERM 1 , with a serial-CRM,
say CRM 2 , that consists of three serial secondary ERMs, say ERM 2.1 to ERM 2.3 , the
stress σ of the resulting parallel-serial-CRM is a summation of the stress σ 1 of the
primary ERM and the stress σ 2 of the serial-CRM (the stresses in the three serial