3.1 Hooke Model
71
10
−3 10
−2 10
−1 10
0 10
1 10
2 10
3
10
−2
10
−1
10
0
10
1
10
2
ω
E
E = 10
2
, 10
1
, 10
0
, 10
−1
, 10
−2
E
10
−3 10
−2 10
−1 10
0 10
1 10
2 10
3
10
−2
10
−1
10
0
10
1
10
2
ω
C
E = 10
2
, 10
1
, 10
0
, 10
−1
, 10
−2
C := 1/E
Fig. 3.5 Specific Hooke model: Storage stiffness modulus and amplitude E (ω) ≡ E a (ω) (left)
and storage compliance modulus and amplitude C (ω) ≡ C a (ω) (right) plotted against the angular
frequency ω for five decades of elasticity moduli E
Table 3.2 Algorithmic update for the specific Hooke model
identical to the storage moduli that are displayed in Fig. 3.5. The phase shift angle
between the harmonically oscillating total stress and strain and its tangent are also
denoted the loss angle and the loss factor, respectively. Obviously, the loss factor and
thus the loss angle are identically zero for all angular frequencies.
3.1.2 Specific Hooke Model: Algorithmic Update
The trivial (algorithmic) update for the specific Hooke model is summarized in
Table 3.2.
3.1.3 Specific Hooke Model: Response Analysis
The following elementary strain and stress histories (Zig-Zag, Sine, Ramp) will also
be used throughout for the response analysis of the other material models to be