PSI - Issue 28

Victor Rizov et al. / Procedia Structural Integrity 28 (2020) 1212–1225 Author name / Structural Integrity Procedia 00 (2019) 000–000

1215

4

4 R p R

0 C G G e 

,

(3)

where

4 0 R R   .

(4)

In (3), C G is the value of the shear modulus in the centre of the beam cross-section, p is a parameter that controls the material inhomogeneity in radial direction. The value of the shear modulus in the centre of the beam cross-section varies exponentially along the beam length

l q x

C D G G e  ,

(5)

where

x l   0 .

(6)

C G in the free end of the beam, q is a parameter that controls the material

D G is the value of

In (5),

inhomogeneity in the length direction of the beam.

Fig. 2. Linear viscoelastic models.

In the present paper, the time-dependent behaviour due to the stress relaxation is analyzed by using two linear viscoelastic models under a constant applied shear strain,  .