PSI - Issue 42

Jaynandan Kumar et al. / Procedia Structural Integrity 42 (2022) 806–812 Jaynandan Kumar, Anshul Faye / Structural Integrity Procedia 00 (2019) 000–000

809

4

Here, R d is the residual vector associated with the damage. N i is the shape function of i th node in the element. H is the local source term for crack growth. d e is the damage in the element which is calculated at the gauss point.

φφ, e =

K i j

( B T i DB j + ∇ T

i τ

j )d V

(12)

x N

e ∇ x N

B h e

dd , e =

K i j

[ N i (1 + H

j + ∇ T N i l 2

j ]d V

e ) N

(13)

e ∇N

B h e

Where, K φφ and K dd are the sti ff ness matrix associated with the deformation and damage respectively. The symbol e in the equations represent the local element.

2.4. Identification of Material parameters

Material parameters of the constitutive model are obtained by calibrating the model against the bi-axial experimen tal data are given in the Di Achille et al (2011) in a least-square sense. All stress-strain curves under di ff erent biaxial conditions, in both circumferential and longitudinal directions, are considered simultaneously for fitting purpose. Fit ted curves are shown with a solid line in Fig.1. Representative material parameters thus obtained are given in table-1. The phase-field parameters, g iso c and g ani c , are obtained by matching the strength values in longitudinal and circum ferential direction, which is available from literature as 1019 ± 160 kPa and 864 ± 102 kPa, respectively (Raghavan, 1996). Fibre angle α is chosen such that a unique set of parameters defines failure strength in both directions. Thus a unique set of parameters governing the anisotropic deformation and failure of tissues is obtained.

Table 1. Elastic and phase-field parameters obtained by curve fitting R 2 = 0 . 8424

k1

k2

gc iso / le

gc ani / le

µ

α

1.000

5.3853

33.8548

34.35

10.054

29.992

The stress-stretch response of the tissues in circumferential and axial directions for the obtained parameters are shown in Fig. 1(a).