PSI - Issue 35

Kai Friebertshauser et al. / Procedia Structural Integrity 35 (2022) 159–167 K. Friebertsha¨user and M. Werner and K. Weinberg / Structural Integrity Procedia 00 (2021) 000–000

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Table 2. Material and model parameters for the concrete cylinder Parameter Unit

Values in Fig. 3 (i) and (ii)

Values in Fig. 3 (iii)

[kg m − 3 ]

Density ρ

2300

2300

Young’s modulus E Poisson’s ratio ν Gri ffi th’s parameter G c

[MPa]

50000

50000

0 . 2

0 . 2

[-]

1 ]

[N m − [mm] [mm]

1

1

1 . 2

2 . 5

Grid spacing ∆ x

Horizon δ

3 . 618

7 . 536

number of points N

[-]

309000

290151

Fig. 7. Comparison of the computed damage D k with the experiment for the (i) horizontal and (ii) inclined pad configuration

Fig. 8. Damage in the mid-surface of the curved pad configuration (iii) at t = 1 . 38 ms, p = 9 . 66 bar and approximating function (16) with parameters a = 0 . 23 and b = 12 . 5

show also a good qualitative agreement of the shape of the cracks and fragments with the results of our supporting experimental investigations.

Acknowledgements

The authors gratefully acknowledge the support of the Deutsche Forschungsgemeinschaft (DFG) under the project WE2525-14 / 1.

Appendix A. Velocity-verlet algorithm for time integration

Algorithm 1 shows how the equation of motion (see Eq. (5)) is solved and how the initial- and boundary conditions are applied.