Mathematical Physics - Volume II - Numerical Methods

Chapter 5. Review of Development of the Smooth Particle Hydrodynamics (SPH) Method

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These results indicate that the stress waves continue to propagate through the softening zone and are close to the nonlocal solution.

Figure 5.38: Analytical solution and the nu merical results for longitudinal stress at response time t = 3 / 2 · L / c e ; SPH-experiment 3.

Figure 5.39: : Internal energy for 0 ≤ t ≤ 2 · L / c ; SPH experiment 3.

Finally, the physical size of the damage area, shown in Figure 5.40, is constant with a finite size of 4 h = 10 [ mm ] and is independent of the interparticle distance. Together the results from experiments 2 and 3 show that the width of the damage zone is dependent on the smoothing length h , not the interparticle distance ∆ p . This suggests that when modelling a problem including material damage the smoothing length should not be smaller than the characteristic length of the damage and should be set to the characteristic length if the particle resolution permits.

Figure 5.40: Localisation of damage within a limited area 4 h in size ( h = 2 . 5 [ mm ] ) around the bar symmetry plane at response time t = 3 / 2 · L / c e (fringe level: damage [-]. The damage distribution is independent of the interparticle distance ∆ p ; SPH experiment 3.