Mathematical Physics - Volume II - Numerical Methods

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

196

Figure 5.26 shows a graphical representation of the damage zone at response time t = 3 / 2 · L / c e . Damage is averaged over 5 particles along the length of the bar. This number is constant for all particle spacings ( ∆ p ) considered, however this may be difficult to observe in Figure 5.26 because of the significant difference in maximum damage magnitude (see Figure 5.24). The width of the damage zone depends on the chosen interparticle distance.

Figure 5.26: Localisation of damage within a limited area 4 h in size h = 1 . 3 · ∆ p around the bar symmetry plane at response time t = 3 / 2 · L / c e (fringe level: damage [-]. SPH experiment 1. Development of damage in the centre of the bar, presented in Figure 5.26, shows that the increase of the smoothing length results in increase of the size of the damage zone.