Mathematical Physics - Volume II - Numerical Methods

5.11 Non-Local properties of SPH

191

Value

Label Samples Magnitude Unit

1 . 55 · 10 − 9 70800

Tonnes/mm 3

ρ E ν

Density

Young’s Modulus

MPa

Poisson’s ratio

0.125 0.022 0.060

Damage initiation strain ε

ε f

Failure strain

Table 5.3: Input data for isotropic CDM model with linear strain-softening for FE (DYNA3D) and SPH (MCM) codes.

The bar was loaded in tension by applying constant velocity in opposite directions to its ends. In order to induce the softening regime in material, the applied velocity has to be between.

Figure 5.14: Spatial discretisations used in the FE (DYNA3D) simulation of the strain softening bar.

To provide a reference data set for comparison with SPH, and to illustrate the mesh dependency of the FE model, the bar problem was simulated with the nonlinear transient FE code DYNA3D, using the local constitutive model described above. Four different spatial discretisation densities (mesh densities) were considered: the bar was discretised with 31, 101 151 and 201 elements along x axis, as shown in Figure 5.14 Similarly, in the SPH simulations, the bar was discretised with three different particle densities, determined by inter-particle spacings: ∆ p = 1 . 98 , 1 . 32 and 0 . 995 [ mm ] , as shown in Figure 5.15.