The Finite Element Method (FEM) is a mesh-based numerical method, which is conventionally used in engineering computational mechanics. However, the FEM has limited application in many complex problems such as free surface problems and large deformations. In order to deal with the problem of limited application, the Smoothed Particle Hydrodynamics (SPH) Method was developed in 1977. This method is mesh free by replacing the nodes used in FEM by particles. Since there is no connectivity between particles, the SPH Method avoids element distortion and is applicable to solving problems of high velocity impact and penetration behavior into solid materials.
As with other mechanics calculations, the SPH Method is governed by momentum and energy conservation laws, which are expressed as interparticle forces. Each particle within the SPH numerical calculation has a fixed mass and follows the fluid motion, which is evaluated by the approximation function. Furthermore, the smoothing length is computed by the divergence function and the distance between each couple of particles is checked to see that it is smaller than twice the smoothing length. By determining the smoothing length as the influence neighbor sphere radius, enough particles are kept in the neighbor sphere to validate continuum variables and avoid problems in material compression and expansion. After that, keeping the same number of particles is equal to keeping the same mass of particles in the neighbor sphere. The minimum and maximum values required for the smoothing length are 0.2 and 2, respectively, times the initial smoothing length, while the default value is 1.2 times the initial smoothing length.
References
1. T. Sakakibara, T. Tsuda, and R. Ohtagaki, “A Study of Quasi-static Problem by SPH Method”, 10th Int. LS-DYNA Users Conf., 2008
2. C.E. Zhou, G.R. Liu, and X. Han, “Classic Taylor-Bar Impact Test Revisited Using 3D SPH”, Computational Methods, 2006
3. J.L. Lacome, “Smoothed Particle Hydrodynamics”
the velocity of particles on the z-axis (impact direction) in Taylor Impcat test cylinder (material: 6061-T6 Al; initial velocity: 207m/s; particle #: 11340)
ballistic impact results of Ti6Al4V with initial velocity 1200 m/s
As with other mechanics calculations, the SPH Method is governed by momentum and energy conservation laws, which are expressed as interparticle forces. Each particle within the SPH numerical calculation has a fixed mass and follows the fluid motion, which is evaluated by the approximation function. Furthermore, the smoothing length is computed by the divergence function and the distance between each couple of particles is checked to see that it is smaller than twice the smoothing length. By determining the smoothing length as the influence neighbor sphere radius, enough particles are kept in the neighbor sphere to validate continuum variables and avoid problems in material compression and expansion. After that, keeping the same number of particles is equal to keeping the same mass of particles in the neighbor sphere. The minimum and maximum values required for the smoothing length are 0.2 and 2, respectively, times the initial smoothing length, while the default value is 1.2 times the initial smoothing length.
References
1. T. Sakakibara, T. Tsuda, and R. Ohtagaki, “A Study of Quasi-static Problem by SPH Method”, 10th Int. LS-DYNA Users Conf., 2008
2. C.E. Zhou, G.R. Liu, and X. Han, “Classic Taylor-Bar Impact Test Revisited Using 3D SPH”, Computational Methods, 2006
3. J.L. Lacome, “Smoothed Particle Hydrodynamics”
the velocity of particles on the z-axis (impact direction) in Taylor Impcat test cylinder (material: 6061-T6 Al; initial velocity: 207m/s; particle #: 11340)
ballistic impact results of Ti6Al4V with initial velocity 1200 m/s
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