Numerical Simulation of Stress Wave Propagation in Brittle Granular Materials Using Material Point Method

Dongxin Liu, Luming Shen

School of Civil Engineering, The University of Sydney, NSW, 2006, Australia

Earthquake is regarded as a catastrophe all around the world. One of the major research areas in earthquake engineering is to investigate the reactions of soil particles under the earthquake waves. This study illustrates the results of stress wave propagation in brittle granular materials using Material Point Method (MPM) and helps us understand how the brittle grain particles fail under the loading of high rate stress wave. As one of the innovative meshfree methods, the MPM is an extension to solid mechanics problems of a hydrodynamics code which, in turn, evolved from the particle-in-cell method [1-2]. The motivation of the development was to simulate those problems with history-dependent internal state variables, such as contact/impact, penetration/perforation and metal forming without invoking master/slave nodes and global remeshing. The essential idea is to take advantages of both Eulerian and Lagrangian methods. The MPM can not only identify the contact between each grain clearly, but also address the mesh distortion issues common in mesh-based methods due to the large deformation of particles [3]. In this study, a 3-dimensional MPM simulation is performed to investigate the dynamic responses of a 10-glass bead chain under impact of a steel bar. Figure 1 demonstrates the propagation of the maximum principal stress in glass beads under the impact of steel bar at different times. This figure shows that the maximum tensile stress positions first appear on the top of the second glass sphere and then appear at the same area in the latter spheres. The preliminary results indicate that the friction coefficient of glass beads, impact velocity and the length of steel bar will have significant effect on the failure positions in the glass beads.

References

[1] D. Sulsky, Z. Chen, and H. L. Schreyer, Comp. Meth. Appl. Mech. Eng. 118 1

(1994)

[2] Z. Chen, W. Hu, L, Shen, X. Xin, and R. Brannon, Eng. Fract. Mech. 69 17 (2002)

[3] S. G. Bardenhagen, J. U. Brackbill, and D. Sulsky, Comp. Meth. Appl. Mech. Eng.

187 3 (2000)