0000000000585701
AUTHOR
M. Kellomaki
Dynamic fragmentation of a two-dimensional brittle material with quenched disorder
Fragmentation of a two-dimensional brittle material caused by a rapid impact has been analyzed. Computer simulations together with simple arguments are used to obtain a qualitative understanding of crack formation, which is then used to derive an exponential fragment size distribution valid in the large fragment size limit. In the limit of small fragments this distribution is solved numerically, and it is found to obey a scaling law with the exponent {minus}1.5. These results suggest that two different mechanisms are operative in the fragmentation process: branching of propagating cracks determines the small fragment size limit, and merging of the nucleated cracks determines the large size …
Elastic waves in random-fibre networks
The propagation of the first displacement maximum of a semi-infinite wavetrain in a two-dimensional random-fibre network is analysed. Model calculations and numerical simulations are used for demonstrating that two qualitatively different wavefront velocities appear in the network. A transient wave, which travels fast and whose amplitude decreases exponentially, dominates the short-time behaviour when the bending stiffness of the fibres is small and the driving frequency is high. This mode can be described by a one-dimensional model. The transient-wave mode propagates even if the bending stiffness of the fibres vanishes, in which case the normal sound velocity is zero. The usual, and slower…
Rigidity and Dynamics of Random Spring Networks
The static and dynamic elastic properties of two-dimensional random networks composed of Hookean springs are analyzed. These networks are proved to be nonrigid with respect to small deformations, and the floppy mode ratio is calculated exactly. The vibrational spectrum is shown to consist only of zero-frequency and localized modes. The exponential decay of the amplitude and velocity of the transient wave front are shown to be exactly described by a quasi-one-dimensional model of noninteracting paths of propagation.