Comment on “Scaling behavior in explosive fragmentation”

We discuss the data analysis and the conclusions based upon the analysis given in the paper by Diehl et al. Following the suggestion in the Comment on our previous work by Astrom, Linna, and Timonen [Phys. Rev. E 65,048101 (2002)], we performed extensive molecular-dynamics simulations to confirm that our numerical results for the mass distribution of fragments after the "explosion" of thermalized samples are consistent with the scaling form n(m)∼m - ( α + 1 ) f(m/M 0 ), where ∫(m/M 0 ) is a cutoff function, M 0 is a cutoff parameter, and the exponent a is close to zero.

Exponential and power-law mass distributions in brittle fragmentation

Generic arguments, a minimal numerical model, and fragmentation experiments with gypsum disk are used to investigate the fragment-size distribution that results from dynamic brittle fragmentation. Fragmentation is initiated by random nucleation of cracks due to material inhomogeneities, and its dynamics are pictured as a process of propagating cracks that are unstable against side-branch formation. The initial cracks and side branches both merge mutually to form fragments. The side branches have a finite penetration depth as a result of inherent damping. Generic arguments imply that close to the minimum strain (or impact energy) required for fragmentation, the number of fragments of size $s…

Unconstrained periodic boundary conditions for solid state elasticity

We introduce a method to implement dynamics on an elastic lattice without imposing constraints via boundary or loading conditions. Using this method we are able to examine fracture processes in two-dimensional systems previously inaccessible for reliable computer simulations. We show the validity of the method by benchmarking and report a few preliminary results.

Universal Dynamic Fragmentation inDDimensions

A generic model is introduced for brittle fragmentation in $D$ dimensions, and this model is shown to lead to a fragment-size distribution with two distinct components. In the small fragment-size limit a scale-invariant size distribution results from a crack branching-merging process. At larger sizes the distribution becomes exponential as a result of a Poisson process, which introduces a large-scale cutoff. Numerical simulations are used to demonstrate the validity of the distribution for $D=2$. Data from laboratory-scale experiments and large-scale quarry blastings of granitic gneiss confirm its validity for $D=3$. In the experiments the nonzero grain size of rock causes deviation from th…

Dynamic aspects in brittle fragmentation

Dimensional effects in dynamic fragmentation of brittle materials.

It has been shown previously that dynamic fragmentation of brittle $D$-dimensional objects in a $D$-dimensional space gives rise to a power-law contribution to the fragment-size distribution with a universal scaling exponent $2\ensuremath{-}1∕D$. We demonstrate that in fragmentation of two-dimensional brittle objects in three-dimensional space, an additional fragmentation mechanism appears, which causes scale-invariant secondary breaking of existing fragments. Due to this mechanism, the power law in the fragment-size distribution has now a scaling exponent of $\ensuremath{\sim}1.17$.