Journal of Engineering Mechanics ASCE, 121 (1995), 1016-1025.


Milan Jirásek and Zdenek P. Bazant
Northwestern University
Evanston, Illinois 60208, U.S.A.


Fracture of quasibrittle materials with a large zone of distributed cracking is simulated by the particle model (discrete element method). The particles at micro-level interact only by central forces with a prescribed force-displacement or stress-strain relation which exhibits post-peak softening and is characterized by micro-strength and micro-fracture energy. It is shown that a regular lattice, even though it can closely approximate isotropic elastic properties, exhibits strong directional bias favoring propagation along a few preferred directions. A randomly generated particle model has no such bias and, with a proper choice of the micro-level constitutive law, can realistically simulate fracture of an ice floe during impact on a rigid obstacle.

Summary and Conclusions

The particle model (discrete element method) can effectively simulate fracture of quasibrittle materials with large zones of distributed cracking. Even if the material does not have a particulate structure, the model is a convenient device to endow a strain-softening material with a characteristic length that serves as a localization limiter, similarly to nonlocal continuum models. The particle size reflects the maximum size of inhomogeneities in the material.

Fracture simulation of a circular specimen is a good test of isotropy. Although a regular lattice of particles can closely approximate isotropic elastic and strength properties, it cannot fracture behavior of isotropic material. Even if the micro-strength values are randomized, there is a strong directional bias favoring propagation along the lines of the regular lattice. A randomly generated particle system, on the other hand, approximates isotropic fracture properties well.

Simple estimates of the critical time step at the limit of numerical stability of an explicit algorithm have been derived and the deceptive way in which fracturing can obscure numerical instability pointed out.

The random particle model gives realistic results in simulating the fracture of a large moving sea ice floe hitting an obstacle.

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EPFL / July 1, 1996 /