Journal of Engineering Mechanics ASCE, 121 (1995), 1016-1025.
PARTICLE MODEL FOR QUASIBRITTLE FRACTURE
Milan Jirásek and Zdenek P. Bazant
AND APPLICATION TO SEA ICE
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 /