Abstract :
Fracture processes in brittle disordered
materials like many geo-materials (rock, ice, concrete,
cement, etc.) are a trade off between local
stress concentrations caused by the heterogeneity
of such materials, and local strength. At those locations
where the ratio between stress and strength
exceeds a critical threshold value, cracking may
initiate. Depending on the size of the cracks they
can be arrested by stronger and stiffer elements in
the structure of the material, or they will propagate
and become critical.Critical cracks lead to localisation
of deformations and to softening. In currently
popular cohesive crack models still some continuum
ideas remain, namely the notion of stress,
whereas the localisation of deformations is handeled
correctly by means of displacements. During
softening themacro-crack traverses the specimen’s
cross-section, thereby gradually decreasing the
effective load-carrying area. This growth process
is affected both by structure (specimen) size and
boundary conditions, and a better description of
softening may be achieved by using load and displacement
as state variables. In this paper, a new
method of modelling fracture is proposed by using
fracture potentials (F − r relations) at variousobservation scales, from atomistic and molecular
to macroscopic. The virtual material can be interpreted
as being built up from spherical elements;
the fracture potential describes the interactions between
the spheres. Since the spherical elements
interact at their contacts-points only, a force-separation
law (F-r) suffices. Size/scale effects are dealt
with directly in the F-r relation; size/scale effects
on strength are merely a special point in the entire
description and do not require a separate law.
