Dynamic Behavior of Concrete: Constitutive Models - Dynamic Behavior of Concrete and Seismic Engineering - page 89

Porosity is introduced not on the geometric level, but through an inner variable
that controls the evolution of stiffness Kn, as is the case with the Holmquist and
Johnson-type model.
Figure 2.24. Domain of the contact forces and state equation (from [CAM 99])
2.6.8.2. Donzé
- Reference: [DON 98].
- Type: interaction between particles.
- One original feature of this model is definition of the interactions between
particles. Two interacting elements are not necessarily in contact. Two elements a
and b of radii R a and R b will be in interaction if J (R a + R b ) ! D a,b , with the
interaction coefficient J (! 1), D a,b being the distance between the centers of EDs.
This definition of interacting elements is different from the one typically used with
spherical EDs, where only the elements in contact interact (J= 1). This definition of
initial interactions allows us to increase the number of interactions for one element,
and therefore to model the action of the matrix between the concrete aggregates. The
interaction force between two EDs has a normal component F n and a tangential
component F s . Figure 2.11 shows the cyclic loading response of the bonding
between two EDs. A Mohr-Coulomb criterion is used to characterize the failure of
the bonding between two EDs.