Dynamic Behavior of Concrete: Constitutive Models - Dynamic Behavior of Concrete and Seismic Engineering - page 88

2.6.8. Discrete element method

Modeling a medium as an assembly of particles is an alternative to
representation as a continuous medium. The concept has been applied to both fluid
and solid mechanics, and to pulverulent media where there is an identity between the
model's particle and the grain of the material. It has recently been extended to
cohesive media. Two approaches co-exist in this frame:

- The medium is treated as undeformable particles with a mass (ED). The
stresses and strains are represented by interactions between the particles (distance
and binding force). Thus, behavior, both elastic and inelastic, is completely
expressed by the linking conditions of EDs [CUN 97].
- The medium is considered as if composed of EDs which are deformable solids ,
the behavior of which is described through elasticity and plasticity in continuum
mechanics. The links between EDs only express local phenomena, such as contact
loss and friction [MOR 96].

2.6.8.1. Camborde and Mariotti
- Reference: [CAM 99].
- Type: interactions between particles.
- Each particle is representative of a mesoscopic scale consisting of a few
aggregates, cement and empty space. Initially, each link that is of the cohesive type
transmits compression and traction loads. Two types of elastic forces are present
(Figure 2.23): the normal strength of stiffness Kn and the shear force of stiffness Ks.

The inelastic behavior involves a traction failure threshold T on F n and a Mohr-
Coulomb shear failure threshold on F s , defined by the cohesion C and a friction
angle I. In a traction failure (F n < 0), the link is simply suppressed. In a shear failure
(F n > 0), we change from a cohesive type law to a friction type law (2.24).

'U n =U t n - U (t-1) n

'U s =U t s - U (t-1) s

Ks

Kn

' U '

Figure 2.23 . Details of the particles' interaction normal displacement,̓ s

n

tangential displacement (distortion) ( from [CAM 99])