International Journal for
Numerical and Analytical Methods in Geomechanics, 30 (2006), 71-90
PLASTIC MODEL WITH NON-LOCAL DAMAGE APPLIED TO CONCRETE
University of Glasgow, Scotland
Czech Technical University in Prague,
The present paper deals with a certain class of regularized models for
concrete failure, combining plasticity with nonlocal damage. The
plastic part is local and uses a yield condition formulated in the
effective stress space. Softening is incorporated through the damage
part of the model. Damage is considered as isotropic and linked to the
evolution of plastic strain. The regularized version of the model is
based on weighted spatial averaging of the damage-driving variable.
Conditions for a mesh-independent description of the localized zone of
inelastic strains are studied using one- and two-dimensional examples
solved by simple nonlocal damage-plasticity models, in two dimensions
with nonassociated flow. Then, the framework is applied to an advanced
model for concrete. Structural examples of tensile and compressive
failure are presented.
In the present study we have proposed a framework for nonlocal
damage-plastic models, combining local plastic part with
integral-type nonlocal damage. The damage evolution is driven by the
The examples of tensile, shear and compressive failure show that the
dissipation associated with the failure process for this type of
regularized damage-plastic models is mesh-independent. Furthermore, we
have analyzed two approaches that enforce a continuous strain profile
of inelastic strain:
Finally, it has been shown that the nonlocal damage-plastic model for
concrete can provide a mesh-independent description of various
combinations of tensile and compressive failure, even in cases when the
traditional approach based on a local formulation with fracture-energy
motivated adjustment of the softening modulus fails.
- The plastic hardening modulus is larger than the critical plastic
hardening modulus, and the local damage-driving variable is replaced by
its nonlocal counterpart.
- The local damage-driving variable is replaced by a linear
combination of its local and nonlocal value with a suitable value of
parameter m (m>1), as proposed by Vermeer and
To keep the number of parameters limited, only one scalar damage
variable was considered here. Clearly, this choice restricts the range
of applicability of the model. Generalizations to isotropic
formulations with several damage variables and to anisotropic
formulations with damage tensors should be explored in the future.
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