International Journal for Numerical and Analytical Methods in Geomechanics, 30 (2006), 71-90


Peter Grassl
University of Glasgow, Scotland
   Milan Jirásek
Czech Technical University in Prague, Czech Republic


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 plastic strain.

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.

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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CVUT / 2 March 2006 /