# Plasticity and Damage Mechanics for Modeling Concrete Failure

[Doktorsavhandling]

Concrete structures exhibit strongly non-linear and complex mechanical behavior. Hence, they are nowadays often analyzed by means of the finite element method, whereby a realistic description of the material behavior is decisive for the validity of the results. Concrete is a cohesive-frictional material, in which the stress transfer in many load cases is accomplished by frictional forces. Consequently, the three-dimensional stress-strain behavior is highly pressure-sensitive ranging from quasi-brittle behavior in tension to almost ductile response in high confined compression. Moreover, failure process in tension and low confined compression is accompanied by localization of deformations in the form of cracks and shear bands.

In the present thesis, constitutive models based on plasticity and damage mechanics have been developed to describe the pressure-sensitive response and the localization of deformations.

One of the advantages of stress-based plasticity models is the simple and direct calibration of the stress state. The yield surface corresponds at a certain stage of hardening to the strength envelope of concrete and has, therefore, a strong physical meaning. Moreover, the split into elastic and plastic strains is suitable to describe the irreversible deformations and volumetric expansion in compression. Nevertheless, the theory of plasticity fails to describe the degradation of stiffness associated with the failure process of concrete in tension and low confined compression.

Damage mechanics models, on the other hand, are suitable to describe the stiffness degradation observed in experiments. Yet, damage models alone fail to describe the irreversible deformations and volumetric expansion associated with compressive failure.

Combinations of plasticity and damage models are able to describe the main characteristics of concrete failure in tension and compression. The plastic-damage model developed in the present thesis consists of a stress-based plasticity model and a scalar damage model. The plasticity model is based on the effective stress to guarantee local uniqueness of the combined model. The isotropic damage model is based on the plastic strain, which permits a clear definition of the softening regime and thus simplifies the calibration. Moreover, the stress evolution approach of the damage model is explicit, which results in a computationally efficient combination of local plasticity and integral-type nonlocal damage for regularization of localized deformations.

**Nyckelord: **concrete, plasticity, damage, localization, nonlocal

Denna post skapades 2006-09-28. Senast ändrad 2013-09-25.

CPL Pubid: 2333