Jacky Mazars

A description of micro- and macroscale damage of concrete structures

Abstract Some particularities of the microstructure of concrete are first presented: they lead us to conclude that damage by microcracking is the main phenomenon in the mechanical behavior of the material. An isotropic elastic damage model is then proposed by using the coupling of two damage variables, D t (tensile effects) and D c (compressive effects). The model is built according to the framework of thermodynamics, and then we show that it is possible to describe the birth and growth of cracks, using a combination linear elastic damage mechanics and linear elastic fracture mechanics. Some results attest the interest in that kind of approach.

From damage to fracture mechanics and conversely: A combined approach

Fracture mechanics and damage mechanics are two correlated theories. In some instances, e.g., for large specimens, crack propagation may be viewed equivalently as a sudden localization of damage. Relationships based on thermodynamic considerations between the two theories are presented in this paper. They lead to the definition of the equivalent crack concept, in passing from a damage zone to a fracture problem and, conversely, a damage zone is determined which is equivalent to a crack. Different possible applications are presented showing that, for the same problem, the two concepts can be used depending on the situation. Furthermore a solution to calculate fracture energy for large specimens, when damage parameters deduced from classical tests are known, is proposed to illustrate the capability of these equivalences.

Damage model for concrete‐like materials coupling cracking and friction, contribution towards structural damping: first uniaxial applications

This paper is concerned with the development of a damage model for concrete materials exhibiting a residual hysteretic behaviour at a fixed level of damage. This feature is obtained by coupling damage mechanics and friction phenomena. In its complete form, the damage variable by means of which the stiffness decrease is obtained in an orthotropic second-order tensor. Its evolution is governed by the tensile part of the strain tensor. The sliding between the crack lips is assumed to have a plasticity-like behaviour with non-linear kinematic hardening. The sliding stress depends on the level of damage. Such a model assumes the evolution of two yield surfaces: a fracture one and a sliding one. If unilateral effects need to be taken into account for cyclic loading analysis (crack closure modelling), the damage evolution remains isotropic. The effectiveness of this model in reproducing a part of damping when subjected to dynamic loading is exemplified through two structural case studies. Copyright

Mixed mode fracture in plain and reinforced concrete : some results on benchmark tests

Three different models for concrete based on local and non-local approaches have been adopted to investigate the mechanical behaviour of plain and reinforced concrete when undergoing mixed-mode fracture. The purpose of the research is to understand the results of some benchmark tests, to compare the models with each other and with experiments, and to estimate the reliability of the modelling. To create a sound basis for the comparison, the discretizations, the boundary conditions and the material data are considered, when possible, as unified parameters for the different models in each benchmark test.

Size Effect in Brazilian Split-Cylinder Tests: Measurements and Fracture Analysis

The size effect in the split cylinder (Brazillian) tensile test is studied experimentally and analyzed theoretically. Tests of a very broad size range, 1:26, were conducted on cylindrical discs of constant thickness made from concrete with aggregate of a maximum size of 5 mm. The results confirm the existence of size effect and show that up to a certain critical diameter d, the curve of nominal strength versus diameter approximately agrees with the law proposed by Bazant for the size effect caused by energy release due to fracture growth. For larger sizes, there appears to be a deviation from the size-effect law. These and other study findings are discussed.

Size effect and continuous damage in cementitious materials

The dependence between the mechanical properties of concrete structures and their sizes is a problem addressed in this paper. Two types of size effect are distinguished: the first one is probabilistic and is related to random distributions of defects in a volume of material; the second one is purely deterministic and is related to fracture propagation in brittle heterogeneous media. These two aspects are combined in a continuous damage model. The initiation of damage is probabilistic and the evolution of damage is nonlocal. Comparisons with experiments on notched and unnotched bending beams show that the model provides a realistic prediction of the various size effects.

'Crush-crack' : a non-local damage model for concrete

SUMMARY A model is presented based on the non-local damage theory. It sets out to describe the behavior of concrete under free-variable loads, which are constant in sign. Its purpose is to analyze shear behavior and high strain-gradient localized problems, and it takes Mazar’s model as a starting point with reference to the basic idea of a scalar isotropic non-local damage controlled by principal tensile strains. In addition, the other two main features are an internal variable denoted to the control or reversible volumetric expansion in compression, and irreversible strains aimed at modelling crushing in compression and cracks both in tension and compression. As a consequence, induced-anisotropy, dilatancy and path-dependency can be reproduced. In particular, the modelling of micro- and macrocracks makes it possible to capture mixed-mode cracking as well as aggregate interlock, which requires a residual stiffness to guarantee the transmission of transversal and normal stresses for assigned slips.The model requires the knowledge of the material response in uniaxial tension and compression, and biaxial compression tests which can be introduced directly by adopting experimental curves, or by means of a reduced number of parameters. The effectiveness of the model is shown through comparisons with several sets of experimental tests on both small specimens, assumed to be homogeneous, and boundary value problems.

Orthotropic behavior of concrete with directional aspects: modelling and experiments

Abstract This paper presents a model for brittle material such as concrete based on continuum damage theory. The particular physical phenomena analyzed here are the elastic anisotropy induced by damage, the evolution of permanent strains, which are considered to be related to damage and a directional effect such as the closure of cracks which are all clearly illustrated by different experiments. These observations lead us to propose a set of damage variables and a new thermodynamic potential. The choices which have been made are discussed and the result of the identification on a compression test is shown. Then, different comparisons between classical or new tests performed at L.M.T. and the prediction of the model illustrate the significance of our approach. To demonstrate the usefulness of this type of damage model, the prediction of a recent biaxial test on concrete is shown and then the well-known results on the non-influence of the loading path on the behavior are also retrieved.

Simplified modelling strategies to simulate the dynamic behaviour of R/C walls

A continuous damage model and different simplified numerical strategies are proposed to simulate the behaviour of reinforced concrete (R/C) walls subjected to earthquake ground motions. For 2D modelling of R/C walls controlled primarily by bending, an Euler multilayered beam element is adopted. For 3D problems, a multifibre Timoshenko beam element having higher order interpolation functions has been developed. Finally, for walls with a small slenderness ratio we use the Equivalent Reinforced Concrete model. For each case, comparison with experimental results of R/C walls tested on shaking table or reaction wall shows the advantages but also the limitations of the approach.

Efficient approaches to finite element analysis in earthquake engineering

Abstract This paper deals with the modeling of reinforced concrete structures subjected to earthquake ground motion. Due to the complex behavior of both materials and structures, efficient numerical tools are developed herein in order to keep accuracy and robustness for large scale computations. We focus our attention on the use of simplified multifiber beam element describing the response of structural components and on macro-element accounting for soil–structure interaction.