A three dimensional damage model with induced damage anisotropy is proposed for quasi-brittle materials such as concrete. The thermodynamics framework is used, considering then a single 2nd order tensorial damage variable whatever the intensity and the sign of the loading. The quasi-unilateral conditions of microcracks closure are written on the hydrostatic stress only. Altogether with the consideration of damage laws ensuring a damage rate proportional to the positive part of the strain tensor this is sufficient to model a strongly different behavior due to damage in tension and in compression. A proof of the positivity of the intrinsic dissipation due to such an induced anisotropic damage is given. An efficient scheme for the implementation of the damage model in commercial Finite Element codes is then detailed and numerical examples of structural failures are given. Plain concrete, reinforced and pre-stressed concrete structures are computed up to high damage level inducing yielding of the reinforcement steels. Local and nonlocal computations are performed. A procedure for the control of rupture is proposed. It is a key point making the computations with anisotropic damage truly efficient.

International audienceA testing device is presented for the experimental study of dynamic compaction of concrete under high strain rates. The specimen is confined in a metallic ring and loaded by means of a hard-steel Hopkinson pressure bar (80 mm diameter, 6 m long) allowing for the testing of specimens large enough regarding the aggregate size. The constitutive law for the metal of the ring being known, transverse gauges glued on its lateral surface allow for the measurement of the confining pressure. The hydrostatic and deviatoric responses of the specimen can then be computed. The proposed method is validated by several numerical simulations of tests involving a set of four different concrete-like behaviours and different friction coefficients between the cell and the specimen. Finally, three tests performed with the MB50 concrete at three different strain rates are processed with the method and are compared with literature results for the same material under quasi-static loadings

The objective of this study is to develop a model for concrete with an emphasis on tension and compaction. Compaction of concrete is physically a collapse of the material voids. It produces plastic strains in the material and, at the same time, an increase of the bulk modulus. The model is based on mechanics of porous materials, damage and plasticity. The computational implementation has been carried out in the Lagrangian ®nite element code DYNA3D. In order to show the in¯uence of compaction, simulations of a split Hopkinson test performed on con®ned concrete and on a concrete rod submitted to an impact have been carried out. The examples demonstrate the importance of compaction during an impact, which has a tendency of strengthening the concrete structure.

In a concrete structure subjected to an explosion, for example a concrete slab, the material is subjected to various states of stress which lead to as many mode of rupture. Close to the explosive, a state of strong hydrostatic compression is observed. This state of stress produces an irreversible compaction of the material. Away from the zone of explosion, confinement decreases and the material undergoes compression with a state of stress, which is slightly triaxial. Finally, the compression wave can be reflected on a free surface and becomes a tensile wave, which by interaction with the compression wave, produces scabbing. We present in this paper a model aimed at describing these three failure modes. It is based on visco-plasticity and rate dependent damage in which a homogenisation method is used in order to include the variation of the material porosity due to compaction. The model predictions are compared with several experiments performed on the same concrete. Computations of split Hopkinson tests on confined concrete, a tensile test with scabbing, and an explosion on a concrete slab are presented.