Anisotropic damage and dynamic behavior of reinforced concrete structures until failure

Dynamic loadings such as impact on reinforced concrete structures lead to degradations and structural failures significantly different to the ones observed for quasi-static loadings. Local effects (spalling, compaction...) and global mechanisms (bending, shear, perforation...) are experimentally observed. Wave propagation due to dynamics loadings can lead to failure in tension in a part of a structure or a component previously in compression. Induced damage anisotropy in concrete is partly responsible for the dissymmetry of behavior between tension and compression. Concrete anisotropy can be modelled by means of a second order damage tensor. In the damage model considered, damage growth is governed by the positive extensions. The model, written in the thermodynamics framework, is robust and is able to compute efficiently Reinforced Concrete (RC) structures. The initial anisotropic model is here extended to dynamics by introducing a viscosity law to govern dynamic damage evolution. The strain rate effect observed experimentally in tension (strength increases with strain rate) is reproduced. In compression no strain rate is introduced since inertial forces seem sufficient to reproduce the strength enhancement in dynamics. One also focuses on regularization issues. For high strain rates the solution is regularized since the characteristic time introduced indirectly defines an internal length and since the damage rate is bounded by a maximum damage rate parameter (visco/delay damage law). This visco/delay regularization is efficient at large strain rates, otherwise, the delay in damage evolution is too small to let damage grow in a wide enough zone. For quasi-static or low speed dynamic cases, the regularization is gained by means of classical non-local damage. For intermediary loading rates where both the strain rate effect and the non-local regularization are needed, a non-local delay-damage model is written (and used in 3D computations). The example of a dynamic tension test by spalling is given. The strain rate range in which each method is efficient is obtained. The model presented is validated by simulating impact tests on reinforced concrete beams. These tests have been carried out at the CEA Saclay on a drop tower. (author)