An anisotropic damage constitutive law enhanced with mixed-modes strong discontinuity kinematics application to the description of multi-cracking of RC components

International audienceCracking of quasi-brittle materials like concrete can be assessed by continuum damage based laws. Recent constitutive laws, based on a continuum description of the media, succeed in representing the main features related to the complex behavior of quasi-brittle materials such as cracking, crack closure effect and permanent strains [1, 2]. However, cracking is described in a diffuse way and quantifying cracking features such as openings or spacing becomes a challenge. Post-processing methodologies are needed to estimate the aforementioned quantities [3]. The use of displacement discontinuities embedded into a standard finite element has shown its efficiency in describing cracking. The kinematics of a classical finite element is enhanced by a displacement jump, which represents the crack opening. In our work, the Strong Discontinuity Approach (SDA) is used [4]. Numerically, the enhancement related to the displacement jump takes places locally in the element. The nonlinear behavior is handled by a tension/separation law characterizing the energy dissipation on the discontinuity. The objective of our work is the development of a kinematic enhanced damage based model to represent cracking patterns of reinforced concrete components subjected to complex loadings. A damage model, based on micromechanical assumptions, is used [5]. This model allows accounting, in a natural manner, for particular crack families orientations in reinforced concrete membrane elements. A discrete damage formulation is considered by introducing p couples of microcracking densities and directional tensors, denoted by et961;pNp. Microcracking densities et961;p are considered as internal variables and the directional tensors Np constructed as the tensor product of the normal to the crack. The model can represent either mode-I, mode-II and mixed mode cracking mechanisms. This model is then enhanced with the strong discontinuity kinematics. The main features of the enriched model will be exposed. Numerical simulations on reinforced concrete components such as shearwalls will be shown to illustrate the efficiency of the model and compared to experimental results