This paper presents a review of the different models for concrete based on continuum damage theory, formulated at the Laboratoire de Mécanique et Technologie (Cachan, France). Derived in the framework of the thermodynamics of irreversible processes, each formulation is based on physical observation. Induced anisotropy, ductile behavior, and directional effects such as the closure of cracks are discussed and adequate damage models are proposed. Finally, the numerical implementations performed give a good description of the failure process as well as an accurate prediction of the behavior of concrete and reinforced concrete structures.

Among the “theories” applied to model concrete behavior, damage mechanics has proven to be efficient. One of the first models for concrete introduced into such a framework is Mazars’ damage model. A new formulation of this model, called the “μ model” and based on a coupling of elasticity and damage within an isotropic formulation, is proposed herein for the purpose of 3D cyclic and dynamic loadings. Unilateral behavior (i.e., crack opening and closure) is introduced by use of two internal variables. A threshold surface is then associated with each of these variables. The shape of such surfaces has been chosen to model as accurately as possible concrete behavior under various loadings, i.e., tension, compression, shear, biaxial and triaxial, in the aim of simulating a large number of loading types (monotonic, cyclic, seismic, blast, impact, etc.). Applications of this model are presented on plain or reinforced concrete elements subjected to a range of loadings (e.g., multiaxial, cyclic, dynamic). A comparison with experimental results serves to demonstrate the effectiveness of these various selected options.