A PROBABILISTIC FORMULATION OF THE DAMAGE EVOLUTION LAW

The inhomogeneous character of composites has many consequences regarding their behaviour. Using a two-level approach (micro- and macro-), a scalar is constructed where the damage of a representative volume of material is no longer considered as deterministically known, but results from a probabilistic formulation. A probabilistic elastic-brittle behaviour is assumed at the micro-level and the evolution law of damage results as a sum, through a loose parallel bundle of size Nt (Daniel's model) over all the micro-states. The approach developed appears as an intermediate model between those arising in the fields of Damage Mechanics and Probabilistics Brittle Fracture. The model has been implemented in a finite element code and some significant results are presented. A concrete specimen is loaded in pure compression and pure tension, with the external boundary conditions remaining deterministic. The interaction between the external loading and the inhomogeneities creates some anisotropy and it is found that the specimen behaves more like a structure than like a theoretical volume of material. © 1990.