Calibration of non local damage model with size effect law

The calibration of non-local models, which contain an internal length, has been among the major issues conditioning the implementation of this kind of failure models. Direct calibration from uniaxial testing, where the state of strain remains homogeneous throughout the specimen, is impossible. The softening law is not directly accessible because the state of strain cannot remain homogeneous during the entire test. In the absence of local information on the displacement field and on microcracking in the fracture process zone, the calibration has to rely on inverse analysis. This paper presents such a procedure based on three point bend size effect tests on notched specimens. The complete load deflection curves are used for the identification of the constitutive relations. Manual calibration is discussed first with the help of Bažant’s size effect law, which is related to peak loads only. Then, automatic calibration is described. It is shown that an optimal set of model parameters can be obtained within a reasonable number of iterations. The identification concerns generally three sizes of specimens. We show the contribution of a fourth size on the quality of the identification. The results have a dispersion, which results from the heterogeneity of the material, and from the dimensions of specimens. Finally the simulations have also their defect and we try to integrate the hazard of conception of the mesh. We look the influence of the mesh onto the parameters identified and on the size effect law.