Static strength of brittle materials under multiaxial nonuniform stress states: A novel statistical model for assessing size effects

In this paper, a model for the assessment of size effects on quasi-static strength of brittle materials subjected to applied load inducing a nonuniform stress distribution within the material volume is proposed. An equivalent stress computed through finite element analysis is introduced in the model to account for the effect of the stress gradient within the loaded volume. The defect size distribution is modelled, differently from the literature, with the largest extreme value distribution. The proposed model has been validated with datasets available in the literature and obtained through bending tests on concrete specimens. For each type of test, the model permits to properly assess size effects. Due to its general formulation, a model for the strength variation with respect to the loaded volume, regardless of the testing type, was also obtained, further proving its effectiveness.