FE calculations of a deterministic and statistical size effect in concrete under bending within stochastic elasto-plasticity and non-local softening

The numerical FE investigations of a deterministic and statistical size effect in unnotched concrete beams of similar geometry under quasi-static three point bending were performed within elasto-plasticity with non-local softening. The FE analyses were carried out with four different beam sizes. Deterministic calculations were performed with the uniform distribution of a tensile strength. In turn, in statistical calculations, the tensile strength took the form of spatially correlated random fields described by a truncated Gaussian distribution. In order to reduce the number of statistical realizations without losing the calculation correctness, Latin hypercube sampling was applied. The numerical outcomes showed a strong coupled deterministic and stochastic size effect which was compared with the size effect laws by Bazant and by Carpinteri.