Notched concrete beams under bending -- calculations of size effects within stochastic elasto-plasticity with non-local softening

Numerical FE investigations of a deterministic and statistical size effect in notched concrete beams of a similar geometry under three-point bending were performed. The FE analyses were carried out with four different beam sizes. Deterministic calculations were performed assuming constant values of tensile strength. In turn, in statistical calculations, the tensile strength took the form of random spatial fields described by a truncated Gaussian random distribution. In order to reduce the number of stochastic realizations without loosing the accuracy of the calculations, Latin hypercube sampling was applied. The numerical results were compared with the corresponding laboratory tests. The numerical outcomes show that the bearing capacity of beams and their ductility increase with decreasing specimen size. If the distribution of the tensile strength is stochastically distributed, the mean beam strength is always smaller than the deterministic value.