Bending of marble with intrinsic length scales : A gradient theory with surface energy and size effects

Abstract
A gradient bending theory is developed based on a strain energy function that includes the classical Bernoulli-Euler term, the shape correction term (microstructural length scale) introduced by Timoshenko, and a term associated with surface energy (micromaterial length scale) accounting for the bending moment gradient effect. It is shown that the last term is capable to interpret the size effect in three-point bending (3PB), namely the decrease of the failure load with decreasing beam length for the same aspect ratio. This theory is used to describe the mechanical behaviour of Dionysos-Pentelikon marble in 3PB. Series of tests with prismatic marble beams of the same aperture but with different lengths were conducted and it was concluded that the present theory predicts well the size effect.