Gradient-enriched linear-elastic tip stresses to perform the high-cycle fatigue assessment of notched plain concrete

Gradient Elasticity (GE) allows the stress analysis to be performed by taking into account the size of the dominant source of microstructural heterogeneity via a suitable length scale parameter. This is done by simply assuming that the material under investigation obeys a linear-elastic constitutive law, albeit equipped with additional spatial strain gradients. From a practical point of view, the most important implication of this modus operandi is that gradient-enriched linear-elastic stresses at the notch tips are always finite, this holding true also in the presence of sharp stress risers (such as cracks). In the present investigation, the accuracy of two different GE based design strategies was checked against a number of experimental results generated by testing, under cyclic four-point bending, plain concrete samples containing different geometrical features. The high level of accuracy which was obtained by directly using gradient-enriched linear-elastic notch stresses strongly supports the idea that GE is a powerful tool suitable for designing notched concrete components against high-cycle fatigue. This result is very promising also because the required stress analysis can directly be performed by using standard Finite Element (FE) solvers.