Cohesive stresses and size effects in elasto-plastic and quasi-brittle materials

Abstract

A novel approach to the derivation of Bažant’s size effect law is presented. Contrarily to the original Lagrangian derivation which hinged on energetic consideration, a Newtonian approach based on local stress intensity factors is presented. Through this approach, it is shown that Bažant’s size effect law is the first (and dominant) term in a series expansion for the nominal stress. Furthermore, analytical expressions forB are derived for selected specimen geometries. It is also shown that size effect is exhibited not only by quasi-brittle materials (such as concrete), but by elasto-plastic materials too. Finally, for three point bend concrete specimens, it is shown that a nonlinear fracture mechanics analysis (with non-zero tensile strength) is practically identical to a linear elastic fracture mechanics analysis with zero fracture toughness.