Size effect on nominal flexural strength of concrete beams influenced by damage gradient

Abstract Based on the first-order gradient damage theory where a damage gradient D ,m and internal characteristic length parameter l m were introduced into the constitutive equations, an approach is proposed to consider the influence of damage gradients on the size effect of concrete beams. In the numerical implementation of the first-order gradient damage theory, damage values at Gauss points are calculated in each iterative step of non-linear finite element analysis, then the damage gradients of Gauss points are calculated by using the finite difference method. Geometrically similar unnotched pure bending concrete beams with a fixed ratio 4 of length to depth are simulated. The results show that the nominal flexural strength M nom increases linearly with the internal characteristic length parameter l m and decreases monotonically with the beam depth d . When l m equals to zero, the nominal flexural strength M nom becomes a constant. Otherwise, the size effect markedly increases with the internal characteristic length parameter l m . A gradient damage size effect law (GDSEL) is proposed to predict the size effect of unnotched concrete beams. When the beam depth d  → ∞, the GDSEL produces a horizontal asymptote in the plot of M nom versus d .