The Numerical Simulation Of Size Effect On Concrete Strength Based On The First-order Damage Gradient Theory

The macro mechanical response of concrete is influenced by its mesoscopic structures.The classical constitutive models and the empirical models cannot capture the macro-micro correlation.Although the numerical simulations can reflect some regularities of size effect on strength of concrete,their results are mesh dependence and difficult to reveal the physical nature.We try to describe the size effect of concrete in the form of gradient damage constitutive,so that we can avoid the trivial mesoscopic structures simulations and overcome the mesh-dependence.Firstly,the damage gradient and the internal length scale(the key representative of the concrete mesoscopic structures)are introduced into the classical damage constitutive.Based on the first-order gradient damage theory,the correlation on the macro mechanical response of concrete between its mesoscopic structures is established,and the size effect of concrete is described in the form of gradient damage constitutive.By using the non-uniform finite difference mesh based on the Gauss Point in the resolve of the damage gradient,we developed a numerical algorithm for the gradient damage constitutive.Finally,a nonlinear finite element program is written and be used in the simulations of the size effect on strength of concrete beams under pure bending and three points bending.The results show that:(1)By introducing the damage gradient and internal length scale into the classical damage constitutive,the first-order gradient damage theory can describe the size effect of concrete under various of structure shapes and loading conditions,which create a new approach to studying the size effect of concrete.(2)With the increase of the internal length scale,the influence of damage gradient become stronger and the size effect is more pronounced.If the heterogeneity of concrete cannot be negligible,the influence of damage gradient on the macro mechanical response of concrete cannot be negligible.(3)With the increase of the specimen size,the nominal strength of unnotched beams decreased.The nominal strength tends to a constant value,while specimen size tends to infinite.(4)The initial damage affects the ultimate value of concrete nominal strength.With the increase of the initial damage,the ultimate value of concrete nominal strength decreased.(5)The size effect of unnotched concrete beams can be described by the gradient damage size effect law proposed in this paper.