Crush-crack': a non-local damage model for concrete

Abstract

A model is presented based on the non‐local damage theory. It sets out to describe the behavior of concrete under free‐variable loads, which are constant in sign. Its purpose is to analyze shear behavior and high strain‐gradient localized problems, and it takes Mazar's model as a starting point with reference to the basic idea of a scalar isotropic non‐local damage controlled by principal tensile strains. In addition, the other two main features are an internal variable denoted to the control or reversible volumetric expansion in compression, and irreversible strains aimed at modelling crushing in compression and cracks both in tension and compression. As a consequence, induced‐anisotropy, dilatancy and path‐dep endency can be reproduced. In particular, the modelling of micro‐ and macrocracks makes it possible to capture mixed‐mode cracking as well as aggregate interlock, which requires a residual stiffness to guarantee the transmission of transversal and normal stresses for assigned slips. The model requires the knowledge of the material response in uniaxial tension and compression, and biaxial compression tests which can be introduced directly by adopting experimental curves, or by means of a reduced number of parameters. The effectiveness of the model is shown through comparisons with several sets of experimental tests on both small specimens, assumed to be homogeneous, and boundary value problems.

Strain gradient theory based on a new framework of non-local model

“…The governing equations of the present boundary problem consist of the integral type constitutive equations (14-16), the equilibrium equation (39), and the boundary conditions Eqs. (40)(41)(42).…”

“…In order to achieve objective and properly convergent numerical solutions for localized damage, Bazant [37] and Bazant and Chang [38] proposed formulations of a non-local strain-softening theory. The non-local formulation of Mazars' model was advanced by di Prisco and Mazars [39]. Kennedy and Nahan [40] proposed a non-local anisotropic damage model.…”

Non-local damage model based on displacement averaging

“…It is important to note that 0I K and a I K vanish if the distance x I − x K between points I and K is larger than the non-local interaction radius R. So the sums in (15) and (16) do not need to be taken over all Gauss points K or L but only over those that are located inside the sphere or circle of radius R centred at point I . Moreover, since the coefficients a I K are needed at every iteration of every incremental step and do not vary during the simulation, they should be evaluated only once and then stored, rather than recomputed each time they are needed.…”

“…where a IK are the non-local interaction coefficients defined in (16). To increase efficiency, one can substitute the strain approximation and transform the sum over Gauss points into a sum over nodes.…”

“…Various aspects of non-local damage theory were studied e.g. in References [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”