Calculations of fracture process zones on meso-scale in notched concrete beams subjected to three-point bending

Modelling of concrete fracture at aggregate level using FEM and DEM based on X-ray μCT images of internal structure

“…A simple isotropic damage continuum model describes the material degradation with the aid of only a single scalar damage parameter D growing monotonically from zero (undamaged material) to one (completely damaged material) [3][4][5]30,39]. A damage variable D is associated with a degradation of the material due to the propagation and coalescence of micro-cracks and micro-voids.…”

“…At the meso-scale, concrete may be considered as a composite material wherein four important phases may be separated: cement matrix, aggregate, interfacial transition zones ITZs and macro-voids [2,[4][5][6][7]. In particular, the presence of aggregate and ITZs is important since the volume fraction of aggregate can be as high as 70-75% in concrete and ITZs with the thickness of about 50 lm are always the weakest regions in usual concretes [2], wherein cracking starts (because of their higher porosity).…”

“…The concrete behaviour at the meso-scale may be described with continuum finite element (FE) models [4,5,[11][12][13] and discrete models [2,14,15]. Within discrete methods, the most popular ones are: the classical particle discrete element method (DEM) [16][17][18][19][20][21], interface element models with constitutive laws based on non-linear fracture mechanics [22,23] and lattice methods [2,15,[24][25][26][27][28].…”

“…3D X-ray micro-computed tomography and 2D scanning electron microscope (SEM). The FE simulations of tensile deformation were carried out with a simple isotropic continuum constitutive damage model enhanced by a characteristic length of micro-structure by means of a non-local theory [5,30]. The DEM calculations were performed with the three-dimensional spherical discrete element model YADE, which was developed at University of Grenoble [31,32].…”

Computational modelling of concrete behaviour under static and dynamic conditions

“…In turn, other researchers conclude that the characteristic length is not a constant and it depends on the type of the boundary value problem and the current level of damage [43]. Based on our both numerical simulations of concrete and reinforced concrete beams under bending and experiments using a digital image correlation DIC technique in order to measure the width of a localized zone on the concrete surface [44][45][46], the characteristic length l c of micro-structure was found to be about 5 mm in usual concrete (using the Gauss distribution function). A proper non-local transformation requires that a non-local field corresponding to a constant local field remains constant in the vicinity of a boundary.…”