Michał Nitka

Discrete element method simulations of fracture in concrete under uniaxial compression based on its real internal structure

The paper describes experimental and numerical results of concrete fracture under quasi-static uniaxial compression. Experimental uniaxial compression tests were performed on concrete cubic specimens. Fracture in concrete was detected at the aggregate level by means of three non-destructive methods: three-dimensional X-ray microcomputed tomography, two-dimensional scanning electron microscope and manual two-dimensional digital microscope. The discrete element method was used to directly simulate experiments. Concrete was modelled as a random heterogeneous four-phase material composed of aggregate particles, cement matrix, interfacial transitional zones and macrovoids based on experimental images. Two- and three-dimensional analyses were carried out. In two-dimensional analyses, the real aggregate shape was created by means of clusters of spheres. In three-dimensional calculations, spheres were solely used. A satisfactory agreement between numerical and experimental results was achieved in two-dimensional analyses. The model was capable of accurately predicting complex crack paths and the corresponding stress–strain responses observed in experiments.

A DEM—FEM two scale approach of the behaviour of granular materials

We study the macroscopic behaviour of granular material, as a consequence of the interactions of individual grains at the micro scale. A two‐scale approach of computational homogenization is considered. On the micro‐level, we consider granular structures modelled using the Discrete Element Method (DEM). Grain interactions are modelled by normal and tangential contact laws with friction (Coulomb’s criterion). On the macro‐level, we use a Finite Element Formulation (FEM). The upscaling technique consists in using the response of the DEM model at each Gauss point of the FEM discretisation to derive numerically the constitutive response. In this process, a tangent operator is generated together with the stress increment corresponding to the strain increment in the Gauss point. In order to get more insight on the consistency of the resulting constitutive response, we compute the determinant of the acoustic tensor associated with the tangent operator. This quantity is known to be an indicator of a possible loss...

Periodic Stick-Slip Deformation of Granular Material Under Quasi-static Conditions

Stick-slip motion is generally observed in situations involving dry friction. It is commonly present in granulates and results from interactions at micro-scale. Analysing the data base collected during a series of small scale model tests the evidence was found of periodic deformation mode, induced within the granular material by a series of very small displacement increments. Image analysis was used to study the phenomenon. It was found that there exist minimum displacement of the external boundary necessary to produce ‘plastic localization’, being a function of the external load and grain coarseness.

Discrete Modelling of Micro-structural Phenomena in Granular Shear Zones

The micro-structure evolution in shear zones in cohesionless sand for quasi-static problems was analyzed with a discrete element method (DEM). The passive sand failure for a very rough retaining wall undergoing horizontal translation towards the sand backfill was discussed. To simulate the behaviour of sand, the spherical discrete model was used with elements in the form of rigid spheres with contact moments.

Two Scale Model (FEM-DEM) For Granular Media

The macroscopic behavior of granular materials, as a consequence of the interactions of individual grains at the micro scale, is studied in this paper. A two scale numerical homogenization approach is developed. At the small-scale level, a granular structure is considered. The Representative Elementary Volume (REV) consists of a set of N polydisperse rigid discs (2D), with random radii. This system is simulated using the Discrete Element Method (DEM) – molecular dynamics with a third-order predictor-corrector scheme. Grain interactions are modeled by normal and tangential contact laws with friction (Coulomb’s criterion). At the macroscopic level, a numerical solution obtained with the Finite Element Method (FEM) is considered. For a given history of the deformation gradient, the global stress response of the REV is obtained. The macroscopic stress results from the Love (Cauchy-Poisson) average formula including contact forces and branch vectors joining the mass centers of two grains in contact. The upscaling technique consists of using the DEM model at each Gauss point of the FEM mesh to derive numerically the constitutive response. In this process, a tangent operator is generated together with the stress increment corresponding to the given strain increment at the Gauss point. In order to get more insight into the consistency of the two-scale scheme, the determinant of the acoustic tensor associated with the tangent operator is computed. This quantity is known to be an indicator of a possible loss of uniqueness locally, at the macro scale, by strain localization in a shear band. The results of different numerical studies are presented in the paper. Influence of number of grains in the REV cell, numerical parameters are studied. Finally, the two-scale (FEM-DEM) computations for simple samples are presented.