Katalin Bagi

Stress and strain in granular assemblies

Abstract The aim of this paper is to clarify the meaning of the mechanical state variables stress and strain in the case of random granular assemblies. Stress and strain are expressed in terms of local, micro-level variables with the help of two complementary geometrical systems. The two expression show a strong duality which is also analysed in the paper.

Contact rolling and deformation in granular media

The paper considers rotations at different scales in granular materials: the rotations of individual particles, the rolling and rigid-rotation of particle pairs, the rotational interactions of a particle within its cluster of neighbors, and the rotation of material regions. Numerical, Discrete Element Method (DEM) simulations on two- and three-dimensional (2D and 3D) assemblies show that particle rotations are diverse, that they increase with strain until the material begins to soften, and that they are expressed in spatial patterns, even at small strains. The interactions of a pair of particles are a combination of three modes: a contact deformation mode, a contact rolling mode, and a mode of rigid pair motions. Definitions are presented for each mode, including four different definitions of contact rolling. A rolling curl is also defined, which describes the cumulative rolling of neighboring particles around a central particle or sub-region. At a larger scale, material deformation and rotation are measured within small sub-regions of material, and the material deformation can be attributed to separate contributions of contact rolling, contact deformation, and the rigid-rotation of particle pairs. The diversity and extend of contact rolling were measured in 2D and 3D simulations. A dominant rolling pattern was observed, which resembles the interactions of rolling gears. This pattern can extend to distances of at least six particle diameters from a central particle.

Microstructural stress tensor of granular assemblies with volume forces

This paper focuses on the discrete expression of stress tensors of assemblies containing discrete particles with volumetric loads acting on them in addition to boundary forces. Instead of the concept of continuum point, a domain containing a finite number of grains is considered. This domain is replaced by a suitably chosen equivalent continuum whose average stress is expressed-assuming that the grains are in equilibrium-in terms of contact forces and properly defined branch vectors. Symmetry of the stress tensor is also analyzed.

A quasi-static numerical model for micro-level analysis of granular assemblies

Abstract This paper introduces a quasi-static numerical model based on the displacement method and on the compilation of global equilibrium equations of granular assemblies. The model is able to describe large displacements, rearrangements and local instabilities.

A Definition of Particle Rolling in a Granular Assembly in Terms of Particle Translations and Rotations

The paper presents a definition of particle rolling for the interactions of two and three-dimensional particles of arbitrary shape, in case of infinitesimal particle translations and rotations. The definition is based on a purely kinematical analysis, and it is shown to satisfy the objectivity condition.

Computational Modeling of Masonry Structures Using the Discrete Element Method

The Discrete Element Method (DEM) has emerged as a solution to predicting load capacities of masonry structures. As one of many numerical methods and computational solutions being applied to evaluate masonry structures, further research on DEM tools and methodologies is essential for further advancement. Computational Modeling of Masonry Structures Using the Discrete Element Method explores the latest digital solutions for the analysis and modeling of brick, stone, concrete, granite, limestone, and glass block structures. Focusing on critical research on mathematical and computational methods for masonry analysis, this publication is a pivotal reference source for scholars, engineers, consultants, and graduate-level engineering students.

Discrete Element Analysis of the Minimum Thickness of Oval Masonry Domes

ABSTRACT This study focuses on domes the ground plan of which, instead of the more common circular shape, is an oval, and aims at finding the minimally necessary uniform wall thickness for domes of different geometries loaded by their selfweight. The discrete element code 3DEC was applied because of its capability of simulating the collapse mechanisms of masonry structures. Results on the minimal wall thickness, corresponding masonry volume and failure mechanisms for different dome geometries are presented. Three ranges of the friction coefficient were found. For very low frictional resistance collapse happens with pure frictional sliding, for any arbitrarily large wall thickness. In the range of relatively high (i.e., realistic) friction coefficients the structure collapses without any sliding if the wall is not sufficiently thick, and in the observed range of the friction coefficient the necessary wall thickness is nearly insensitive to its value (collapse initiates with hinging cracks only). Between the two domains an intermediate behavior was found: combined cracking and sliding collapse modes occur for insufficient wall thickness, and the minimal thickness strongly depends on the friction coefficient. The critical and transitional friction coefficients separating the failure modes were determined for different eccentricities of the groundplan.

Numerical analysis of loose and bonded granular materials

Abstract A quasi-static numerical algorithm is introduced for the analysis of quasi-static state-changing processes of granular materials. The paper presents the application possibilities of the model. Both sand-like and cemented materials can be analysed; rearrangements, instabilities, local slips, crack opening, etc., can easily be followed.

Discrete Element Analysis of the Shear Resistance of Planar Walls with Different Bond Patterns

The paper presents discrete element simulations of the in-plane horizontal shear of planar walls having different bond patterns. The aim of the analysis was to decide whether the shear resistance could be improved by applying patterns containing vertical bricks. The results show that the presence of vertical bricks increases the shear resistance in case of low vertical confining load only, and the length-to-height ratio of the wall also significantly affects the shear resistance.

Analysis of a Lunar Base Structure Using the Discrete-Element Method

A lunar base structure must provide protection against various hazards such as bombardment by meteorites, radiation, or extreme changes in temperature. A possible structural solution was proposed in the literature. The lunar base, planned to be built in a long, narrow valley with solid rock walls, would consist of three main elements: a masonry vault, supported by the rock walls of the valley; a regolith layer a few meters thick on top of it to dissipate radiation and the kinetic energy of impacting meteorites, and to balance temperature; and inflatable units under the arch to serve as a living area for humans. The objective was to check the feasibility of this idea from a structural mechanics point of view. A two-dimensional discrete-element model of the vault-regolith system was constructed, and the behavior of the structure under its own weight was analyzed. Initial simulations on the effect of meteorite impacts were conducted, but a significantly improved model would be required to continue this analy...