Jacek Tejchman

Numerical study on patterning of shear bands in a Cosserat continuum

SummaryNumerical simulation of patterns of shear bands in biaxial compression tests using an elasto-plastic Cosserat constitutive equation is presented. Random distribution of the material properties acts as a trigger for the localized deformation. Two types of stress-strain curves, namely strain softening and strain softening followed by strain hardening, are investigated. It is shown that the characteristic of the stress-strain curve is crucial for the patterning of shear bands. While calculations with the stress-strain curve with solely softening yield only one single shear band, a flock of shear bands can be obtained with the stress-strain curve with softening followed by hardening. Benefited from the characteristic length provided by the Cosserat elasto-plastic constitutive equation, the dependence of the calculation on the mesh-size is avoided.

Shearing of a narrow granular layer with polar quantities

The paper deals with numerical investigations of the behaviour of granular bodies during shearing. Shearing of a narrow layer of sand between two very rough boundaries under constant vertical pressure is numerically modelled with a finite element method using a hypoplastic constitutive relation within a polar (Cosserat) continuum. The constitutive relation was obtained through an extension of a non-polar one by polar quantities, viz. rotations, curvatures, couple stresses using the mean grain diameter as a characteristic length. This relation can reproduce the essential features of granular bodies during shear localization. The material constants can be easily determined from element test results and can be estimated from granulometric properties. The attention is laid on the influence of the initial void ratio, pressure level, mean grain diameter and grain roughness on the thickness of shear zones. The results of shearing are also compared to solutions without the polar extensions. The FE-calculations demonstrate that polar effects manifested by the appearance of grain rotations and couple stresses are significant in the shear zone, and its thickness is sensitive to the initial void ratio, mean grain diameter and layer height. The effect of the pressure level is rather low within the considered range.

Numerical Simulation of Shear Band Formation with a Polar Hypoplastic Constitutive Model

Abstract Recently, a hypoplastic constitutive model based on non-linear tensorial functions was proposed by Wu and Bauer [1] for granular materials. The model covers a broad range of stress level and initial density and is applicable for both initial deformation and fully developed plastic flow. In the present paper, the hypoplastic constitutive model is implemented in a finite element code to investigate the shear band formation in granular materials during biaxial compression tests. Emphasis is placed on the effect of the stress level and of the initial density on shear banding. Initiation of shear bands is triggered by an imperfection in the initial material properties. Comparison between the numerical calculations and the experimental results shows satisfying agreement. The advantages of the hypoplastic approach are outlined.

Silo-music and silo-quake experiments and a numerical Cosserat approach

Abstract During silo emptying dynamical effects, viz. vibrations (called silo music) and shocks (called silo quake) come into being in a silo fill. Model and full-scale experiments were carried out to investigate these dynamical phenomena. Model tests were performed with a slender perspex cylinder. Silo music was observed with a dry sand, and silo quake was registered with a weakly cohesive sand. Full-scale tests were carried out in a silo in Poland filled with rape seeds. Pronounced pulsations during silo emptying were registered. Experiments with a dry sand were modelled with a finite element method, with consideration of inertial forces, on the basis of an elasto-plastic Cosserat type theory following Miihlhaus. Calculations were performed for a velocity controlled mass flow and a free outflow. Comparison between the numerical calculations and the experimental results shows rather satisfactory agreement.

FE-studies on the influence of initial void ratio, pressure level and mean grain diameter on shear localization

The paper is concerned with shear localization in the form of a spontaneous shear zone inside a granular material during a plane strain compression test. The influence of an initial void ratio, pressure and a mean grain diameter on the thickness of a shear zone is investigated. A plane strain compression test with dry sand is numerically modelled with a finite element method taking into account a polar hypoplastic constitutive relation which was laid down within a polar (Cosserat) continuum. The relation was obtained through an extension of a non-polar hypoplastic constitutive law according to Gudehus and Bauer by polar quantities: rotations, curvatures, couple stresses and a characteristic length. It can reproduce the essential features of granular bodies during shear localization. The material constants can be easily calibrated. The FE-calculations demonstrate an increase in the thickness of the shear zone with increasing initial void ratio, pressure level and mean grain diameter. Polar effects manifested by the appearance of grain rotations and couple stresses are only significant in the shear zone. A comparison between numerical calculations and experimental results shows a satisfying agreement. Copyright

Patterns of shear zones in granular bodies within a polar hypoplastic continuum

SummaryThe paper deals with numerical investigations on the patterning of shear zones in granular bodies. The behavior of dry sand during plane strain compression tests was numerically modelled with a finite element method using a hypoplastic constitutive relation within a polar (Cosserat) continuum. The constitutive relation was obtained through an extension of a non-polar one by polar quantities, viz. rotations, curvatures, couple stresses using the mean grain diameter as a characteristic length. This relation can reproduce the essential features of granular bodies during shear localisation. During FE-calculations, the attention was laid on the influence of boundary conditions and the distribution of imperfections in the granular specimen on the formation of patterns of shear zones.

Technical concept to prevent the silo honking

Abstract During emptying of tall cylindrical silos made of aluminium, the phenomenon of the silo honking is often created. The silo honking appears in the form of an annoying noise connected to strong vibrations of silo walls. Full-scale experiments in aluminium silos containing polymer granulates were performed to investigate this phenomenon. During experiments, accelerations and deformations of the wall, and sound pressures inside and outside the silo were measured. A reliable, practical method to completely suppress the silo honking and to significantly reduce dynamic pulsations during silo emptying was proposed and described in detail. The method was verified with model experiments and full-scale tests.

Continuous and Discontinuous Modelling of Fracture in Concrete Using FEM

The book analyzes a quasi-static fracture process in concrete and reinforced concrete by means of constitutive models formulated within continuum mechanics. A continuous and discontinuous modelling approach was used. Using a continuous approach, numerical analyses were performed using a finite element method and four different enhanced continuum models: isotropic elasto-plastic, isotropic damage and anisotropic smeared crack one. The models were equipped with a characteristic length of micro-structure by means of a non-local and a second-gradient theory. So they could properly describe the formation of localized zones with a certain thickness and spacing and a related deterministic size effect. Using a discontinuous FE approach, numerical results of cracks using a cohesive crack model and XFEM were presented which were also properly regularized. Finite element analyses were performed with concrete elements under monotonic uniaxial compression, uniaxial tension, bending and shear-extension. Concrete beams under cyclic loading were also simulated using a coupled elasto-plastic-damage approach. Numerical simulations were performed at macro- and meso-level of concrete. A stochastic and deterministic size effect was carefully investigated. In the case of reinforced concrete specimens, FE calculations were carried out with bars, slender and short beams, columns, corbels and tanks. Tensile and shear failure mechanisms were studied. Numerical results were compared with results from corresponding own and known in the scientific literature laboratory and full-scale tests.

FE-studies on rapid flow of bulk solids in silos

Abstract This paper contains results of numerical modelling of the onset of silo flow for granular material in a model silo with convergent walls. The calculations were performed with a finite element method based on a polar elasto-plastic constitutive relation by Mühlhaus. It differs from the conventional theory of plasticity by the presence of Cosserat rotations and couple stresses using a mean grain diameter as a characteristic length. The characteristic length causes that numerical results do not depend upon the mesh discretisation. The model tests on rapid silo flow of glass beads performed by Renner in a glass hopper with a large wall inclination from the bottom were numerically simulated. The FE-calculations were performed for plane strain by taking into account inertial forces and linear viscous damping. A satisfactory agreement between numerical and experimental results was obtained. In addition, the FE-calculations were performed for very rough walls. Advantages and limitations of a continuum approach for simulations of rapid silo flow were outlined.

Bedding effects in bulk solids in silos: experiments and a polar hypoplastic approach

This paper is concerned with bedding effects in granular bulk solids in silos. Finite element (FE)-analyses were performed for a cylindrical thin-walled steel model silo with imperfections containing dry sand. Numerical calculations were carried out for an axisymmetric case with a polar hypoplastic constitutive relation which can capture the salient properties of granular materials. In the FE-calculations, different types of wall displacements along the silo height were taken into account to model roughly the formation of buckles due to initial imperfections of the silo wall. The effects of the initial void ratio and mean grain diameter of bulk solids, initial stress state, wall roughness, and size and form of buckles were studied. The numerical results clearly show that the modelling of a bedding effect of bulk solids in silos by means of springs is too simple and can lead to strongly unrealistic predictions of the bedding modulus.