Boundary effects on behaviour of granular material during plane strain compression

The paper investigates the boundary effect on the behaviour of granular materials during plane strain compression using finite element method. A micro-polar hypoplastic constitutive model was used. The numerical calculations were carried out with different initial densities and boundary conditions. The behaviour of initially dense, medium dense and loose sand specimen with very smooth or very rough horizontal boundary was investigated. The formation of shear zones gave rise to different global and local stress and strain. Comparisons of the mobilized internal friction, dilatancy and non-coaxiality between global and local quantities were made.     

Modeling of textural anisotropy in granular materials with stochastic micro-polar hypoplasticity

The paper deals with a numerical analysis of the effect of textural anisotropy on the behaviour of cohesionless granular materials with consideration of shear localization. For a simulation of the mechanical behaviour of a granular material during a monotonic deformation path, an isotropic micro-polar hypoplastic constitutive model was used. To describe textural effects, spatially correlated random fields of the initial void ratio were subject to rotation against the horizontal axis. The 2D random fields were generated using a conditional rejection method. The results were compared with those obtained with an anisotropic micro-polar constitutive model for a uniform distribution of the initial void ratio. The calculations were carried out with an initially dense granular specimen during plane strain compression under constant lateral pressure.     

Comparative FE-studies of shear localizations in granular bodies within a polar and non-local hypoplasticity

Paper presents a FE-analysis of shear localizations in granular bodies with a finite element method based on a hypoplastic constitutive law. The law can reproduce essential features of granular bodies in dependence on the void ratio, pressure level and deformation direction. To simulate the formation of a spontaneous shear zone inside of cohesionless sand during plane strain compression, a hypoplastic law was extended by polar and non-local terms. The effect of both models on the thickness of a shear zone was compared.     

Computational limit analysis of rigid-plastic bodies in plane strain

This paper deals with the computational methods for limit analysis of plane strain problems. The finite element mathematical programming formula (FE-MPF) for determining the upper bound load multiplier established by the authors earlier is adopted and modified for plane strain problems. The penalty method is used to impose the incompressibility constraint. The FE-MPF is solved by a direct iteration procedure without the need of a searching process. This algorithm is not sensitive to the volumetric locking effect. And it can be easily extended to the limit analysis of three dimensional problems. The results of numerical examples are satisfactory and show the stable convergency of the present algorithm.     

Non-normality and bifurcation in plane strain tension and compression

The bifurcations of a rectangular block subject to plane strain tension or compression are investigated. The block material is taken to be incompressible and is characterized by an incrementally linear constitutive law for which “normality” does not necessarily hold. The consequences of non-normality regarding bifurcation are given primary emphasis here. The characteristic regimes of the governing equations (elliptic, parabolic and hyperbolic) are detennined. In each of these regimes both symmetric and antisymmetric diffuse bifurcation modes are available. Additionally, in the hyperbolic and parabolic regimes, bifurcation into a localized shear band mode is also possible. Particular attention is given to the limiting cases of long wavelength and soon wavelength diffuse bifurcation modes. The range of parameter values is identified for which bifurcation into some localized mode may precede bifurcation into a long wavelength diffuse mode. Some difficulties associated with employing a linear incremental solid in a bifurcation analysis, when primary interest is in the bifurcation of an underlying elastic-plastic solid, are also discussed.     

Shear band formation in thermo-viscoplastic solids under plane strain compression

The plane strain compression of a rectangular block is numerically investigated for the study of dynamic shear band development in thermo-elasto-viscoplastic materials from an internal inhomogeneity. As expected, it plays an important role in triggering the onset of shear, localization as well as thermal softening. And the competition between the strain, strain-rate hardening and thermal softening exists throughout the process. It is found that shear band develops at a 45-degree angle to the compression axis. In the light of given patterns of deformation and temperature, shear band evolution accelerated by thermal softening is retarded by the inertial effects. Interestingly, a similar temperature band is also formed along the trajectory of the localized deformation band. The calculations also show the energy evolution during the coupled thermo-mechanical process of shear band propagation. Finally, the mesh effect is discussed in terms of the numerical results from two different meshes. The project is supported by the National Natural Sciences Foundation of China.     

The strain rate intensity factor in the plane strain compression of thin anisotropic metal strip

Using an available analytic solution for instantaneous plane strain compression of a plastically anisotropic strip between two parallel plates the strain rate intensity factor is found assuming Hill’s quadratic yield criterion. The distribution of material properties is uniform. The effect of parameters characterizing plastic anisotropy of the strip on the magnitude of the strain rate intensity factor is demonstrated. A possibility to replace the strain rate intensity factor with the plastic work rate intensity factor is discussed. Singular behavior of the plastic spin in the vicinity of the friction surface is revealed and discussed.     

On the strong ellipticity for orthotropic micropolar elastic bodies in a plane strain state

In the present paper we consider an orthotropic micropolar elastic material subject to a state of plane strain. In this context, we establish necessary and sufficient conditions for the strong ellipticity of constitutive coefficients. Furthermore, we study existence of progressive plane waves under the strong ellipticity conditions previously determined. Finally, we detail the results obtained for a specific class of materials related to tetragonal systems.     

Modeling of deformation and rotation bands and of deformation induced grain boundaries in IF steel aggregate during large plane strain compression

A computation using crystal plasticity modeling of an actual IF steel aggregate plane strain compression deformation, underlines the formation of different deformation bands morphologies and grain splitting occurrence, already experimentally observed by different authors. The model based on dislocation densities as internal variables, developed in the framework of finite deformation and implemented in the Finite Element Method, is able to capture the main characteristics of different inhomogeneities and to analyze their formation and further development with strain, from the determination of the active and latent slip systems, and also from the quantification of their dislocation densities and corresponding glide rates evolutions. The respective boundary conditions and material properties effects are discussed.     

Plasticity size effects in tension and compression of single crystals

The effect of size and loading conditions on the tension and compression stress-strain response of micron-sized planar crystals is investigated using discrete dislocation plasticity. The crystals are taken to have a single active slip system and both small-strain and finite-strain analyses are carried out. When rotation of the tensile axis is constrained, the build-up of geometrically necessary dislocations results in a weak size dependence but a strong Bauschinger effect. On the other hand, when rotation of the tensile axis is unconstrained, there is a strong size dependence, with the flow strength increasing with decreasing specimen size, and a negligible Bauschinger effect. Below a certain specimen size, the flow strength of the crystals is set by the nucleation strength of the initially present Frank-Read sources. The main features of the size dependence are the same for the small-strain and finite-strain analyses. However, the predicted hardening rates differ and the finite-strain analyses give rise to some tension-compression asymmetry.     

Motion of bodies in a granular bed

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 27–30, March–April, 1991.     

Effects of texture on shear band formation in plane strain tension/compression and bending

In this study, effects of typical texture components observed in rolled aluminum alloy sheets on shear band formation in plane strain tension/compression and bending are systematically studied. The material response is described by a generalized Taylor-type polycrystal model, in which each grain is characterized in terms of an elastic–viscoplastic continuum slip constitutive relation. First, a simple model analysis in which the shear band is assumed to occur in a weaker thin slice of material is performed. From this simple model analysis, two important quantities regarding shear band formation are obtained: i.e. the critical strain at the onset of shear banding and the corresponding orientation of shear band. Second, the shear band development in plane strain tension/compression is analyzed by the finite element method. Predictability of the finite element analysis is compared to that of the simple model analysis. Third, shear band developments in plane strain pure bending of a sheet specimen with the typical textures are studied. Regions near the surfaces in a bent sheet specimen are approximately subjected to plane strain tension or compression. From this viewpoint, the bendability of a sheet specimen may be evaluated, using the knowledge regarding shear band formation in plane strain tension/compression. To confirm this and to encompass overall deformation of a bent sheet specimen, including shear bands, finite element analyses of plane strain pure bending are carried out, and the predicted shear band formation in bent specimens is compared to that in the tension/compression problem. Finally, the present results are compared to previous related studies, and the efficiency of the present method for materials design in future is discussed.     

Effect of particle size distribution on micro- and macromechanical response of granular packings under compression

The role of particle size heterogeneity on micro- and macromechanical properties of assemblies of spherical particles was studied using DEM simulations. The response to an imposed load of a granular material composed of non-uniformly sized spheres subjected to uniaxial confined compression was investigated. A range of geometrical and micro-mechanical properties of granular packings (e.g., void fraction, contact force distribution, average coordination number and degree of mobilisation of friction at contacts between particles) were examined, and provided a more accurate interpretation of the macroscopic behaviour of mixtures than has previously been available. The macromechanical study included stress transmission, stiffness and angle of internal friction of the granular assemblies.The degree of polydispersity showed slight effect on both, the void fraction and the elastic properties of the system. The tendency for increase in the lateral-to-vertical pressure ratios was observed with an increasing degree of particle size heterogeneity; however, the different pressure ratios calculated for samples with various degrees of polydispersity lay within the range of data scatter.     

Evolution of plane disturbances in hypoplastic granular materials

Received July 5, 2000 / Published online February 14, 2001     

Influence of damage on properties of strain localization in geomaterials at plane stress and plane strain

Summary By regarding geomaterials under loading as a mixture of intact and damaged parts, we investigate the influence of damage on the properties of strain localization in elastoplastic geomaterials at plane stress and plane strain. Conditions for the onset of strain localization including the effects of damage are derived for the cases of plane strain and plane stress. Discussed are the inclination of the localized band and the hardening modulus corresponding to the onset of strain localization. It is shown that the properties of the strain localization are dependent on the damage and the capacity of bearing hydrostatic pressure by the damaged part, and that damage may induce an earlier onset of strain localization and lead to instability of a geomaterial.accepted for publication 11 March 2004