Simple Shear Simulations Research Articles

The influence of viscous behavior and static shear stress on the cyclic strengths of plastic soil: a numerical study

An accurate understanding of the cyclic behavior of clays and plastic silts is important for system performance predictions during earthquake loading. This paper presents the results of a numerical investigation into the individual and combined influences of static shear stress and viscous strength gain on the cyclic resistance of clays and plastic silts. Using the viscoplastic constitutive model PM4SiltR implemented in the finite difference program FLAC 8.1, the cyclic behaviors of the plastic soils were simulated using single-element cyclic direct simple shear simulations. A parametric analysis was performed with different combinations of viscous strength gains and static shear stresses. The effects of static shear stress and viscous strength gain varied under monotonic and cyclic loading conditions. Numerical findings suggest empirical correlations developed using scant laboratory data may not accurately predict the reduction of cyclic strengths with increasing static shear stress. Furthermore, sizable magnitudes of monotonic viscous strength gains only produced a marginal increase in cyclic strengths. The findings from this study highlight the need for future experimental laboratory testing to validate the numerical findings, to improve the accuracy of performance predictions of geosystems constructed with clays and plastic silts during and following earthquake loading.

Liquefaction of granular materials in constant-volume cyclic shearing: Transition between solid-like and fluid-like states

By means of 3D-DEM cyclic simple shear simulations at constant volume, this paper analyzes the evolution of the internal structure during cyclic liquefaction of dense granular media. Upon liquefaction, the granular system undergoes a fast transition to a regime where the fluid-like shear strain develops. This regime is characterized by low shear modulus, decreasing dilatancy, and reduced shear viscosity. We analyze the internal structure by means of several micro- and meso-scale descriptors, including coordination number, fabric anisotropy, number of clusters, a fraction of maximum cluster size, and a percolation index. We select a typical post-liquefaction cycle in which we highlight several particular states that naturally divide the cycle into different periods. During liquefaction, the system deforms significantly with an enhanced number of binary collisions initially and particle clusters subsequently. Both the coordination number and percolation index increase while fabric anisotropy oscillates. The fluid-like to solid-like transition is characterized by a well-defined value of the coordination number (3.6) when the particles percolate across the system. From the analysis of the micro- and meso-scale behaviors, we further discuss two possible criteria for exiting the fluid-like state based on the excess pore pressure.

Calibrating friction coefficients in discrete element method simulations with shear-cell experiments

Discrete Element Method (DEM) simulations coupled with shear cell experimental results have been used to investigate the flow behaviour of a dry particle assembly of glass beads in the quasi-static regime. Experimental studies have been undertaken using an FT4 powder shear cell apparatus, in parallel with extensive DEM simulations of both homogeneous simple shear and the FT4 shear cell itself. The findings show that it is not possible to accurately predict the bulk friction coefficient with homogeneous simple shear simulations unless both rolling and sliding friction are considered. There are, however, multiple pairs of sliding and rolling friction coefficients which can reproduce the experimental bulk friction coefficient. Sliding test experiments were conducted to yield the coefficient of sliding friction, and hence minimise the set of potentially correct pairs. Simulations of the full FT4 shear cell with two different calibration pairs, along with a pair without rolling friction, were then undertaken to understand the effect of their selection on realistic wall-bounded shearing conditions. Discrepancies were mainly found in the obtained radial contact number and velocity profiles, with increasing friction coefficients - particularly sliding friction - found to inhibit packing and particle velocity in the shear deformation zone. Comparison between homogeneous simple shear and shear cell simulation results showed a significant effect of the wall on the obtained force network, with almost a complete absence of the weakest structures which were seen supporting the strong structures in the simple shear scenario.

Plastic flow during equal-channel angular pressing with arbitrary tool angles

Equal-channel angular pressing (ECAP) allows to rapidly accumulate massive amounts of plastic strain and thus to promote grain refinement in metals, which is one of the main goals of severe plastic deformation methods. While early models have simplified the deformation during ECAP as simple shear, experimental observations and numerical simulations of fan-shaped deformation regions have motivated more elaborate analytical models that explicitly consider material flow through the region of most intense plastic straining. The two most prominent models (Beyerlein and Tomé, 2004), and (Tóth, 2003), allow to successfully predict texture evolution during ECAP, but their most basic versions have originally been limited to 90° ECAP tools. In this contribution, both models are extended to provide a detailed analysis of ECAP tools with arbitrary tool angles (in the practically relevant range from 90° up to 180°) that allows to fully describe novel developments in tool design. Most importantly, it is shown that a single free parameter is sufficient to modify the shape of the plastic deformation region, maintaining the simplicity of the corresponding original models. Explicit solutions are given in terms of strain rates and, by integration along a flow line, for strain tensor components, for equivalent strains per ECAP pass and for deformation gradients. The corresponding strain states predicted by both models are directly compared for arbitrary tool angles. It is further demonstrated that both models lead to similar strains in the two relevant limiting cases. Finally, exemplary fitting of experimental flow line data from Cu billets deformed in 90° and 120° tools allows for direct validation of the extended version of Tóth's model, demonstrating that it provides a sound basis for an in-depth experimental and theoretical analysis of plastic straining during ECAP in different tools and with varying processing parameters.

Undrained cyclic simple shear simulation of liquefiable granular particles subjected to large shear strains up to 100% by 3D DEM

Undrained cyclic simple shear simulation of liquefiable granular particles subjected to large shear strains up to 100% by 3D DEM

Fabric evolution of granular soils under multidirectional cyclic loading

Cyclic behavior of granular soils under multidirectional shaking is significantly different from that under unidirectional loading. In this study, a series of undrained simple shear simulations were conducted using a discrete-element method (DEM) under unidirectional and multidirectional loading conditions. Although the excess pore water pressure within a sample cannot reach the initial confining pressure, large shear strains of a similar amplitude still develop in samples under multidirectional loading. The simulation results further illustrate that granular soils have vastly different liquefaction resistance under different loading conditions. Evolution of soil fabric is also quantitatively studied in terms of inter-particle contacts and particle-void distribution. The same “stable state” of soil fabric will be reached under different multidirectional loading paths, which corresponds to that of a post-failure hardening state under unidirectional loading. The DEM study provides a new perspective in terms of microstructure evolution of granular soils under a variety of loading conditions.

Interface-mediated plasticity of nanoscale Al–Al2Cu eutectics

Laser surface re-melted Al–Al2Cu eutectic alloy with α-Al and θ-Al2Cu nanoscale lamellae exhibits high strength and good plasticity at room temperature, implying that the nanoscale θ-Al2Cu lamellae plastically co-deform with α-Al. Microscopy characterization reveal that plastic deformation of θ-Al2Cu lamellae is accommodated by localized shear on unusual slip planes of {121}Al2Cu. Herein, we elucidate interface-mediated deformation mechanisms of nanoscale Al–Al2Cu eutectics and investigate the structure and properties of the {001}Al‖{001}Al2Cu interface using atomistic simulations. Simulation results reveal that the interface is composed of two sets of misfit dislocations with the displacement shift complete vectors as Burgers vectors. We then conduct simple shear simulations to explore shear response and corresponding mechanisms of the Al–Al2Cu interface, and reveal that interfacial shear is accomplished through the gliding of misfit dislocations on the interface. Plasticity of nanoscale θ-Al2Cu lamellae is examined to be associated with localized shears on {121}Al2Cu planes, which are ascribed to the continuity of slip systems across Al–Al2Cu interfaces and accumulated lattice dislocations at interfaces.

Determination of pressure-viscosity relation of 2,2,4-trimethylhexane by all-atom molecular dynamics simulations

The Newtonian viscosity of 2,2,4-trimethylhexane at 293 K is determined at pressures from 0.1 MPa to 1000 MPa. Non-equilibrium molecular dynamics simulations are performed using AIREBO-M, an all-atom potential for hydrocarbons especially parameterized for high pressures. The steady-state shear stress and viscosity are determined from simple shear simulations at rates between 107 and 5⋅109s−1. At low pressures, simulation rates are low enough to reach the Newtonian regime. At high pressures, results are extrapolated to the Newtonian limit by fitting rate-dependent viscosities to Eyring theory. The variation of viscosity with pressure has an inflection point that is common for small molecules. Deviations from experiment are less than 40%.

Interface-Mediated Plasticity of Nanoscale Al-Al <sub>2</sub>Cu Eutectics

Laser surface re-melted Al-Al2Cu eutectic alloy with α-Al and θ-Al2Cu nanoscale lamellae exhibits high strength and good plasticity at room temperature, implying that the nanoscale θ-Al2Cu lamellae plastically co-deform with α-Al. Microscopy characterization reveal that plastic deformation of θ-Al2Cu lamellae is accommodated by localized shear on unusual slip planes of {121}Al2Cu. Herein, we elucidate interface-mediated deformation mechanisms of nanoscale Al-Al2Cu eutectics and investigate the structure and properties of the {001}Al‖{001}Al2Cu interface using atomistic simulations. Simulation results reveal that the interface is composed of two sets of misfit dislocations with the displacement shift complete vectors as Burgers vectors. We then conduct simple shear simulations to explore shear response and corresponding mechanisms of the Al-Al2Cu interface, and reveal that interfacial shear is accomplished through the gliding of misfit dislocations on the interface. Plasticity of nanoscale θ-Al2Cu lamellae is examined to be associated with localized shears on {121}Al2Cu planes, which are ascribed to the continuity of slip systems across Al-Al2Cu interfaces and accumulated lattice dislocations at interfaces.

Microscale Descriptors for Particle-Void Distribution and Jamming Transition in Pre- and Post-Liquefaction of Granular Soils

AbstractMicromechanical modeling provides significant insight into the fundamental mechanism of soil liquefaction. In this study, a series of undrained cyclic simple shear simulations were conducte...

A Free Interface Model for Static/Flowing Dynamics in Thin-Layer Flows of Granular Materials with Yield: Simple Shear Simulations and Comparison with Experiments

Flows of dense granular materials comprise regions where the material is flowing, and regions where it is static. Describing the dynamics of the interface between these two regions is a key issue to understanding the erosion and deposition processes in natural environments. A free interface simplified model for non-averaged thin-layer flows of granular materials has been previously proposed by the authors. It is a coordinate-decoupled (separated variables) version of a model derived by asymptotic expansion from an incompressible viscoplastic model with Drucker-Prager yield stress. The free interface model describes the evolution of the velocity profile as well as the position of the transition between static and flowing material. It is formulated using the coordinate Z in the direction normal to the topography and contains a source term that represents the opposite of the net force acting on the flow, including gravity, pressure gradient, and internal friction. In this paper we introduce two numerical methods to deal with the particular formulation of this model with a free interface. They are used to evaluate the respective role of yield and viscosity for the case of a constant source term, which corresponds to simple shear viscoplastic flows. Both the analytical solution of the inviscid model and the numerical solution of the viscous model (with a constant viscosity or the variable viscosity of the μ ( I ) rheology) are compared with experimental data. Although the model does not describe variations in the flow direction, it reproduces the essential features of granular flow experiments over an inclined static layer of grains, including the stopping time and the erosion of the initial static bed, which is shown to be closely related to the viscosity for the simple shear case.

Steady state rheology from homogeneous and locally averaged simple shear simulations

Granular materials and particulate matter are ubiquitous in our daily life and they display interesting bulk behaviors from static to dynamic, solid to fluid or gas like states, or even all these states together. To understand how the micro structure and inter-particle forces influence the macroscopic bulk behavior is still a great challenge today. This short paper presents stress controlled homogeneous simple shear results in a 3D cuboidal box using MercuryDPM software. An improved rheological model is proposed for macroscopic friction, volume fraction and coordination number as a function of inertial number and pressure. In addition, the results are compared with the locally averaged data from steady state shear bands in a split bottom ring shear cell and very good agreement is observed in low to intermediate inertia regime at various confining pressure but not for high inertia collisional granular flow.

An Eulerian projection method for quasi-static elastoplasticity

A well-established numerical approach to solve the Navier–Stokes equations for incompressible fluids is Chorin's projection method [1], whereby the fluid velocity is explicitly updated, and then an elliptic problem for the pressure is solved, which is used to orthogonally project the velocity field to maintain the incompressibility constraint. In this paper, we develop a mathematical correspondence between Newtonian fluids in the incompressible limit and hypo-elastoplastic solids in the slow, quasi-static limit. Using this correspondence, we formulate a new fixed-grid, Eulerian numerical method for simulating quasi-static hypo-elastoplastic solids, whereby the stress is explicitly updated, and then an elliptic problem for the velocity is solved, which is used to orthogonally project the stress to maintain the quasi-staticity constraint. We develop a finite-difference implementation of the method and apply it to an elasto-viscoplastic model of a bulk metallic glass based on the shear transformation zone theory. We show that in a two-dimensional plane strain simple shear simulation, the method is in quantitative agreement with an explicit method. Like the fluid projection method, it is efficient and numerically robust, making it practical for a wide variety of applications. We also demonstrate that the method can be extended to simulate objects with evolving boundaries. We highlight a number of correspondences between incompressible fluid mechanics and quasi-static elastoplasticity, creating possibilities for translating other numerical methods between the two classes of physical problems.

Investigation of shear damage considering the evolution of anisotropy

The damage that occurs in shear deformations in view of anisotropy evolution is investigated. It is widely believed in the mechanics research community that damage (or porosity) does not evolve (increase) in shear deformations since the hydrostatic stress in shear is zero. This paper proves that the above statement can be false in large deformations of simple shear. The simulation using the proposed anisotropic ductile fracture model (macro-scale) in this study indicates that hydrostatic stress becomes nonzero and (thus) porosity evolves (increases or decreases) in the simple shear deformation of anisotropic (orthotropic) materials. The simple shear simulation using a crystal plasticity based damage model (meso-scale) shows the same physics as manifested in the above macro-scale model that porosity evolves due to the grain-to-grain interaction, i.e., due to the evolution of anisotropy. Through a series of simple shear simulations, this study investigates the effect of the evolution of anisotropy, i.e., the rotation of the orthotropic axes onto the damage (porosity) evolution. The effect of the evolutions of void orientation and void shape onto the damage (porosity) evolution is investigated as well. It is found out that the interaction among porosity, the matrix anisotropy and void orientation/shape plays a crucial role in the ductile damage of porous materials.

Constitutive modelling approach for evaluating the triggering of flow slides

The paper presents a methodology to evaluate flow slide susceptibility in potentially liquefiable sandy slopes. The proposed approach accounts for both contractive and dilative volumetric behaviour during shearing using the MIT-S1 constitutive model. As a result, it is possible to distinguish among different types of undrained response induced by a rapid shear perturbation. The first part of the paper describes the general methodology for infinite slopes, providing an index of stability for incipient static liquefaction in shallow deposits. The methodology accounts for the anisotropy due to the initial stress state and uses simple shear simulations to assess instability conditions as a function of slope angle, stress state, and density of the soil. The resulting stability charts define the margin of safety against static liquefaction and the depths likely to be affected by the propagation of an instability. The second part of the paper applies the methodology to the well-known series of flow failures in a berm at the Nerlerk site. The MIT-S1 model is calibrated using published data on Nerlerk sands and in situ cone penetration test (CPT) data. The analyses show that in situ slope angles α = 10°–13° are less than the critical slope angle needed for incipient instability. Liquefaction and flow failures were therefore promoted by small perturbations in shear stresses that could be generated by rapid deposition of hydraulic fill.

Simple shear simulation of 3D irregularly-shaped particles by image-based DEM

This paper describes an image-based DEM taking account of the irregular shape of solid particles in a direct manner. A micro X-Ray CT at SPring-8 (a synchrotron radiation facility in Japan) was employed to obtain high quality CT images for detecting correctly the shape of particles. The digitized 3D shape data of each particle was automatically obtained by an original image-processing technique. The particle shape was modeled by a cluster of several spherical elements using dynamic optimization method. The accuracy of the modeling can be controlled by the number of elements forming each particle. Using such modeled particles a series of simple shear simulations were performed for the specimens with various void ratios. It was found that 10-element model can quantitatively reproduce the shear behavior of relatively-dense specimens. On the other hand, in order to well simulate the packing structure and the shear behavior of loose specimens, 10-element model is found to be insufficient and more accurate model would be necessary. This result implies that the overall grain shape that is relevant to the moment transmission between grains is important in densely-packed granular assembly, while small surface angularity plays considerable role in loosely-packed granular assembly.

Porosity localizing instability in a compacting porous layer in a pure shear flow and the evolution of porosity band wavelength

A porosity localizing instability occurs in compacting porous media that are subjected to shear if the viscosity of the solid matrix decreases with porosity ( Stevenson, 1989). This instability may have significant consequences for melt transport in regions of partial melt in the mantle and may significantly modify the effective viscosity of the asthenosphere ( Kohlstedt and Holtzman, 2009). Most analyses of this instability have been carried out assuming an imposed simple shear flow (e.g., Spiegelman, 2003; Katz et al., 2006; Butler, 2009). Pure shear can be realized in laboratory experiments and studying the instability in a pure shear flow allows us to test the generality of some of the results derived for simple shear and the flow pattern for pure shear more easily separates the effects of deformation from rotation. Pure shear flows may approximate flows near the tops of mantle plumes near earth's surface and in magma chambers. In this study, we present linear theory and nonlinear numerical model results for a porosity and strain-rate weakening compacting porous layer subjected to pure shear and we investigate the effects of buoyancy-induced oscillations. The linear theory and numerical model will be shown to be in excellent agreement. We will show that melt bands grow at the same angles to the direction of maximum compression as in simple shear and that buoyancy-induced oscillations do not significantly inhibit the porosity localizing instability. In a pure shear flow, bands parallel to the direction of maximum compression increase exponentially in wavelength with time. However, buoyancy-induced oscillations are shown to inhibit this increase in wavelength. In a simple shear flow, bands increase in wavelength when they are in the orientation for growth of the porosity localizing instability. Because the amplitude spectrum is always dominated by bands in this orientation, band wavelengths increase with time throughout simple shear simulations until the wavelength becomes similar to one compaction length. Once the wavelength becomes similar to one compaction length, the growth of the amplitude of the band slows and shorter wavelength bands that are increasing in amplitude at a greater rate take over. This may provide a mechanism to explain the experimental observation that band spacing is controlled by the compaction length ( Kohlstedt and Holtzman, 2009).

Mechanics of Biophysical Networks with Flexible Cross-links

Various mechanical properties and functions of euchariotic cells largely originate from the cytoskeleton. The predominant cytoskeletal constituent is the biopolymer filamentous actin (F-actin). In the presence of various cross-linking proteins, F-actins can comprise two rather different structures: isotropic orthogonal networks or bundled fibers. Actin bundles are formed mostly by short and stiff cross-linking proteins (like α-actinin and scruin), while large and flexible cross-linkers, such as filamin, lead to an orthogonal network. Orthogonal networks can also be formed at lower concentrations of short cross-linking proteins, but rheological experiments of in vitro F-actin networks showed that the mechanical response of such networks is different from that of networks cross-linked with filamin. Moreover, atomic force microscope stretching experiments on filamin demonstrated the possibility of force-induced domain unfolding, characterized by a sawtooth-like pattern in the force-displacement curve.Here we present a 3D discrete model of F-actin networks that extends our previous, rigidly cross-linked network model by incorporating a flexible cross-linking model for human filamin A (hsFLNa). The implemented hsFLNa element has a highly nonlinear response to stretching, incorporating the transition to a softer response that characterizes filamin domain unfolding. Simple shear simulations of F-actin/hsFLNa networks show that the response of such networks is dominated by the behavior of the hsFLNa cross-linkers, while F-actin behaves almost rigid. We observe that force-induced unfolding of the hsFLNa relaxes the stresses in actin filaments, thus allowing for large network strains. By contrast, the shearing of F-actin networks with rigid cross-links leads to a large number of actin filaments stressed well beyond their breaking force. An increase in actin concentration increases the initial shear modulus, while the maximum network stiffening depends on the hsFLNa axial stiffness. The calculated initial modulus of F-actin/hsFLNa networks is found to be comparable with experimental measurements.

Avaliação de métodos de quantificação da deformação finita por meio de simulações computacionais de deformação progressiva

Computational simulations of pure and simple shear progressive deformations applied on elaborated images (ellipses, irregular fabric and granoblastic fabric) permitted to evaluate the real potentiality of the methods inertia tensor, intercepts and R f /φ (technics by Shimamoto & Ikeda 1976 and Peach & Lisle 1979) in the quantification of finite strain. The results show that, in general, the evaluated methods are efficient to determine aspect ratio and preferential orientation, with exception of some cases and specific conditions, like high strain ratio. The inertia tensor method, originally developed to magmatic fabric analysis, shows analytical results very similar to those yielded by the R f /φ method, classically applied to deformed rock analysis. Both methods displayed good correlation between theoretical and observed values of deformation. The intercept method, also proposed to magmatic fabric analysis, systematically yields subestimated strain ratio on simple shear simulations and superestimated strain ratio on pure shear simulations. Nevertheless, this method displays good results in terms of orientation. In general, the tests qualify the use of the evaluated methods for strain analysis.

Avaliação de métodos de quantificação da deformação finita por meio de simulações computacionais de deformação progressiva

Computational simulations of pure and simple shear progressive deformations applied on elaborated images (ellipses, irregular fabric and granoblastic fabric) permitted to evaluate the real potentiality of the methods inertia tensor, intercepts and R f /φ (technics by Shimamoto & Ikeda 1976 and Peach & Lisle 1979) in the quantification of finite strain. The results show that, in general, the evaluated methods are efficient to determine aspect ratio and preferential orientation, with exception of some cases and specific conditions, like high strain ratio. The inertia tensor method, originally developed to magmatic fabric analysis, shows analytical results very similar to those yielded by the R f /φ method, classically applied to deformed rock analysis. Both methods displayed good correlation between theoretical and observed values of deformation. The intercept method, also proposed to magmatic fabric analysis, systematically yields subestimated strain ratio on simple shear simulations and superestimated strain ratio on pure shear simulations. Nevertheless, this method displays good results in terms of orientation. In general, the tests qualify the use of the evaluated methods for strain analysis.