Dilatant Materials Research Articles

Isotropic seismic radiation from rock damage and dilatancy

SUMMARYWe present semi-analytical and numerical results on isotropic radiation expected to be generated by seismic sources with damaged dilatant materials that sustain during failure an overall shear deformation. The results are derived for inclusions with different stiffness components, including those responsible for shear-volumetric coupling in dilatant material, and different geometries, in a surrounding elastic solid. The obtained relations indicate that the isotropic seismic potency and seismic moment components are proportional to the shear potency components multiplied by the aspect ratio between the thickness and length of the source zone. For a typical rupture zone with a thin tabular geometry, the expected small aspect ratio explains the general seismological observations of small isotropic radiation. However, isotropic radiation induced by dynamic dilation for short and thick sources is more pronounced and may reach for spherical sources sustaining shear deformation 18 per cent of the shear components. Sources that include also tensile components and explosions can produce larger isotropic radiation. The results provide rigorous relations that can be used to estimate different source properties in numerical simulations, experiments and field studies.

Assessment of pseudo-plastic and dilatant materials flow in channel driven cavity: application of metallurgical processes

Non-Newtonian fluid rheology representing the properties of pseudoplastic and dilatant materials has received overwhelming attention due to extensive applications in industrial and technological sectors like in metallurgical processes, shock absorbing materials, smart structures, and devices with adaptive stiffness, damping, emulsions, suspensions and so forth. Thus, in current communication characteristics of power law fluid elucidating attributes of pseudoplastic and dilatant materials in channel driven cavity is addressed. Finite element method (FEM) is implemented to interpret rheological features of power law fluid by varying flow controlling parameters. Discretization of domain at coarse level is performed by using stable first and second order polynomial (P2−P1) shape functions. Square shaped cylinder is placed at (1, 1.5) above the cavity. Hydrodynamics forces like pressure difference drag and lift variations are measured at outer surface of cylinder. The impact of primitive parameters like power law index (n) and Reynold number on velocity, pressure and viscosity for shear thinning and thickening cases is adorned. It is deduced that pressure difference increased against the variation in power law index. In similar way the impact of drag and lift forces mounts by increasing power law index. Reynold number has delineating impact on drag and lift forces near the obstacle. It is also seen that pressure shows optimized non-linear behavior near the obstacle and becomes linear along the downstream as expected in channel flow. It is divulged that pressure drops more rapidly for increasing magnitude of Reynold number. Velocity of fluid increases when power law fluid flow is behaving as shear thinning fluid in comparison to shear thickening case.

Simulating fluid injection in geological media with complex rheologies

Stimulation of geothermal systems by injection of water into wells at high pressures to create fractures and increase permeability of rocks is a widely used technique. Therefore, increasing our understanding about how such actions influence the local state of stress of the reservoir and how fractures propagate through it is necessary to efficiently develop extraction projects and, hopefully, to avoid undesired side effects. Advances in numerical modelling of hydraulic fracturing are thus required. To that end, we improved the modelling and solving capabilities of the software LaMEM by adding plasticity, poro-elasticity and Darcy flow making this code capable of simulate dilatant materials, accounting by the angle of dilatation, and reproduce shear/tensile failures due to local pore pressure increase. This improvement offers us an efficient computational massively-parallel code to model fluid injection and crack propagation in poro-visco-elasto-plastic rocks. Here we give examples of such model.

Micromechanical modelling of granular materials and FEM simulations

We present a micro-mechanical continuum model used for the description of dilatant granular materials with incompressible rotating grains for which the kinetic energy, in addition to the usual translational one, consists of other two terms owing to microstructural motions: in particular, it includes the dilatational expansions and contractions of the granules relative to one another, as well as the rotation movements of each grain compared to the others. Next, we propose a linear theory in which the representations of constitutive functionals are linear with respect to both the volume fraction and the micro-rotation gradients, and to the dissipative variables. At the end we test the linear model on a two-dimensional domain, in which the arising system of partial differential equations is solved using the finite element method; thus we obtain a numerical solution in the case of a simplified granular micromechanics. The obtained computations of the early granular dynamics are consistent with theoretical insights as deduced from the proposed model. Viscous and rotational contributions to the granular dynamics have been identified and compared each others.

Анализ уравнений теории пластичности порошковых металлических систем

В работе дан обзор методов расчета, основных параметров процессов пластического деформирования дилатирующих материалов, типичными представителями которых являются порошковые металлические системы различных химических составов. В их основу положены математические модели, использующие не только качественное объяснение, но и количественное описание эффекта дилатансии. Приведена полная система основных уравнений теории пластичности жесткопластических изотропных дилатирующих сред. Рассмотрен пример расчета установившегося пластического течения в условиях осесимметричной деформации. Показано, что для осесимметричной деформации уравнения относительно проекций вектора скорости на характеристические направления, аналогичны уравнениям для плоской деформации. Установлено, что используемые в настоящее время условия текучести с различной степенью точности описывают виды дилатансии (разрыхление и уплотнение). Поэтому, для более точного решение некоторых задач необходимо уточнение математических моделей условия текучести. Для некоторых процессов, пластического формоизменения при решении системы уравнений дилатирующих сред целесообразно условия текучести представлять в виде отдельных областей: гиперболичной, параболичной и эллиптичной.

Об изменении модулей объемной упругости разрыхляющихся материалов с ростом деформации

Об изменении модулей объемной упругости разрыхляющихся материалов с ростом деформации

Numerical modeling of shear band propagation in porous plastic dilatant materials by XFEM

This paper studies mixed-mode shear band propagation behaviors in porous plastic dilatant materials by the extended finite element method (XFEM). The Drucker-Prager elastoplastic model is combined with the strong discontinuity method to simulate the dilatant shear band. First, the dissipative nature of the localized area with displacement jump is integrated into the constitutive model by introducing a cohesive law. A new contribution lies that the yielding function is modified in the localized region to calculate the cohesive traction within the framework of the XFEM. The shear band propagation direction is determined by the singularity of the acoustic tensor and the corresponding localization vector is computed by the eigenvalue analysis. Then, the XFEM is used to calculate the numerical dilation with both the normal and shear modes for the localization band. Finally, two typical cases for the shear band propagation are used and numerical results are compared with existing works to confirm the efficiency and robustness of the developed method.

An elastoviscoplastic constitutive model for geomaterials: Application to hydromechanical modelling of claystone response to drift excavation

An isotropic elastoviscoplastic constitutive model based on a generalized Hoek-Brown criterion is proposed. The plastic mechanism is characterized by a positive and a negative hardening, and a specific non-associated flow rule allows to take into account the evolution of the dilatancy. Several hydromechanical finite element simulations corresponding to realistic configurations of drift excavations in the underground research laboratory of Bure are presented. Regularization techniques are required to avoid localization phenomena due to softening. A second gradient formulation has been used as it is well suited for dilatant materials such as claystone. Numerical results are discussed and compared with experimental measurements.

Numerical study of shear band instability and effect of cavitation on the response of a specimen under undrained biaxial loading

This paper presents an extension of the local second gradient model to multiphasic materials (solids particles, air, water) and including the cavitation phenomenon. This new development was made in order to model the response of saturated dilatant materials under deviatoric stress and undrained conditions and possibly, in future, the behavior of unsaturated soils. Some experiments have showed the significance of cavitation for the hydromechanical response of materials. However, to date and as far as we are aware, no attempt was made to implement the cavitation as a phase change mechanism with a control of pore pressure. The first part of the results section explores the effects of permeability, dilation angle and loading rate on the stability of shear bands during a localization event. The reasons underlying the band instability are discussed in detail, which helps defining the conditions required to maintain stability and investigating the effects of cavitation without parasite effect of materials parameters or loading rate. The model showed that, if a uniform response is obtained, cavitation triggers localization. However, in case of a localized solution, cavitation follows the formation of the shear band, with the two events being quite distinct.

Fracture mechanics of multimodulus dilatant media

Cracks arising in dilatant and multimodulus materials (different elasticity moduli for different types of the stress state) are under study. The stress and strain distributions in dilatant multimodulus bodies with cracks, which allow estimating the impact of damage on crack resistance characteristics, are investigated.

Pore Pressure Response Following Undrained uCPT Sounding in a Dilating Soil

The generation and dissipation of pore fluid pressures following standard piezocone sounding (uCPT) sounding in silty sands are observed to exhibit many of the characteristics of undrained penetration in dilatant materials; steady excess pore pressures may be subhydrostatic, or may become subhydrostatic during dissipation, and are slow to decay. Enigmatic pore pressure dissipation histories which transit from sub- to supra- and again to subhydrostatic before equilibrating at hydrostatic are consistent with a response where undrained pressures are maximally negative remote from the penetrometer tip. This surprising distribution of induced pore fluid pressures is accommodated in cavity expansion models for a dilating soil. A Mohr-Coulomb constitutive model is established for undrained loading of a soil with pore pressure response defined by Skempton pore pressure parameters. Defined in terms of effective stresses, this allows undrained stresses and pore pressures to be determined following cavity expansion ...

Study on the Crack-Tip in the Pressure-Sensitive Dilatant Materials

In the petroleum engineering, the nonlinear bulk strain or bulk strain rate must be considered in rock deformation, adopting the viscous-elastic theory, a constitutive equation of the pressure-sensitive dilatant materials was established. The governing eqations were deducted in crack-tip field of quasi-static growing crack in pressure-sensitive dilatant materials. And for the mechanical model of a rigid-viscoelastic material interfacial crack, through numerical calculate, the asymptotic solution of the continuous separate variable formal of stress, strain and displacement. The significance of the material parameter in the crack-tip field is discussed. The study of the paper will provide theoretical references for preventing the glide of the mud rock and reducing the arises of the failure of casings of well.

Kinematic models for non-coaxial granular materials. Part I: theory

The purpose of this paper is to present a physically based plasticity model for non-coaxial granular materials. The model, which we shall call the double slip and rotation rate model (DSR2 model), is a pair of kinematic equations governing the velocity field. The model is based on a discrete micro-analysis of the kinematics of particles in contact, and is formulated by introducing a quantity called the averaged micro-pure rotation rate (APR) into the unified plasticity model which was proposed by one of the authors. Our macro-micro mechanical analysis shows that the APR is a non-linear function of, among other quantities, the macro-rotation rate of the major principal axis of stress taken in the opposite sense. The requirement of energy dissipation used in the double-sliding free-rotating model appears to be unduly restrictive as a constitutive assumption in continuum models. In the DSR2 model the APR tensor and the spin tensor are directly linked with non-coaxiality of the stress and deformation rate tensors. We also propose a simplified plasticity model based on the DSR2 model for a class of dilatant materials, and analyse its material stability. Copyright © 2005 John Wiley & Sons, Ltd.

Boundary Condition Disturbed in Shear Banding Analysis by Rudnicki and Rice for Pressure Sensitive Materials

Rudnicki and Rice invistigated the localization of deformation into a shear band resulted from an instability in constitutive description of homogeneous deformation in pressure sensitive dilatant materials. Their analytical method has been used very often for the prediction of shear banding in soil. In their analysis the equilibrium is considered between multiple solutions in the perpendicular direction to a shear band, but the essential requirement is ignored that these multiple solutions are under identical boundary condition. This paper shows concretely the disturbance of boundary condition appeared in the onset of instability in their method. This disturbance results in the fact that their method cannot give useful prediction for ductile fracture in soil.

Shear-induced pressure changes and seepage phenomena in a deforming porous layer - I

We present a model for flow and seepage in a deforming, shear-dilatant sensitive porous layer that enables estimates of the excess pore fluid pressures and flow rates in both the melt and solid phase to be captured simultaneously as a function of stress rate. Calculations are relevant to crystallizing magma in the solidosity range 0.5–0.8 (50–20 per cent melt), corresponding to a dense region within the solidification front of a crystallizing magma chamber. Composition is expressed only through the viscosity of the fluid phase, making the model generally applicable to a wide range of magma types. A natural scaling emerges that allows results to be presented in non-dimensional form. We show that all length-scales can be expressed as fractions of the layer height H, timescales as fractions of H2(nβ′θ+ 1)/(θk) and pressures as fractions of . Taking as an example the permeability k in the mush of the order of magnitude 10−15 m2 Pa−1 s−1, a layer thickness of tens of metres and a mush strength (θ) in the range 108–1012 Pa, an estimate of the consolidation time for near-incompressible fluids is of the order of 105–109 s. Using mush permeability as a proxy, we show that the greatest maximum excess pore pressures develop consistently in rhyolitic (high-viscosity) magmas at high rates of shear (, implying that during deformation, the mechanical behaviour of basaltic and rhyolitic magmas will differ. Transport parameters of the granular framework including tortuosity and the ratio of grain size to layer thickness (a/H) will also exert a strong effect on the mechanical behaviour of the layer at a given rate of strain. For dilatant materials under shear, flow of melt into the granular layer is implied. Reduction in excess pore pressure sucks melt into the solidification front at a velocity proportional to the strain rate. For tectonic rates (generally 10−14 s−1), melt upwelling (or downwelling, if the layer is on the floor of the chamber) is of the order of cm yr−1. At higher rates of loading comparable with emplacement of some magmatic intrusions (∼10−10 s−1), melt velocities may exceed effects due to instabilities resulting from local changes in density and composition. Such a flow carries particulates with it, and we speculate that these may become trapped in the granular layer depending on their sizes. If on further solidification the segregated grain size distribution of the particulates is frozen in the granular layer, structure formation including layering and grading may result. Finally, as the process settles down to a steady state, the pressure does not continue to decrease. We find no evidence for critical rheological thresholds, and the process is stable until so much shear has been applied that the granular medium fails, but there is no hydraulic failure.

Three-dimensional micromechanical modeling of voided polymeric materials

A three-dimensional micromechanical unit cell model for particle-filled materials is presented. The cell model is based on a Voronoi tessellation of particles arranged on a body-centered cubic (BCC) array. The three-dimensionality of the present cell model enables the study of several deformation modes, including uniaxial, plane strain and simple shear deformations, as well as arbitrary principal stress states. The unit cell model is applied to studies on the micromechanical and macromechanical behavior of rubber-toughened polycarbonate. Different load cases are examined, including plane strain deformation, simple shear deformation and principal stress states. For a constant macroscopic strain rate, the different load cases show that the macroscopic flow strength of the blend decreases with an increase in void volume fraction, as expected. The main mechanism for plastic deformation is broad shear banding across inter-particle ligaments. The distributed nature of plastic straining acts to reduce the amount of macroscopic strain softening in the blend as the initial void volume fraction is increased. In the case of plane strain deformation, the plastic flow is observed to initiate across inter-particle ligaments in the direction of constraint. This particular mode of deformation could not have been captured using a two-dimensional, plane strain idealization of cylindrical voids in a matrix. The potential for localized crazing and/or cavitation in the matrix is addressed. It is observed that the introduction of voids acts to relieve hydrostatic stress in the matrix material, compared to the homopolymer. It is also seen that the predicted peak hydrostatic stress in the matrix is higher under plane strain deformation than under triaxial tension (with equal lateral stresses), for the same macroscopic stress triaxiality. The effect of void volume fraction on the macroscopic uniaxial tension behavior of the different blends is examined using a Considère construction for dilatant materials. The natural draw ratio was predicted to decrease with an increase in void volume fraction.

Cylindrical cavity expansion in dilatant cohesive-frictional materials

Cylindrical cavity expansion in dilatant cohesive-frictional materials

Strength, plasticity, and creep conditions for ceramic and other dilatant materials

Huber-Mises conditions of strength and plasticity for materials with different resistances are discussed. The yield strength or shear strength can be taken as a material constant under these conditions. A region of consistent functions based on general postulates is explored and creep equations are derived.

The velocity field for the punch problem for dilatant granular materials

For the problem of indentation of a granular half-space by a smooth rigid punch, an alternative velocity field is obtained for shear-index yield functions, which is fully consistent with the dilatant double-shearing theory proposed for granular materials. The velocity field presented in (1 ), which although a bonafide solution of the governing equations, assumes that the flow is tangential to the bounding slip-line separating the deforming and rigid regions. In other words, in (1) it is assumed that there is no normal component of the flow across this bounding characteristic. This assumption, although physically well motivated, is not fully consistent with the dilatant double-shearing rule that an expansion accompanies any shearing deformation. In this latter situation the normal velocity is discontinuous and this implies the formation of voids in the material. Numerical results are presented comparing the two velocity fields and these conflicting issues are discussed.

Dilatancy fabrics in conglomerates in the Awatere fault zone, New Zealand

Analysis of fabrics of faulted and unfaulted conglomerate within the Awatere fault zone of New Zealand shows that movement on individual faults was accompanied by dilatancy of the clast fabric. The fabric of unfaulted conglomerate is clast-supported. comprising 78% clasts by area. Individual fault zones studied range in width from 4 to 21 cm and have a clay matrix-supported fabric, comprising 33% clasts by area. The abundance of clay within fault zones indicates a highly plastic matrix intruded from the wall rocks into fault zones during localised dilation of the clast fabric. The shear thickening shear-stress-strain-rate relationship typical of dilatant materials suggests that the observed fabrics are more compatible with faults developing slowly as accommodation structures rather than forming rapidly during seismic movements. A rudimentary analysis of the transfer of the minimum lithostatic load through the conglomerate suggests that contact loads between clasts were significantly less than the strength of clasts determined by point load testing. The results provide a mechanism to support a previous interpretation of the fault pattern in terms of dilatant faulting within an oblique divergent tectonic setting.