Simplified Rheological Model Research Articles

Constitutive modelling and pipeline flow of thixotropic viscoplastic wastewater sludge

Due to the inherent rheological complexity of wastewater sludges, conventional sludge pipeline design based on simplified rheological models can result in inefficient sludge transportation systems. These inefficiencies are further exacerbated by a global need for the processing of more concentrated wastewater sludges that have a more pronounced non-Newtonian character, and hence require greater energy for transportation. However, the complex rheology of these materials (typically visco-elastic and thixotropic) requires sophisticated methods for constitutive modelling that are impractical to implement for complex materials such as sewerage sludges. We address this challenge by developing a novel viscoplastic thixotropic constitutive model that exploits the separation of timescales between the thixotropic and viscoelastic processes, leading to simpler and more robust experimental methods, parameter estimation and process simulation methods. This constitutive model combines a kinetic model for thixotropic degradation and agglomeration via a classical structural parameter (λ) approach coupled nonlinearly with a Herschel-Bulkley model to yield a thixotropic viscoplastic model of sludge rheology. Experimental data for thickened digested sludge between 3 and 4.9% solids were collected to validate the assumption for the separation of viscoelastic and thixotropic responses. The fitting procedure was found to be robust and efficient, and several rheological parameters were found to be invariant with solids concentration. Simplified energy calculations for a typical sludge pipeline showed that the pumping energy could be significantly under- or overestimated without considering thixotropy. These simple and robust constitutive models and fitting methods can accurately predict (and hence design and optimise) sludge behaviour over a wide range of wastewater processes.

On the application of simplified rheological models of fluid in the hydraulic fracture problems

In this paper a problem of a hydraulic fracture driven by a non-Newtonian shear-thinning fluid is analysed. For the PKN fracture geometry three different rheological models of fluid are considered: (i) the Carreau fluid, (ii) the truncated power-law fluid, (iii) the power-law fluid. For each of these models a number of simulations are performed. The results are post-processed and compared with each other in order to find decisive factors for similarities/dissimilarities. It is shown that under certain conditions even the basic power-law rheology can be a good substitute for the Carreau characteristics. Although for a particular fluid such a conclusion cannot be made a priori, post-processing based on average values of the fluid shear rates is a very good tool to verify credibility of the results obtained for simplified rheological models. The truncated power-law rheology is a good alternative for the Carreau model. It always produces results that are very similar to those obtained with the equivalent Carreau fluid and simultaneously provides a relative ease of numerical implementation.

Rheological model of viscoelastic–plastic geogrid-reinforced tailings

A non-linear, four-parameter viscoelastic–plastic model is proposed to characterise the mechanical properties of geogrids under long-term and low-stress load. In this study, a simplified rheological model of viscoelastic–plastic geogrid-reinforced tailings was established. The stress analysis of the whole reinforced tailings complex was divided into two stages. The time for the tailings to produce plastic deformation (plastic arrival time) was the cut-off point for the two stages. The first stage (E-VP model) corresponded to the elastic state of tailings during which the stress of geogrids decreased with time, causing the recombination of microstress in tailings until they reached the yield condition. The second stage (P-VP model) corresponded to the plastic state during which the stress of geogrids remained constant, whereas the overall strain of the reinforced complex increased as a result of the geogrid creep. The force of the reinforced complex changed rapidly from the first to the second stage. Owing to the small deformation in the first stage, the overall strain of the complex was mainly caused during the second stage. The plastic arrival time t p of the reinforced tailings complex was significantly influenced by the plastic strain ε p and viscosity coefficient η of geogrids and internal friction angle ϕ of tailings.

Stress-relaxation of crystalline alkali-silica reaction products: Characterization by micro- and nanoindentation and simplified modeling

Alkali-silica reaction (ASR) is a major issue for the durability of concrete structures worldwide. Fostering recent microindentation works on the elastic property of ASR products, this work aims at further characterizing their viscous property. In particular, this study focuses on the relaxation behaviour of ASR crystalline products which are preferentially formed within cracks at the center of the reactive aggregates in real field concrete structures. First, the surface roughness and the chemical composition of ASR products were examined by Scanning Electron Scanning (SEM) and Energy Dispersive X-ray spectroscopy (EDS). Finally, the viscous behaviour of crystalline ASR products was characterized by performing load-relaxation tests by microindentation, providing new knowledge on the relaxation behaviour of the ASR crystalline products which was about 40%. Furthermore, nanoindentation test were also carried out to better understand the possible length-scale effect. In spite of the large scatter, the characterization at lower scale by nanoindentation showed that the ASR rosette crystals have a greater modulus and lower relaxation rate. This is likely due to the fact that the volume probed by nanoindentation is close to the size of ASR crystals and related interfaces. Finally, a simplified rheological model was employed to estimate the viscosity and characteristic time of the ASR crystalline products. The present result provide new knowledge on the viscous behaviour ASR products which can be helpful for better understanding ASR products and improve existing multiscale models.

Transitional Friction Regime Modeling under Boundary Lubrication Conditions

The aim of this work is to elucidate the mode of the boundary lubrication regime regularities as an example of the piston ring friction of the cylinder liner at high contact pressures. Dependencies of the friction coefficient on the contact pressure, on the slip speed and on the temperature were obtained. Experimental results were compared with the known models of friction in the contact of piston-rings. It is found that friction occurs in the boundary lubrication regime at contact pressures above 0.4 MPa. This mode cannot be described by combining models of the hydrodynamic and boundary friction. As a result, a simplified rheological model of the boundary lubricant layer taking into account the effects of lubricating oil multilayer adsorption was offered.

Transitory Dynamics Evaluation inside Driving System of Demolition-Cutting Technological Equipment due to Variable Tool-Material Interactions

Computational dynamics of technological equipments dealing with intensive, shock-like and various working regimes frames the area of this research paper. A widely used type of demolition-cutting equipment supplied by hydrostatical driving system was adopted, and ordinary scenarios of equipment exploitation have been proposed in order to dignify the very short but strong transitory states deeply depending on the material characteristics and the regime parameters. Elastic, dissipative and plastic components have been considered to compose the global characteristic of the processed material interacting with cutting tool. The authors propose a simplified rheological model intended for modeling and simulation of demolished structural elements based on composite materials, like reinforced concrete. This model is very useful for simulation the variable dynamics of the interaction between the demolition-cutting equipments and the composite elements in order to evaluate the parameters evolution within the process, and obviously, to optimize driving system for minimize transitory effects and vibratory evolutions. The advantage of this computational approach results from the reduced resources involved by simulation tasks, taking into account the global evaluation of the resistant forces usually required for this kind of behavioral analysis.

Plastic and viscous shear displacements of a deep and very slow landslide in stiff clay formation

Deep and superficial displacements have been measured since 2005 in a slow active landslide that has occurred in a stiff clay formation of the Italian Southern Apennines. Recently, new inclinometer casings have been installed to achieve further information on the displacement field. In this paper, standard inclinometer profiles and fixed-in-place probe data are analysed over time. New data confirm previous hypotheses on geometry and kinematics and add more information on the viscous component of displacements. The mechanism of movement, in most of the track, essentially corresponds to sliding localized on a shear surface, consistently with stress and strength distribution. However, locally, internal viscous deformations also occur, especially in the weathered and softened zones of the landslide, and contribute to the soil discharge continuity. Viscous displacements can be interpreted by a simplified rheological model based on the Bingham equation. The residual shear strength has been considered as the creep threshold value and the dynamic viscosity has been considered dependent on the stress level, on the basis of long term direct shear tests under controlled shear stresses which were carried out in laboratory.

Reply to "Comment on 'The October 2005 Georgian Bay, Canada, Earthquake Sequence: Mafic Dykes and Their Role in the Mechanical Heterogeneity of Precambrian Crust' by S. Dineva, D. Eaton, S. Ma, and R. Mereu" by G. Ranalli and M. Lamontagne

In a recent study (Dineva et al. , 2007; hereinafter DEA), we established a spatial correlation between the earthquake sequence of 20–24 October 2005 in Georgian Bay (Ontario, Canada) and magnetic anomalies that are most likely caused by mafic dykes. The strike of both determined nodal planes of the mainshock ( m N 4.3) are consistent with the strike of the magnetic anomalies. Focal depths of the earthquake sequence are estimated to be in the range 5–12 km, mostly around 10–12 km. Assuming a highly simplified rheological model that incorporates a quartz-dominated host lithology and a plagioclase composition for the mafic dykes, we estimated the shear strength of mafic dykes to be several orders-of-magnitude greater than the felsic host rocks at 10–12 km depth. Furthermore, we proposed that creep of quartz-dominated rheology, in juxtaposition with much stronger mafic rocks, could lead to strain accumulation and episodic seismicity within this depth range. The factors that control seismicity of stable continental regions remain enigmatic, and we are pleased that our proposed model has stimulated further discussion. Ranalli and Lamontagne (2009; hereinafter RL) comment on several aspects of our hypothesis, asserting that it is critically dependent on various assumed parameters and consequently not established with any level of confidence. Their discussion and our response are organized into two parts: (1) discussion of the choice of parameters used to support our analysis, and (2) a critique of …

Initiation of localized shear zones in viscoelastoplastic rocks

Shear localization is a process of primary importance for the onset of subduction and the evolution of plate tectonics on Earth. In this paper we focus on a model in which shear localization is initiated through shear heating. The rheology employed is linear Maxwell viscoelastic with von Mises plasticity and an exponential dependence of viscosity on temperature. Dimensional analysis reveals that four nondimensional (0‐D) parameters control the initiation of shear zones. The onset of shear localization is systematically studied with 0‐D, 1‐D, and 2‐D numerical models, both under constant stress and under constant velocity boundary conditions. Mechanical phase diagrams demonstrate that six deformation modes exist under constant velocity boundary conditions. A constant stress boundary condition, on the other hand, exhibits only two deformation modes (localization or no localization). Scaling laws for the growth rate of temperature are computed for all deformation modes. Numerical and analytical solutions demonstrate that diffusion of heat may inhibit localization. Initial heterogeneities are required to initiate localization. The derived scaling laws are applied to Earth‐like parameters. For a given heterogeneity size, stable (nonseismic) localization only occurs for a certain range of effective viscosities. Localization is inhibited if viscosity is smaller then a minimum threshold, which is a function of the heterogeneity size. The simplified rheological model is compared with a more realistic and more complex model of olivine that takes diffusion, power law, and Peierls creep into account. Good agreement exists between the models. The simplified model proposed in this study thus reproduces the main physics of ductile faulting. Two‐dimensional late stage simulations of lithospheric‐scale shear localization are presented that confirm the findings of the initial stage analysis.

Geodynamics of the Tarim Basin and the Tian Shan in central Asia

The India‐Asia collision has caused crustal thickening in Tibet by at least a factor of 2. In the last 20–30 Myr of this collision the Tian Shan mountain range has also been reactivated. The Tarim Basin, however, shows little internal deformation. We describe a series of numerical experiments which constrain the effective lithospheric strength parameters of the Tarim Basin and the Tian Shan in the context of a thin viscous sheet model. We use a finite element representation of the thin viscous sheet model to approximate the deformation field in the India‐Asia collision and compare model crustal thickness distributions with that inferred from a local isostatic model of topography. The experiments show that a strong Tarim Basin, while undergoing little internal deformation, transfers strain to the Tian Shan, producing significant crustal thickening in the Tian Shan region. Based only on diagnostic parameters such as the maximum thickening in the Tian Shan and the minimum in the Tarim Basin, the principal features of the topography can be approximately reproduced using models in which either the Tarim Basin is strong, or the Tian Shan is weak, or both. For a rheological model in which the stress versus strain‐rate exponent is n = 3 the strength coefficient for the strong Tarim Basin model, VTarim is between about 1.7 and 2. For the weak Tian Shan model the relative strength coefficient VTian is between about 0.65 and 0.75. If both strong Tarim and weak Tian Shan are included, there is a trade‐off between the required values of VTarim and VTian and the shape of the predicted crustal thickness profiles better matches the observed profiles. The steep topographic slope on the southern margin of the Tarim Basin requires that it is anomalously strong, while the rapid decrease of topographic height to the north of the Tian Shan requires that it is anomalously weak. Similar conclusions are obtained with a rheological model based on n = 10. Simplified rheological models of the lithosphere show that the variations in lithospheric strength may be explained by changes to the Moho temperature of the order of 10° to 30°C.

Viscoelastic effects on the vibration of structural elements liable to buckling

The influence of the material creep on the stability and vibration characteristics of axially compressed structural elements is investigated by means of a simplified rheological model. The stability and the vibration characteristics are illustrated, respectively, by the equilibrium paths along the creep process and the natural frequencies corresponding to each equilibrium configuration. The results obtained contribute to a better understanding of the behavior of structural elements under compressible loading, taking into account the time-dependent characteristics of the material.

SOME MATHEMATICAL ASPECTS OF MASTICATION AND ITS SIMULATION BY MACHINES

ABSTRACTIf the deformation process of a specimen satisfies the condition: H(t) = g(Ho) ·f(t) (Eq. l), where H(t) is the deformed specimen length at time (t), g(Ho) is a function of the initial length (Ho) only and f(t) a function of time only, then the true strain e(t) and the strain rate e(t) are: e(t) = In f(t) (Eq. 2), and e(t) = [d In f(t)] /dt (Eq. 3). These imply that the stress‐strain (or force‐time) relationship of a homogeneous material is independent of the specimen length and is only determined by the rheological properties of the material and the selected function f(t). If the deformation histories produced in mastication satisfy the condition set by Eq (1) it would provide a partial mathematical explanation to why sensory textural‐rheological properties are not affected by the specimen dimensions in contrast to instrumental parameters obtained by existing testing machines. The construction of machines that provide such straining histories is physically possible (they would not, however, be operated at a constant deformation rate), and there‐ fore it is theoretically possible to obtain instrumental parameters that are dimension independent. The concept is demonstrated with some simplified rheological models and its possible application to food testing evaluated.

OPERATIONAL CONDITIONS AND THE STRESS‐STRAIN RELATIONSHIP OF SOLID FOODS—THEORETICAL EVALUATION1

ABSTRACTMany textural evaluation techniques are based on test procedures that involve large compressive deformations and constant deformation rates. These imply that the specimen undergoes a straining history which depends on the specimen length and in which the true strain rate increases progressively. Mathematical simulation of the real conditions in simplified rheological models indicated that single stress‐strain curves may provide misleading information on the true characteristics of the material. I t is shown that the stress‐strain curves of different materials can cross one another a t stmin levels that depend on test conditions. Any comparison under such circumstances may result in inconsistent conclusions. It is suggested that relaxation data may provide the complementary information for the comprehensive characterization of the mechanical properties of foods.

THE ROLE OF THE SPECIMEN DIMENSIONS IN UNIAXIAL COMPRESSION OF FOOD MATERIALS

ABSTRACTThe role of the specimen dimensions in uniaxial compression tests was evaluated by simplified rheological models. These indicated that if the rheological behavior can be represented by a model that contains fracture elements the shape of the stress‐strain would depend on the specimen length. The analysis also indicates that mechanical measurements of foods may not be theoretically comparable if the tests are performed at distinctly different conditions with regard to the specimen dimensions, the level of the deformation and its application rate.