Nonlinear Rheological Model Research Articles

Development of new numerical approach to the flow and segregation behaviors of fresh concrete considering rebar restraint and its application in reinforced lightweight aggregate concrete

Although there are many studies on flow simulation methods for fresh concrete, there are very few studies on casting simulation of reinforced concrete, and in these studies the reinforcing bars are treated only as static boundaries without their restraining effect on the concrete flowing between them. In this study, we first developed a new numerical method based on the MPS method for simulating the flow and segregation behaviors of fresh concrete during casting reinforced member, considering the restraint of reinforcing bars by applying a normal stress to the concrete. Fresh concrete was treated as the double-phase granular fluid that follows a non-linear rheological model, and was represented by matrix mortar, and coarse aggregate particles with actual sizes and random shapes. Then, as an application of this numerical method, the flow and segregation behaviors of lightweight aggregate concrete (LWAC) in an L-shaped box with rebars were numerically investigated in addition to measurement. The comparison of the numerical and experimental results shows that this numerical method allows the LCA volume fraction to be calculated within 3 % error in predicting the segregation behavior of LCA in reinforced LWAC, and improves the accuracy of the flow simulation of LWAC by about 1.5 times. Furthermore, this numerical method can double the accuracy of concrete flow prediction, compared to treating the reinforcement as a static boundary.

Determining the Rheological Parameters of Polymers Using Machine Learning Techniques

Introduction. The paper investigates the methodology for determining the rheological parameters of materials based on the nonlinear Maxwell-Gurevich rheological model using the stress relaxation curves. The review of the main directions of the metaheuristic approaches (local search, evolutionary algorithms) to solving the combinatorial optimization problems is presented. The metaheuristic algorithms for solving some important combinatorial optimization problems with the special emphasis on building decision trees are described. The comparative analysis of the algorithms for solving the regression problem in CatBoost Regressor is carried out. The aim of the work is to determine the rheological properties of polymers using machine learning techniques.Materials and Methods. The objects of the study are the generated data sets obtained on the basis of the theoretical stress relaxation curves. The source data tables for model training across all samples are presented, and the statistical analysis of the source data sets characteristics is carried out. The total number of numerical experiments across all samples amounted to 346020 variations. To develop the models, the CatBoost artificial intelligence techniques were used; the regularization techniques (Weight Decay, Decoupled Weight Decay Regulation, Augmentation) were used to increase the model accuracy; and Z–Score technique was used for data normalization.Results. As a result of the research, the intelligent models for determining the rheological parameters of polymers (initial relaxation viscosity, velocity modulus) have been developed based on the generated data sets on the example of the epoxy binder EDT-10. Based on the testing results of the models with the best parameters, the quality assessments were carried out: for the parameter 𝜂∗0 the range of values MAPE 0.46 — 2.72, MSE 0.15 — 1.09, RMSE 0.19 — 0.44, MAPE 0.46 — 1.27; for the parameter 𝑚∗ — MAPE 0.07 — 0.32, MSE 0.01 — 0.13, RMSE 0.10 — 0.41, MAPE 0.58 — 2.72. The resulting metric values are permissible. The training graphs demonstrate the stability of the process.Discussion and Conclusion. The developed intelligent models are scalable and cross-platform, have practical applied significance that ensures their implementation in a wide range of the scientific and engineering apps.

A nonlinear approach for the simulation of the buffeting response of long span bridges under non-synoptic storm winds

In recent years, extreme atmospheric events are becoming increasingly frequent and unpredictable. These phenomena are often characterized by low-frequency variations of the wind speed and angle of attack, mainly due to large-scale turbulence. These features can be critical for long-span bridges as they can lead the deck in conditions where the nonlinear effects of aerodynamic forces are enhanced. Therefore, it is increasingly important to develop reliable numerical tools to simulate the response of these structures to non-synoptic winds. In this work, a nonlinear rheological model that is able to account for the large variations in wind speed and angle of attack is employed to investigate the dynamic response of two different bridges subjected to two different wind fields. The first scenario is a standard synoptic wind field used as a baseline. On the other hand, the second wind scenario represents an extreme non-synoptic atmospheric event. The results highlight how the nonlinear effects of the aerodynamic forces, in particular those related to the large variation of the angle of attack, could lead to significant changes in the bridges’ response. These effects would not be captured by employing standard linearized methods.

On the Application of Non-Linear Rheological Models In Longitudinal Fracture Analysis of Beams Made of Functionally Graded Materials

On the Application of Non-Linear Rheological Models In Longitudinal Fracture Analysis of Beams Made of Functionally Graded Materials

Flow and heat transfer analysis over a pair of heated bluff bodies in a channel: Characteristics of non-linear rheological models

In this computational study, the tribological characteristics of the flow of a visco-plastic fluid around a pair of cylinders in a channel are thoroughly analyzed. To numerically solve the governing equations, this investigation makes use of the Galerkin's Finite Element Method (FEM) in conjunction with Newton's and PARDISO solvers. The stable finite element pair (P2/P1) has been selected for the space discretization purpose. The impacts of several physically important parameters on the flow characteristics are investigated in depth, including the spacing ratio (GP), the power law index (n), the Bingham number (Bn), and the Reynolds number (Re). When using different gap spacing ratios (GP), the drag coefficient (CD) and lift coefficient CL were found to be strongly dependent on GP. The pressure, velocity, and viscosity profiles are plotted for varying n and Bn. In addition, the velocity behavior is observed along y-direction in a channel through line graphs. Code validation is done as special case when Bn=0andn=1. It has been observed that the gap between the obstacles can influence the overall flow pattern and subsequently the drag and lift forces.

Study on valley deformation of high arch dams based on nonlinear rheological damage model

The scale of the high arch dam project is large, and the water level is high. The construction and water storage effect will significantly impact the rock mass of the high slopes on both sides, especially on the structural planes such as internal faults. Based on the Jinping Ⅰ high arch dam, an improved Nishihara rheological damage model was established to address the phenomenon of valley shrinkage deformation. The stress and deformation states of the rock mass and dam in the reservoir area were calculated, and the results were compared with the conventional elastic–plastic finite element method. The results indicate that the improved parallel Nishihara rheological damage model can better conform to the deformation properties of the internal structural planes of the rock mass, and the calculation results using this model are closer to the actual deformation situation. When considering the structural plane's rheological characteristics, the valley shrinkage deformation law is consistent with the conventional elastic–plastic finite element calculation results, but the magnitude is too large. In addition, when considering the rheological characteristics of the structural plane, the increase in valley shrinkage deformation value further increases the stress and deformation of the high arch dam, which can better reflect the dam's working behavior and ensure the dam's safe operation.

Nonlinear viscoelastic model for time-dependent mechanical characterization of PMMA acrylic bone cements

Acrylic bone cement materials are widely used in prosthetic implants, orthopaedics and others trauma surgery. From the mechanical constitutive behaviour viewpoint, experimental analyses have provided ample evidence that such materials exhibit time-dependent properties. In this context, this work addresses the formulation of a nonlinear viscoelastic model for the behaviour of PMMA bone cements under compressive creep loading. Relying upon experimental data available for four PMMA bone cement types, a nonlinear Burgers-like rheological model is formulated and related parameters calibrated for the mechanical description of the time-dependent behaviour of these materials under isothermal conditions and one dimensional setting. The proposed model reveals relevant in reproducing both instantaneous and delayed properties of studied PMMA bone cements.

A nonlinear rheological shear constitutive model of bolted joints considering initial damage and damage evolution

Understanding the shear mechanics mechanism of bolted joints is of great significance for predicting and preventing geological disasters. Most current studies seldom consider the rheological effects of bolted joints. In this paper, a comprehensive rheological constitutive model is proposed, accounting for initial damage and damage evolution across different rheological stages and bolt characteristics. The model incorporates an elastoplastic Hooke body for instantaneous deformation, parametric nonlinear Kelvin and viscous models for attenuation and steady creep stages, and a visco-plastic model based on time-dependent shear strength for accelerated creep stage. Additionally, a bolt-rock cooperative deformation model is introduced, considering the evolution of the bolt's elastic modulus. The resulting elasto-viscoplastic constitutive model effectively describes the shear rheological behavior of bolted joints, with its validity and superiority demonstrated through comparisons with shear creep tests and the Maxwell model. This research aims to provide valuable theoretical guidance for the construction and reinforcement of rock mass engineering projects.

Collagen fibril tensile response described by a nonlinear Maxwell model

Collagen fibrils are the basic structural building blocks that provide mechanical properties such as stiffness, toughness, and strength to tissues from the nano- to the macroscale. Collagen fibrils are highly hydrated and transient deformation mechanisms contribute to their mechanical behavior. One approach to describe and quantify the apparent viscoelastic behavior of collagen fibrils is to find rheological models and fit the resulting empirical equations to experimental data. In this study, we consider a nonlinear rheological Maxwell model for this purpose. The model was fitted to tensile stress-time data from experiments conducted in a previous study on hydrated and partially dehydrated individual collagen fibrils via AFM. The derivative tensile modulus, estimated from the empirical equation, increased for decreasing hydration of the collagen fibril. The viscosity is only marginally affected by hydration but shows a dependency with strain rate, suggesting thixotropic behavior for low strain rates.

Pipe Flow of Viscoplastic Fluids and Analytical Predictions of Concrete Pumping Based on the Shear-Stress-Dependent Parabolic Model

This study investigates the Hagen–Poiseuille pipe flow of viscoplastic fluids, focusing on analytical predictions of concrete pumping using the shear-stress-dependent parabolic model, extending analytical studies to a nonlinear rheological model with easily accessible experimental parameters. Research novelty and highlights encompass solving the steady laminar pipe flow for viscoplastic fluids described by the parabolic model, presenting detailed results for the two-fluid parabolic model, and introducing a computational app implementing theoretical findings. The parabolic model outperforms linear models, such as the Bingham model, in accuracy by accounting for the nonlinearity in the flow curves (i.e., shear stress and shear rate relations) of pumped concrete. The influence of rheological parameters on these relations is analyzed, and their versatility is demonstrated by a Wolfram Mathematica-based application program. The analytical approach developed in this work is adaptable for other models with shear stress as the independent variable, offering valuable insights into viscoplastic fluid flows.

A Rheological Model with Integer and Non-Integer Orders Nonlinearities for Predicting Stress Relaxation Behavior in Viscoelastic Materials

Viscoelastic materials are widely used as devices for vibration control in modern engineering applications. They exhibit both viscous and elastic characteristic when undergoing deformation. They are mainly characterized by three time-dependent mechanical properties such as creep, stress relaxation and hysteresis. Among them, stress relaxation is one of the most important features in the characterization of viscoelastic materials. This phenomenon is defined as a time-dependent decrease in stress under a constant strain. Due to the inherent nonlinearity shown by the material response over a certain range of strain when viscoelastic materials are subjected to external loads, nonlinear rheological models are needed to better describe the experimental data. In this study, a singlenonlinear differential constitutive equation is derived froma nonlinear rheological model composed of a generalized nonlinear Maxwell fluid model in parallel with a nonlinear spring obeying a power law for the prediction of the stress relaxation behavior in viscoelastic materials. Under a constant strain-history, the time-dependent stress is analytically derived in the cases where the positive power law exponent, α ˂ 1 and α ˃1. The Trust Region Method available in MATLAB Optimization Toolbox is used to identify the material parameters. Significant correlations are found between the experimental relaxation data taken from literature and exact analytical predictions. The obtained results show that the developed rheological model with integer and non-integer orders nonlinearities accurately describes the experimental relaxation data of some viscoelastic materials.

ON THE CONVEXITY OF POTENTIAL OF NONLINEAR ELASTIC MEDIA MODEL WITH TENSOR DAMAGE PARAMETER

For solving problems of the theory of elasticity using nonlinear models, the question of the convexity of the potential used and the proof of the uniqueness of the solution are of decisive importance. The present work is devoted to the determination of conditions for the local strict convexity of the potential for the nonlinear elasticity model, which ensure the uniqueness of the solution to the problem in a sufficiently small neighborhood of the desired solution. The considered model is a generalization of a scalar nonlinear rheological model of brittle solid deformation for the case of the tensor damage parameter, the principal values of which describe the reduction in the cross-sectional area of the material in three orthogonal directions. An additional term of the second order in deformation in the elastic potential makes it possible to describe the dependence of the elastic moduli on the type of the stress-strain state, the dilatancy of the material under shear deformation, as well as the nonlinear deformation response even at low loads. The introduced damage tensor of the second rank makes it possible to describe the damage-induced anisotropy of the elastic properties of the material. Conditions of local strict convexity in the principal axes of the strain tensor are obtained in this work for the general case of misaligned strain and damage tensors. To illustrate the obtained convexity conditions, two special cases of the damage tensor type are considered: a transversely isotropic fractured medium with coaxial strain and damage tensors, and a transversely isotropic medium with obliquely oriented fracturing. For both cases, the dependence of the limiting values of damage on the parameter of the degree of anisotropy is shown. It is shown that in the case of weak damage anisotropy, the potential convexity conditions for the scalar damage parameter give a minorant estimate of the maximum allowable damage for various types of stress-strain state. For obliquely oriented fracturing, the dependences of the maximum permissible damage on the degree of anisotropy, the angle of inclination and the type of stress-strain state are plotted.

Which Is an Appropriate Quadratic Rheological Model of Fresh Paste, the Modified Bingham Model or the Parabolic Model?

The physical meaning and calculating process of the rheological parameters of two nonlinear rheological models, the parabolic model and the modified Bingham model, were compared. The fluidity test and a rheological experiment on cementitious materials were performed. The Couette inverse problem is a key issue in measuring and solving the rheological parameters of fresh cementitious materials. The solution of the Couette inverse problem based on the modified Bingham model is discontinuous when the coefficient of the quadratic term is equal to zero, resulting in a large deviation between the fitting curve and the rheological experimental data. The credibility of the rheological parameters of the pastes calculated based on the modified Bingham model is low. The formulas for calculating yield stress, fiducial differential viscosity and the degree of shear thickening or shear thinning of the parabolic model have been developed. The credibility of the rheological parameters of the pastes calculated based on the parabolic model is high. The flow performance of the paste can be clearly characterized by the rheological parameters calculated with the parabolic model.

Research on the Creep Model of Deep Coal Roadway and Its Numerical Simulation Reproduction

The long-term stability of coal mine roadway engineering is critical to the safe mining of coal resources and the protection of the surface environment. In this paper, the creep test of coal samples in coal roadway was carried out by multi-stage constant load method, and the test results showed that when the stress level was low, the creep curve had a attenuated stage and a steady-state stage, and the steady-state creep rate tended to increase with the increase in the stress level; When the stress level was higher than the yield stress, the creep rate curve appeared to have an acceleration stage after the steady-state stage. The instability failure mode of the coal sample was mainly shear failure with local tension failure. For this, a New Fractional-order Nonlinear Viscoelastic-plastic Rheological Model (NFNVRM) was established by introducing Abel elements and Nonlinear elements, and the constitutive equation of the model was deduced. The new model can fully reflect the stable decay stage and accelerated rheological stages of coal samples, and the parameter identification curve was consistent with the experimental results, which verifies the correctness and reasonableness of the NFNVRM. Meanwhile, based on the FLAC3D secondary development interface, the constitutive equations of the NFNVRM were written into the software to obtain new Dynamic Link Library (DLL) files. The simulation results were consistent with the experimental results when the DLL file was called. Finally, the NFNVRM.dll was applied to predict the surrounding rock deformation of an S mine. The study's findings offer suggestions for environmental protection.

Analytical predictions of concrete pumping: Extending the Khatib–Khayat model to Herschel–Bulkley and modified Bingham fluids

It has been widely reported that self-compacting concrete and other cement-based materials are shear-thickening materials. However, there is a lack of an analytical model on the prediction of flow rate–pressure drop relation in the pumping of concrete that takes into account both the presence of the lubrication layer and the shear-thickening behavior of fresh concrete. This work fills this gap by extending analytical predictions of concrete pumping in the presence of a lubrication layer to nonlinear rheological models including the Herschel–Bulkley model and the modified Bingham model. In doing so, a new method is developed to obtain the flow rate–pressure drop relation for the steady Hagen–Poiseuille coaxial flow of two immiscible, incompressible fluids. Analytical expressions are presented for the flow rate–pressure drop relation, shear rate distribution, and velocity distribution based on the two-fluid Herschel–Bulkley model and separately based on the two-fluid modified Bingham model. With those analytical expressions, volumetric flow rate vs. pressure loss curves can be readily constructed, given values for the other eight quantities: three for the rheological properties of the bulk concrete, three for the rheological properties of the fluid in the lubrication layer, pipe radius, and thickness of the lubrication layer.

Nonlinear rheological models and their application to describe the mechanical behavior of highly oriented polymer materials

The nonlinear viscoelasticity of uniaxial oriented polymer materials is considered. To explain the deformation mechanisms of oriented polymers and the possibility of predicting their mechanical behavior in various operating modes, new nonlinear rheological models have been proposed. The application of the simplest rheological model of a real viscoelastic solid to the description and explanation of the recovery process in polymer materials is studied. From the standpoint of rheology, a model of an ideal viscoelastic solid is introduced. Using the balance equation for the number of transitions through energy barriers, a method for calculating the new nonlinear rheological model has been proposed. To eliminate the shortcomings of the ideal viscoelastic solid model associated with the impossibility of predicting creep and stress relaxation modes for long times, a generalized rheological model of a real viscoelastic solid was obtained. In the corrected model, the simplest elements are connected in parallel, which means the presence of not one, but several energy barriers in the materials, the transmission through which have their own relaxation times. To describe the recovery processes in polymer materials, the model of an ideal viscoelastic solid is supplemented by a parallel connected elastic spring. An additional Hooke spring replaces the interfibrillar interaction between the individual elements of the structure and is responsible for possible obstacles during jump-like transitions through the energy barrier. Using the method of rheological models and describing interfibrillar bonds within the framework of the theory of elasticity, a constitutive equation was obtained for the case of recovery processes. Based on the constitutive equation of viscoelasticity for uniaxial oriented polymer materials, a new nonlinear highly elastic element is introduced, which replaces the Maxwell’s element in the theory of linear viscoelasticity. A new rheological model of parallel connection of elastic elements is shown. An explanation of the retardation of the recovery process in polymers is given. The simplest rheological model of a real viscoelastic solid is proposed, in which an elastic spring is responsible for interfibrillar bonds. A constitutive equation is obtained that describes the recovery process in polymers. This equation can be integrated by quadratures and gives a solution that is an analogue of the Newton-Leibniz formula for the proposed model. It is shown that the deformation recovery process in polymer does not depend on the level of initial deformation and the loading method. The obtained result is confirmed by experimental data for polyamide and polyethylene film yarns. When specifying a certain initial level of deformation, generalized recovery curves of these materials are obtained. The proposed simplest rheological model of a real viscoelastic solid makes it possible to predict the reducing properties of polymer materials. And also makes it possible to determine the height of the energy barrier and the magnitude of the elastic modulus in the model. Based on the new rheological models, it is planned in the future to consider the issues of modeling and forecasting different modes of deformation.

Analysis of one‐dimensional nonlinear rheological consolidation of saturated clay considering self‐weight stress and Swartzendruber's flow rule

AbstractConsidering the nonlinear rheological properties of saturated clay, the modified unified hardening (UH) constitutive relation was introduced to describe the nonlinear rheological deformation. Meanwhile, Swartzendruber's flow law was used to simulate the non‐Darcian flow of pore water in the progress of rheological consolidation. Consequently, a nonlinear rheological consolidation model (NRCM), for one‐dimensional consolidation, that simultaneously incorporates nonlinear stress‐strain‐time relationship, Swartzendruber's flow, self‐weight stress, and variable permeability coefficient has been developed here. The finite volume method (FVM) was utilized to solve the NRCM system, and its effectiveness was verified by comparing with the existing consolidation data. The parametric analysis results indicate that the soil's nonlinear rheological effect induced the excess pore water pressure (EPWP)’s accumulation in the initial loading. This phenomenon became more significant when considering the self‐weight stress or as the initial overconsolidated parameter, soil thickness, and seepage parameter increased. In contrast, it weakened with the increase of external loading. Additionally, considering the self‐weight stress slowed down the whole dissipation of EPWP in the initial period of loading. Nevertheless, it accelerated the nonlinear consolidation process in the middle and late loading stages.

A new anisotropic poroelasticity model to describe damage accumulation during cyclic triaxial loading of rock

SUMMARY Crustal rocks undergo repeated cycles of stress over time. In complex tectonic environments where stresses may evolve both spatially and temporally, such as volcanoes or active fault zones, these rocks may experience not only cyclic loading and unloading, but also rotation and/or reorientation of stresses. In such situations, any resulting crack distributions form sequentially and may therefore be highly anisotropic. Thus, the tectonic history of the crust as recorded in deformed rocks may include evidence for complex stress paths, encompassing different magnitudes and orientations. Despite this, the ways in which variations in principal stresses influence the evolution of anisotropic crack distributions remain poorly constrained. In this work, we build on the previous non-linear anisotropic damage rheology model by presenting a newly developed poroelastic rheological model which accounts for both coupled anisotropic damage and porosity evolution. The new model shares the main features of previously developed anisotropic damage and scalar poroelastic damage models, including the ability to simulate the entire yield curve through a single formulation. In the new model, the yield condition is defined in terms of invariants of the strain tensor, and so the new formulation operates with directional yield conditions (different values for each principal direction) depending on the damage tensor and triaxial loading conditions. This allows us to discern evolving yield conditions for each principal stress direction and fit the measured amounts of accumulated damage from previous loading cycles. Coupling between anisotropic damage and anisotropic compaction along with the damage-dependent yield condition produces a reasonable fit to the experimentally obtained stress–strain curves. Furthermore, the simulated time-dependent cumulative damage is well correlated with experimentally observed acoustic emissions during cyclic loading in different directions. As such, we are able to recreate many of the features of the experimentally observed directional 3-D Kaiser ‘damage memory’ effect.

Relaxation function experimental study of the warp strain at slow and regular weaving motion

The combination of the nonlinear rheological models to the simple pendulum in the conditions of the forced oscillations simulates the action of the let-off motion with weights. The experimental study considers the dynamic balance during the unfolding of the warp in function of the adjustments of the let-off motion. The stress of the warp threads carries out the mechanical transition from the loom’s adjustments towards the fabric quality. A rotatable plan of factorial experimentation indirectly explores the process of interaction of threads during the intersection.

Viscoelasticity Modeling of Dielectric Elastomers by Kelvin Voigt-Generalized Maxwell Model.

Dielectric elastomers (DEs) are polymer materials consisting of a network of polymer chains connected by covalent cross-links. This type of structural feature allows DEs to generate large displacement outputs owing to the nonlinear electromechanical coupling and time-dependent viscoelastic behavior. The major challenge is to properly actuate the nonlinear soft materials in applications of robotic manipulations. To characterize the complex time-dependent viscoelasticity of the DEs, a nonlinear rheological model is proposed to describe the time-dependent viscoelastic behaviors of DEs by combining the advantages of the Kelvin–Voigt model and the generalized Maxwell model. We adopt a Monte Carlo statistical simulation method as an auxiliary method, to the best knowledge of the author which has never reportedly been used in this field, to improve the quantitative prediction ability of the generalized model. The proposed model can simultaneously describe the DE deformation processes under step voltage and alternating voltage excitation. Comparisons between the numerical simulation results and experimental data demonstrate the effectiveness of the proposed generalized rheological model with a maximum prediction error of 3.762% and root-mean-square prediction error of 9.03%. The results presented herein can provide theoretical guidance for the design of viscoelastic DE actuators and serve as a basis for manipulation control to suppress the viscoelastic creep and increase the speed response of the dielectric elastomer actuators (DEA).