Search Results (93)

This paper presents a finite element implementation of a fractional rheological consolidation model in ABQUS, in which the fractional Merchant model governs the mechanical behavior of the soil skeleton, and the water flow is controlled by the fractional Darcy’s law. The implementation generally involves two main parts: subroutine-based fractional constitutive models’ development and their coupling. Considering the formal similarity between the energy equation and the mass equation, the fractional Darcy’s law was implemented using the UMATHT subroutine. The fractional Merchant model was then realized through the UMAT subroutine. Both subroutines were individually verified and then successfully coupled. The coupling was achieved by modifying the stress update scheme based on Biot’s poroelastic theory and the effective stress principle in UMAT, enabling a finite element analysis of the fractional consolidation model. Finally, the model was applied to simulate the consolidation behavior of a multi-layered foundation. The proposed approach may serve as a reference for the finite element implementation of consolidation models incorporating a fractional seepage model in ABAQUS. Full article

A linear stability analysis is performed for a power-law liquid film flowing down an inclined rigid plane over a deformable solid layer. The deformable solid is modeled using a neo-Hookean constitutive equation, characterized by a constant shear modulus and a nonzero first normal stress difference in the base state at the fluid–solid interface. To solve the linearized eigenvalue problem, the Riccati transformation method, which offers advantages over traditional techniques by avoiding the parasitic growth seen in the shooting method and eliminating the need for large-scale matrix eigenvalue computations, was used. This method enhances both analytical clarity and computational efficiency. Results show that increasing solid deformability destabilizes the flow at low Reynolds numbers by promoting short-wave modes, while its effect becomes negligible at high Reynolds numbers where inertia dominates. The fluid’s rheology also plays a key role: at low Reynolds numbers, shear-thinning fluids ($n<1$) are more prone to instability, whereas at high Reynolds numbers, shear-thickening fluids ($n>1$) exhibit a broader unstable regime. Full article

With the increasing construction of engineering structures on soft soils, accurately assessing their consolidation behavior has become crucial. To address this, Terzaghi’s one-dimensional consolidation model was revisited. The elastic behavior of soil skeleton was modified by incorporating viscous effects using the fractional derivative Merchant model (FDMM), while the linear Darcy’s law governing flux–pressure relations was extended by introducing time memory formalism through the fractional derivative Darcy model (FDDM). The governing equation is derived by incorporating the resulting constitutive behavior of both the soil skeleton and water flow into the Terzaghi’s formulation of the poroelasticity problem. The proposed rheological consolidation model is solved by a forward time-centered space scheme (FTCS). After verifying the numerical procedure with published data, the influence of parameters on both the average degree of settlement and the pressure was comprehensively studied. Full article

Fluid flow along an inclined channel phenomenon is crucial in several geophysical, environmental, engineering, biological, and industrial processes, and in aerodynamics and hemodynamics. This present study examines the effect of a constant magnetic field on the entropy production rate in a steady flow of Casson fluid along an inclined heated channel. The governing equations for the flow of velocity, temperature, and entropy generation are formulated based on the Casson constitutive relations and thermodynamics’ first and second laws. The exact solutions are constructed for the dimensionless equations and validated with previous results in the literature. The effects of various fluid parameters on the flow, heat transfer, and entropy production rate are conducted and reported graphically with adequate discussion. The impact of the Hartmann number parameter reveals a decrease in both flow velocity and entropy generation rate, meanwhile it also enhances the fluid temperature distribution across the inclined channel. An opposite trend is, however, observed with the Casson fluid parameter. Full article

Friction has a significant impact on chip formation, so modeling it accurately is crucial in numerical cutting simulations. However, there is still controversy regarding the application scope and effectiveness of various friction models. A two-dimensional orthogonal cutting thermomechanical coupled finite element model is established. Critical strain values, recrystallization temperature, and recrystallization flow stress are introduced, and a power-law-modified softening coefficient is used to modify the standard Johnson–Cook constitutive model to simulate material mechanical properties. Zorev’s friction model, velocity-dependent friction model, and temperature-dependent friction model are separately employed to describe the friction behavior between the tool and workpiece. The contact and friction characteristics between the workpiece and tool, material damage, and temperature field are evaluated. Predicted cutting forces are compared and analyzed with experimental values. The friction coefficient can adjust the contact length between the tool and chip, the high-temperature range on the tool surface, and the fluctuation of temperature throughout the entire cutting process. The friction coefficient is more sensitive to sliding velocity, and the temperature distribution is more sensitive to the friction model than to different working conditions. Whether by modifying the friction coefficient or maximum friction shear stress, and regardless of whether adding parameters affected by velocity or temperature changes the fluctuation range, period, and local peaks of the cutting force prediction curve, improving the accuracy of predictions within certain working condition ranges to some extent. However, the overall trend of error fluctuations obtained from these friction models is similar, and the accuracy of predictions from these friction models tends to become more inaccurate with increasing cutting thickness. Full article

Modeling of friction stir welding (FSW) is challenging, as there are large gradients in both strain rate and temperature (typically between 450 and 500 °C in aluminum alloys) that must be accounted for in the constitutive law of the material being joined. Constitutive laws are most often calibrated using flow stresses from hot compression or hot torsion testing, where strain rates are much lower than those seen in the stir zone of the FSW process. As such, the current work employed a recently developed method to measure flow stresses at high strain rates and temperatures in AA 2219-T67, and these data were used in the development of a finite element (FE) simulation of FSW. Because heat generation during FSW is primarily a function of friction between the rapidly spinning tool and the plate, the choice of friction law and associated parameters were also studied with respect to FE model predictions. It was found that the Norton viscoplastic friction law provided the most accurate modeling results, for both the transient and steady-state phases of an FSW plunge experiment. It is likely that the superior performance of the Norton law was its ability to account for temperature and rate sensitivity of the plate material sheared by the tool, while the Tresca-limited Coulomb law favored contact pressure, with essentially no temperature or rate dependence of the local material properties. With optimized friction parameters and more accurate flow stresses for the weld zone, as measured by a high-pressure shear test, a 65% overall reduction in model error was achieved, compared to a model that employed a material law calibrated with hot compression or hot torsion test results. Model error was calculated as an equally weighted comparison of temperatures, torques, and forces with experimentally measured values. Full article

Shale is a common rock in oil and gas extraction, and the study of its nonlinear mechanical behavior is crucial for the development of engineering techniques such as hydraulic fracturing. This paper establishes a new coupled elastic–plastic damage model based on the second law of thermodynamics, the strain equivalence principle, the non-associated flow rule, and the Drucker–Prager yield criterion. This model is used to describe the mechanical behavior of shale before and after peak strength and has been implemented in ABAQUS via UMAT for numerical computation. The model comprehensively considers the quasi-brittle and anisotropic characteristics of shale, as well as the strength degradation caused by damage during both the elastic and plastic phases. A damage yield function has been established as a criterion for damage occurrence, and the constitutive integration algorithm has been derived using a regression mapping algorithm. Compared with experimental data from La Biche shale in Canada, the theoretical model accurately simulated the stress–strain curves and volumetric–axial strain curves of shale under confining pressures of 5 MPa, 25 MPa, and 50 MPa. When compared with experimental data from shale in Western Hubei and Eastern Chongqing, China, the model precisely fitted the stress–strain curves of shale at pressures of 30 MPa, 50 MPa, and 70 MPa, and at bedding angles of 0°, 22.5°, 45°, and 90°. This proves that the model can effectively predict the failure behavior of shale under different confining pressures and bedding angles. Additionally, a sensitivity analysis has been performed on parameters such as the plastic hardening rate b, damage evolution rate B_ω, weighting factor r, and damage softening parameter a. This research is expected to provide theoretical support for the efficient extraction technologies of shale oil and gas. Full article

Due to their nature, using shear thickening fluids (STFs) in engineering applications has sparked an interest in developing energy-dissipating systems, such as damping devices or shock absorbers. The Rheinforce technology allows the design of customized energy dissipative composites by embedding microfluidic channels filled with STFs in a scaffold material. One of the reasons for using microfluidic channels is that their shape can be numerically optimized to control pressure drop (also known as rectifiers); thus, by controlling the pressure drop, it is possible to control the energy dissipated by the viscous effect. Upon impact, the fluid is forced to flow through the microchannel, experiencing the typical entry flow until it reaches the fully developed flow. It is well-known for Newtonian fluid that the entrance flow is responsible for a non-negligible percentage of the total pressure drop in the fluid; therefore, an analysis of the fluid flow at the entry region for STFs is of paramount importance for an accurate design of the Rheinforce composites. This analysis has been numerically performed before for shear-thickening fluids modeled by a power-law model; however, as this constitutive model represents a continuously growing viscosity between end-viscosity plateau values, it is not representative of the characteristic viscosity curve of shear-thickening fluids, which typically exhibit a three-region shape (thinning-thickening-thinning). For the first time, the influence of these three regions on the entry flow on an axisymmetric pipe is analyzed. Two-dimensional numerical simulations have been performed for four STFs consisting of four dispersions of fumed silica nanoparticles in polypropylene glycol varying concentrations (7.5–20 wt%). Full article

This study uses a sigmoidal function to describe the plastic strain hardening of metallic materials, considering temperature and strain rate effects. The effectiveness of this approach is evaluated and systematically compared with other hardening laws. Incorporating temperature and strain rate effects into the parameters of this sigmoidal-type hardening law enables a more precise description and prediction of the plastic deformation of materials under different combinations of temperature and strain rate. The temperature effect is coupled using a simplified Arrhenius model, and the strain rate effect is coupled with a modified Johnson–Cook model. The sigmoidal-type hardening law is integrated with an asymmetric yield criterion to address complex behavior, such as anisotropy and strength differential effects. The calibration and validation of the constitutive model involve examining uniaxial tensile/compressive flow curves in various directions and biaxial tensile/compressive flow curves for diverse metallic alloys, proving the proposed model’s broad applicability. Full article

To conduct a more in-depth study of the flow mechanism of power-law fluids within sewage pumps, this paper focuses on self-priming sewage pumps, with typical power-law fluid (Carboxymethyl Cellulose, CMC) as the conveying medium. The constitutive equations for sewage and typical power-law fluid (CMC solution) were established using the power-law model. Through numerical calculation methods, the non-steady flow field inside the pump of different concentration power-law fluids was analyzed from various aspects such as velocity, pressure, vorticity, and wall shear stress. The pressure pulsations at key locations in the pump flow field were monitored and analyzed. At the rated flow rate, when the concentration of CMC solution increased from 0.5% to 2.0%, the channel pressure and tongue pressure decreased by 16.5% and 3.5%, respectively. This indicates that the pressure on the impeller blades, within the flow passages, and at the tongue of the volute all decrease with the increase in concentration of CMC solution. This may alter the fluid flow pattern, leading to more vortex motion and shear deformation, while also reducing the pump’s pressure boosting capability, thereby affecting the pump’s performance stability. It can be inferred from quantitative comparisons that changes in rheological properties had a significant impact on the flow characteristics of sewage pumps. This paper reveals that some flow characteristics of power-law fluids in sewage pumps, providing a theoretical and reference basis for the performance optimization and flow mechanism research of sewage pumps. Full article

The term “viscoelastic pipe” refers to high polymer pipes that exhibit both elastic and viscoelastic properties. Owing to their widespread use in water transport systems, it is important to understand the transient flow characteristics of these materials for pipeline safety. Despite extensive research, these characteristics have not been sufficiently explored. This study evaluates the impact of friction models on the transient flow of viscoelastic pipes across various Reynolds numbers by employing an energy analysis approach. Given the complexity and computational demands of two-dimensional models, this paper compares the accuracy of one-dimensional and quasi-two-dimensional models. Notably, the superiority of the quasi-two-dimensional model in simulating viscoelastic pipelines is demonstrated. Owing to the interaction between pressure waves and fluid within viscoelastic pipes, fluid–structure coupling significantly attenuates pressure waves during transmission. These findings shed light on the constitutive properties of viscoelastic pipes and the influence of pipe wall friction models on transient hydraulic characteristics, building upon prior studies focused on elastic pipes. Nevertheless, numerous factors affecting transient flow in viscoelastic pipes remain unexplored. This paper suggests further analysis of strain effects, starting with temperature and pipe dynamics, to enhance the understanding of the coupling laws and flow mechanisms in viscoelastic pipelines. Full article

We present a macroscale constitutive model that couples magnetism with thermal, elastic, plastic, and damage effects in an Internal State Variable (ISV) theory. Previous constitutive models did not include an interdependence between the internal magnetic (magnetostriction and magnetic flux) and mechanical fields. Although constitutive models explaining the mechanisms behind mechanical deformations caused by magnetization changes have been presented in the literature, they mainly focus on nanoscale structure–property relations. A fully coupled multiphysics macroscale ISV model presented herein admits lower length scale information from the nanoscale and microscale descriptions of the multiphysics behavior, thus capturing the effects of magnetic field forces with isotropic and anisotropic magnetization terms and moments under thermomechanical deformations. For the first time, this ISV modeling framework internally coheres to the kinematic, thermodynamic, and kinetic relationships of deformation using the evolving ISV histories. For the kinematics, a multiplicative decomposition of deformation gradient is employed including a magnetization term; hence, the Jacobian represents the conservation of mass and conservation of momentum including magnetism. The first and second laws of thermodynamics are used to constrain the appropriate constitutive relations through the Clausius–Duhem inequality. The kinetic framework employs a stress–strain relationship with a flow rule that couples the thermal, mechanical, and magnetic terms. Experimental data from the literature for three different materials (iron, nickel, and cobalt) are used to compare with the model’s results showing good correlations. Full article

In this work, we propose a new three-dimensional constitutive equation related to a third-grade fluid. This proposal is based on experimental work for which the viscosity term and the terms related to viscoelasticity may depend on the shear rate, in accordance with a power-law type model. The numerical implementation of this fluid model is rather demanding in terms of computational calculation and, in this sense, we use the Cosserat theory related to fluid dynamics, which makes the transition from the three-dimensional fluid model to a one-dimensional fluid model for a specific geometry under study which, in this case, is a straight tube with constant circular cross-section. Based on this approximation theory, the one-dimensional fluid model is solved by assuming an ordinary differential equation involving: an unsteady mean pressure gradient; an unsteady volume flow rate; the Womersley number; and the viscosity and viscoelasticity parameters. Consequently, for specific data, and using the Runge–Kutta method, we can obtain the solution for the unsteady volume flow rate and we can present simulations to the three-dimensional velocity field. Full article

We propose a methodology for the rheological characterization of a semisolid metal slurry using experimental squeeze-flow data. The slurry is modeled as a structural thixotropic viscoplastic material, obeying the regularized Herschel–Bulkley constitutive equation. All rheological parameters are assumed to vary with the structure parameter that is governed by first-order kinetics accounting for the material structure breakdown and build-up. The squeeze flow is simulated using finite elements in a Lagrangian framework. The evolution of the sample height has been studied for wide ranges of the Bingham and Reynolds numbers, the power-law exponent as well as the kinetics parameters of the structure parameter. Systematic comparisons have been carried out with available experimental data on a semisolid aluminum alloy (A356), where the sample is compressed from its top side under a specified strain of 80% at a temperature of 582 °C, while the bottom side remains fixed. Excellent agreement with the experimental data could be achieved provided that at the initial instances (up to 0.01 s) of the experiment, the applied load is much higher than the nominal experimental load and that the yield stress and the power-law exponent vary linearly with the structure parameter. The first assumption implies that a different model, such as an elastoviscoplastic one, needs to be employed during the initial stages of the experiment. As for the second one, the evolution of the sample height can be reproduced allowing the yield stress to vary from 0 (no structure) to a maximum nominal value (full structure) and the power-law exponent from 0.2 to 1.4, i.e., from the shear-thinning to the shear-thickening regime. These variations are consistent with the internal microstructure variation pattern known to be exhibited by semisolid slurries. Full article

Measuring the flow properties of fiber-laden fresh concrete poses a substantial challenge because not only the fraction of fibers but also their orientation process during the measurement influence the measured quantities. Numerical simulations of the flow in a ball probe rheometer are used to determine the fiber orientation process during the measurement of the flow properties and its influence on the measured variables. Through analytical considerations and comparison with measurement results, it can be shown that the constitutive law applied can reproduce the real flow behavior very well, taking the fiber orientation into account. At the same time, it is investigated why no orientation influence on the torque is recognizable in the experimental measurement curves, although the orientation process demonstrably exceeds the duration of the measurement process. The results show that fluid inertia is overcome before the recognizable onset of fiber orientation, and the spatially inhomogeneous flow minimises the impact of the orientation process on torque. The simulation model aligns well with experimental outcomes, indicating a linear increase in effective viscosity with increasing fiber volume fraction. The findings can be used to accurately measure the objective material parameters of the orientation-considering constitutive law using ball probe rheometers, so that an accurate prediction of the flow process of fresh concrete with fibers is made possible, for example for the simulation of formwork fillings. Full article