Viscoplastic Material Research Articles

Start-up shear flow of a shear-thinning fluid that approximates the response of viscoplastic fluids

In this paper we study a start-up shear flow of a recently proposed model of a shear-thinning fluid that mimics the response of a class of viscoplastic materials, namely the flow between parallel plates, one of which is fixed and the other is started impulsively. In simple shear flows while the generalized viscosity blows up, the shear stress is yet finite and thus the fluid is able to mimic the response of viscoplastic fluids. The analytical solution of the velocity profile is obtained using the semi-inverse approach for a perturbation approximation. The partial differential equation for the perturbation approximation is solved numerically, and compared with the analytical solution in order to validate the numerical scheme. The full equations are then solved numerically and the effect of the various material moduli are assessed by introducing appropriate dimensionless variables.

Model tests and corresponding numerical simulations on cave model subjected to thermo-mechanical loading

Geological repository of high-level nuclear waste (HLNW), the most feasible approach for the safe and permanent treatment of HLNW without human intervention, has been investigated for years by many researchers. In some countries, real facilities for the geological repository are already under construction. In Japan, however, due to complicated geologic conditions, especially underground water and fractured rock masses, and the high risk of natural disasters, ensuring the long-term stability of the method remains a struggle. The influential factors include underground water, heat generation from radioactive waste, and thermal and chemical weathering of the surrounding rock mass as a natural barrier. It is difficult to estimate and verify the long-term stability for up to one hundred thousand years, a complicated thermal–hydraulic-mechanical-chemical coupling behavior, via any field test. The objective of the study is to develop a numerical method for predicting the long-term stability of geological repositories. As the first step toward realizing this objective, heating and loading tests on cave model made of man-made rock specimens that are composed of diatoms, gypsum, and water, which are viscoplastic materials, were conducted, based on which a newly proposed numerical method with finite element method (FEM) was used to describe the thermal, mechanical, and time-dependent behavior of the model tests for a geological repository. To ensure the accuracy of the numerical calculations, all the material parameters in the thermoelasto-viscoplastic model with consideration of overconsolidation, the structure, and the influence of intermediate stress were determined via triaxial compression/creep tests under various temperatures, confining stresses, and loading rates. Finally, the validity of the numerical method was demonstrated by model tests over a limited time span.

A Lagrangian differencing dynamics method for granular flow modeling

In this paper, a new Lagrangian differencing dynamics (LDD) method is presented for the simulation of granular flows. LDD is a truly meshless method, which employs second-order consistent spatial operators derived from the Taylor expansion and point renormalization. A decoupled pressure-velocity formulation is employed to derive the pressure Poisson equation, which ensures smooth pressure results in time. Granular media are modeled as viscoplastic materials with the Drucker-Prager yield surface. The velocity equation is formulated and solved in an implicit form, in order to handle large viscosities from the constitutive model. Furthermore, a position-based dynamics technique is used to maintain uniform distribution of the Lagrangian points. The presented LDD method for granular flows is validated by simulating two numerical examples. The results are compared with experimental and numerical data from the literature.

Simulating dense granular flow using the μ(I)‐rheology within a space‐time framework

AbstractA space‐time framework is applied to simulate dense granular flow. Two different numerical experiments are performed: a column collapse and a dam break on an inclined plane. The experiments are modeled as two‐phase flows. The dense granular material is represented by a constitutive model, the (I)‐rheology, that is based on the Coulomb's friction law, such that the normal stress applied by the pressure is related to the tangential stress. The model represents a complex viscoplastic material behavior. The interface between the dense granular material and the surrounding light fluid is captured with a level set function. Due to discontinuities close to the the interface, the mesh requires a sufficient resolution. The space‐time approach allows unstructured meshes in time and, therefore a well‐refined mesh in the temporal direction around the interface. In this study, results and performance of a flat and a simplex space time discretization are verified and analyzed.

To calculation of stresses in drawing of anisotropic viscoplastic material

Relations for calculation of stresses arising in the deformation zone during isothermal drawing without thinning the wall of cylindrical articles from a flat sheet blank are proposed. The stresses are determined by a joint solution of the equilibrium equations and plasticity condition for the plane stress state. The workpiece material is assumed to be transversely isotropic, the deformation is carried out under conditions of viscoplasticity. The deformation hardening and stress relaxation due to manifestation of viscosity of the material in the heating zone is taken into account. Tensile meridional stresses are defined as the sum of stresses in the workpiece flange, stresses caused by bending and straightening of the workpiece on the radial surface of the matrix, as well as friction on the planes of the clamp and the matrix. The received information on stresses in a flange allows to estimate power modes of drawing and damageability of workpiece material. On the basis of the obtained relations, the calculations of stresses and isothermal drawing forces for aluminum and titanium alloys at processing temperature of 450 and 930 оC, respectively, were performed. The dependences of the drawing force on the tool movement rate, which varied in the range from 1 to 10 mm/min, which corresponds to the viscoplasticity mode, are presented. It is established that in the given temperaturevelocity conditions the considered alloys show viscous properties that has considerable influence on the power mode of drawing. A comparison of the results of the force calculation with and without viscosity is performed. It is noted that the deformation degree, tool geometry and anisotropy of mechanical properties of the original material also have a significant effect on the drawing force. The obtained results can be used in design of processes for drawing workpieces from hard-to-deform aluminum and titanium alloys, which are used in aviation and space technology, the deformation of which is carried out under conditions of viscoplastic flow.The work was performed within the framework of the grant for state support of the leading scientific schools of the Russian Federation NSh-2601.2020.8.

Development of LSTM networks for predicting viscoplasticity with effects of deformation, strain rate and temperature history

Abstract In this paper, long short-term memory (LSTM) networks are used in an original way to model the behavior of a viscoplastic material solicited under changing loading conditions. The material behavior is dependent on history effects of plasticity which can be visible during strain rate jumps or temperature changes. Due to their architecture and internal state (memory), the LSTM networks have the ability to remember past data to update their current state, unlike the traditional artificial neural networks (ANNs) which fail to capture history effects. Specific LSTM networks are designed and trained to reproduce the complex behavior of a viscoplastic solder alloy subjected to strain rate jumps, temperature changes or loading-unloading cycles. The training datasets are numerically generated using the constitutive viscoplastic law of Anand which is very popular for describing solder alloys. The Anand model serves also as a reference to evaluate the performances of the LSTM networks on new data. It is demonstrated that this class of networks is remarkably well suited for replicating the history plastic effects under all the tested loading conditions.

Experimental determination and numerical simulation of temperature dependent material and damage behaviour of additively manufactured polyamide 12

Temperature dependent material and damage behaviour of additively manufactured polyamide 12 was analysed. Two different types of tests were carried out. Very slow isothermal and non-isothermal tensile tests at various temperature levels. The results served as basis for the determination of the parameters of the numerical simulation. In a previous study, it was observed that the viscoplastic material model of Chaboche and the damage model of Gurson-Tvergaard-Needleman are very well suited to the material and damage behaviour at room temperature. This work presents that the material model of Chaboche and the damage model of Gurson-Tvergaard-Needleman can be used for isothermal tensile tests at various temperature levels to simulate material and damage behaviour of selectively laser-sintered polyamide 12, with the requirement that the parameters are adjusted for each temperature level. Furthermore, the temperature dependence of the GTN parameters and a sensitivity analysis is presented. Finally, by extending the Chaboche model with the Johnson-Cook approach and coupling it with the Gurson-Tvergaard-Needleman damage model, the material and damage behaviour can be applied under non-isothermal test conditions.

Finite element simulation of the Portevin–Le Chatelier effect in highly reinforced metal matrix composites

ABSTRACT The Portevin–Le Chatelier effect in an AlCu/AlO composite with a large volume fraction (60%) of ceramic particles is investigated from a numerical point of view using a strain-ageing visco-plastic material model for the metallic matrix and several different finite element meshes based on real microstructures. Even for this very large volume fraction, some serrations are observed on the experimental tensile stress/strain curves, together with the propagation of bands of localised plasticity. The finite element model succeeds in reproducing the serrations and the propagation of bands experimentally observed, and allows a fine analysis of the spatio-temporal evolution of the bands of localised plastic strain rate. Different volume fractions are then virtually generated, tested, and compared to outline the influence of this second phase on the Portevin–Le Chatelier effect.

An efficient anisotropization technique to transform isotropic nonlinear materials into unidirectional and bidirectional composites

This work presents a procedure to transform an isotropic nonlinear and rate-dependent material model into orthotropic. This transformation relies on a fast computation modifying the material inelastic evolution along any desired direction. With this concept, the constitutive law of the pure isotropic, nonlinear and rate-dependent material is fully preserved. This paper shows a direct application to describe the nonlinear response of unidirectional (UD) or bidirectional (BD) fiber-reinforced polymer composites. Imposing one constraint leads to a UD composite, whilst imposing two orthogonal directions leads to a BD composite. The proposed methodology is implemented as user-defined material for Finite Element solvers. To prove the method, two different visco-plastic material models used to describe isotropic polymer resins are anisotropized to obtain their corresponding composite counterparts. The mechanical response of the simulations are compared qualitatively and quantitatively to experimental tests on a UD coupon under off-axis tensile test under different load directions. Consistency between the UD and BD anisotropization formulations is proved under tension, shear and different loading directions. Additionally, a complete study of computational performance is addressed to assess the anisotropization’s feasibility to be applied in modeling and design of new laminated and multilayer-based structures exhibiting nonlinear material response.

Numerical simulation of unstable suction transients in unsaturated soils: the role of wetting collapse

AbstractFluid injection is one of the major triggering factors of instability in unsaturated soils. Robust simulation tools are therefore required to examine hydrologic transients in such a class of inelastic materials. In this paper, the governing equations imposing the balance of mass and momentum in deformable unsaturated porous media are inspected from an analytical perspective. Our main goal is to examine the role of volume collapse on the stability of suction transients. Distinct scenarios are considered in terms of material behavior, distinguishing the case of elastoplastic and viscoplastic materials. It shows that in elastoplastic materials the mathematical ill‐posedness of the partial differential equations leads to a diffusive instability of the pore pressure field, signaled by the loss of stress controllability under water injection. By contrast, the introduction of viscosity restores the mathematical well‐posedness and ensures the positive diffusivity. Numerical implications of these findings have been explored through simulations of water injection with a 1D finite element solver. It shows that an increase of the soil hydraulic sensitivity (i.e., a marked deterioration of the yield stress upon suction removal) can deteriorate the diffusive stability and prevent the computation of suction changes across a collapsible soil layer. While the incorporation of minor amounts of viscosity can restore numerical stability by suppressing the constitutive singularity. Such numerical results have been corroborated by the computation of local stability indicators based on controllability theory, which proved to be robust diagnostic tools to identify the culprit of runaway instability emerging from coupled hydro‐mechanical processes.

Natural convection of a viscoplastic fluid in an enclosure filled with solid obstacles

In this work, the natural convection of a viscoplastic fluid inside an enclosure filled with many obstacles is solved numerically. The enclosure is characterized by differentially heated vertical walls, while the obstacles are heat-conducting square blocks. Due to the nature of the viscoplastic material, it is seen that if the buoyancy force is not strong enough, the whole fluid can be unyielded, and the heat transfer takes place only by conduction. The Bingham constitutive equation is chosen to represent the yield-stress material. Steady-state velocity and temperature fields are obtained for a wide range of Rayleigh and Bingham numbers and several numbers of blocks. We show that increasing the yield-stress has a quantitative effect on reducing the fluid circulation, and consequently, the heat transfer rate. At a certain yield-stress level, the fluid motion is abruptly interrupted. The critical Bingham number for complete unyielding does not depend on the Rayleigh or Prandtl numbers. However, the obstacles' configuration has a significant effect on this transition. Flow vs. no-flow diagrams and average Nusselt number correlations are proposed as aid for thermal engineering of similar arrangements.

English

A new model is proposed to mimic the response of a class of seemingly viscoplastic materials. Using the proposed model, the steady, fully developed flow of the fluid is studied in a cylindrical pipe. The semi-inverse approach is applied to obtain an analytical solution for the velocity profile. The model is used to fit the shear-stress data of several supposedly viscoplastic materials reported in the literature. A numerical procedure is developed to solve the governing ODE and the procedure is validated by comparison with the analytical solution.

An extended linear method to evaluate the viscoplastic behavior of boron steel at large strain with full-field measurements

The reliable parameter identification method of the constitutive behavior under large strain conditions is essential for accurate simulation in the hot stamping and warm-cutting process. In this paper, the linear stress-strain curve identification (LSSCI) method is extended to identify the viscoplastic behavior of boron steel at large strain based on the full-field measurements in the Gleeble system. An inverse LSSCI method to evaluate the strain rate sensitivity under different temperatures based on full-field measurements is presented. To overcome the fluctuation of the identified stress-strain curve at large strain, a constrained optimization method is proposed to solve the linear system. The numerical and experimental cases are performed to verify the accuracy and reliability of the proposed LSSCI method. The verification result shows that the identification error of the extended LSSCI method is generally less than 1%, and the maximum error is not more than 4%. The influence of strain rate, specimen shape, constitutive model, noise and discretization on the identification curves have been studied, the results show that the extended LSSCI method is robust when applied to viscoplastic material identification. To accurately describe the viscoplastic behavior of Boron steel at large strain, a unified viscoplastic (UVP) model is proposed based on the dislocation density evolution under elevated temperature. Finally, the tensile testing of shear and notched specimen are carried out to verify the accuracy and reliability of the proposed UVP model, the comparison of load-stroke curve shows that the large deformation behavior of the boron steel under various conditions can be accurately predicted by the UVP model with the parameters from the proposed LSSCI method.

Influence of Heat and Mass Transfer on Peristaltic Transport of Viscoplastic Fluid in Presence of Magnetic Field through Symmetric Channel with Porous Medium

In the present paper, we discussed the influence of heat and mass transfer on peristaltic transport of viscoplastic fluid in presence of magnetic field through symmetric channel with porous medium. The constitutive equation of Bingham plastic model is chosen to describe viscoplastic material. The nonlinear partial differential equations that described the motion of flow are simplified under assumptions of low Reynolds number and long wavelength. These equations are solved by mean of the regular perturbation method which is restricted to the smaller values of Bingham and Grashof numbers. Series solution for the axial velocity, temperature and concentration distribution have been computed. The flow quantities have been illustrated graphically for different interesting parameters. The pressure rise and trapping phenomena are also examined graphically. MATHEMATICA software is used to plot all figures.

Simulation of the viscoplastic extrusion process using the radial point interpolation meshless method

Additive manufacturing is an emergent technology, which witnessed a large growth demanded by the consumer market. Despite this growth, the technology needs scientific regulation and guidelines to be reliable and consistent to the point that is feasible to be used as a source of manufactured end-products. One of the processes that has seen the most significant development is the fused deposition modeling, more commonly known as 3D printing. The motivation to better understand this process makes the study of extrusion of materials important. In this work, the radial point interpolation method, a meshless method, is applied to the study of extrusion of viscoplastic materials, using the formulation originally intended for the finite element method, the flow formulation. This formulation is based on the reasoning that solid materials under those conditions behave like non-Newtonian fluids. The time stepped analysis follows the Lagrangian approach taking advantage of the easy remeshing inherent to meshless methods. To validate the newly developed numerical tool, tests are conducted with numerical examples obtained from the literature for the extrusion of aluminum, which is a more common problem. Thus, after the performed validation, the algorithm can easily be adapted to simulate the extrusion of polymers in fused deposition modeling processes.

Polyelectrolyte layer grafting effect on the rotational electroosmotic flow of viscoplastic material

Due to growing importance of study of bio-fluids in rotational microfluidic platforms, discussion of flow of viscoplastic materials in such situations becomes very important. Bio-fluids also generally flow in soft channel microfluidic environment and therefore studying the effect of softness of channels on flow of such viscoplastic bio-fluids becomes critical. We, in the present study, investigate the effect of the rotation of the channel and yield stress of the fluid on the flow of viscoplastic material in a soft microchannel for three constitutive models viz. Bingham, Casson and Herschel–Bulkley models. It is found that the soft grafted layer, the channel rotation and the fluid yield stress play vital roles in determining the flow behaviour. We find that that larger rotational speeds tend to destabilize the flow. We also find the critical rotational speed for which secondary flow magnitude is maximum. We also find that this non-linear interaction between rotation of channel and fluid yield stress leads to the generation of multiple yield planes within the flow domain. Our study will help in obtaining good designs of rotational microfluidic platforms for studying bio-fluids with yield stress.

A new stress-updating algorithm for viscoplasticity

Material behavior beyond the elastic limit can be rate-dependent, and this rate sensitivity can be captured by the viscoplastic material models. To describe the viscoplastic material behavior in structural analysis, an efficient numerical framework is necessary. In this paper an algorithm is proposed for metals for which von Mises yield surface along with Peric’s viscoplastic model is employed. The efficiency and accuracy of the technique is examined by comparison with different numerical studies. The convergence rate of the proposed algorithm is investigated. Characteristics of the viscoplastic behavior such as relaxation are illustrated in the selected case studies. Finally, application of the algorithm in practice is demonstrated by a boundary value problem.

Cell Junction Mechanics beyond the Bounds of Adhesion and Tension.

Cell-cell junctions, in particular adherens junctions, are major determinants of tissue mechanics during morphogenesis and homeostasis. In attempts to link junctional mechanics to tissue mechanics, many have utilized explicitly or implicitly equilibrium approaches based on adhesion energy, surface energy, and contractility to determine the mechanical equilibrium at junctions. However, it is increasingly clear that they have significant limitations, such as that it remains challenging to link the dynamics of the molecular components to the resulting physical properties of the junction, to its remodeling ability, and to its adhesion strength. In this perspective, we discuss recent attempts to consider the aspect of energy dissipation at junctions to draw contact points with soft matter physics where energy loss plays a critical role in adhesion theories. We set the grounds for a theoretical framework of the junction mechanics that bridges the dynamics at the molecular scale to the mechanics at the tissue scale.

A method for determining equivalent hardening responses to approximate sheet metal viscoplasticity

Recently developed elevated temperature metal forming technologies improve material formability and address the springback issues of cold forming. However, the behaviour of alloys at elevated temperatures is viscoplastic and therefore considerably more complex than under cold forming conditions. This complex behaviour creates a barrier for industrial designers when designing for elevated temperature processes, and therefore leads to these processes often being overlooked. To overcome this barrier, a new method is proposed here to determine simpler strain hardening responses that are equivalent to the viscoplastic responses of alloys at elevated temperatures. The equivalent hardening responses are expressed by single material hardening curves and their hardening exponents are taken as parameters to approximate sheet metal viscoplasticity. This method therefore makes it possible to develop early-stage design guidelines that consider different materials and stamping processes. The method was successfully applied to two viscoplastic alloys under hot stamping conditions to determine equivalent hardening responses. The feasibility of the method has been assessed through comparing finite element simulations using the determined equivalent material models with ones using viscoplastic models. The result showed that the thinning distributions obtained were consistent in both cases, providing evidence that the method can be applied to a range of component designs.•The proposed equivalent material models are simpler than existing viscoplastic material models and can be derived directly from experimental stress-strain data.•Creating design guidelines from equivalent hardening exponents enables a straightforward way to compare between cold and hot stamping capabilities. This comparison makes it possible to make manufacturing process and material selection decisions quickly and effectively at the onset of a design process.•Design guidelines enabled by the proposed method are critical resources to encourage the uptake of new elevated temperature metal forming technologies that facilitate lightweighting and improved environmental efficiency.

A finite strain framework for steady-state problems: Hyperelasto-viscoplasticity

A numerical framework for analyzing steady-state elastic–plastic material deformation at finite strains is developed and demonstrated in the present work. The framework is an extension of the original method by Dean and Hutchinson (1980) develop to analyze steady-state crack propagation, under a small strain assumption, in which the history-dependent material response is captured through streamline integration. Steady-state problems are encountered in numerous engineering processes, and the original studies of crack growth have already been extended to include rolling and drawing, though within a small strain framework. However, the investigation of such manufacturing processes, where strains greater than 10% easily develop, requires a finite strain formulation to provide accurate results. The framework proposed in the present work offers an efficient and accurate method to extract the steady-state solution at finite strains without encountering the numerical issues related to traditional Lagrangian procedures. Furthermore, the framework also accounts for elastic unloading compared to many existing numerical steady-state schemes as they are often restricted to rigid plasticity. The new numerical framework employs a hyperelastic material model, in terms of a Neo-Hookean material, combined with an isotropic viscoplastic material behavior. However, the framework is not limited to any specific hyperelastic material model, nor any specific model for the plastic behavior. The finite strain steady-state framework has been verified through comparison to a traditional Lagrangian analysis conducted in ANSYS. The benchmark case constitutes a plane strain drawing process where the thickness of the specimen is reduced by drawing it between two circular cylindrical tools.