Performance of an elasto-viscoplastic model in some benchmark problems (original) (raw)
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Finite elements for thixotropic elasto-viscoplastic flows
2015
This work aims at performing finite element approximations for entry flows of thixotropic elasto-viscoplastic fluids, using the structured fluid model introduced in de Souza Mendes (2011). The constitutive equation is based on a modification of the Oldroyd-B viscoelastic equation, with variable viscosity and relaxation time. According to this model, both the relaxation time and the viscosity are functions of a scalar parameter-denoted herein by structure parameter-that deals with microscopic changes in the material microstructure. All results are obtained using a four-field GLS-type method, aiming at determining the accurate morphology and position of the unyielded regions in entry flows of elasto-viscoplastic fluids through an one-to-four sudden expansion.
Thixotropic elasto-viscoplastic model for structured fluids
A constitutive model for structured fluids is presented. Its predictive capability includes thixotropy, viscoelasticity and yielding behavior. It is composed by two differential equations, one for the stress and the other for the structure parameter-a scalar quantity that represents the structuring level of the fluid. The equation for stress is obtained in accordance with a simple mechanical analog composed by a structuring-level-dependent Maxwell element in parallel with a Newtonian element, leading to an equation of the same form as the Jeffreys (or Oldroyd-B) equation. The relaxation and retardation times that arise are functions of the structure parameter. The ideas found in de Souza Mendes, J. Non-Newtonian Fluid Mech., 2009, 164, 66 are employed for the structure parameter equation as well as for the dependencies on the structure parameter of the structural viscosity and structural shear modulus. The model is employed in constant-rate, constant-stress, and oscillatory shear flows, and its predictive capability is shown to be excellent for all cases.
2013
A constitutive model for elasto-viscoplastic thixotropic materials is proposed. It consists of two differential equations, one for the stress and the other for the structure parameter, a scalar quantity that indicates the structuring level of the microstructure. In contrast to previous models of this kind, the structure parameter varies from zero to a positive and typically large number. The lower limit corresponds to a fully unstructured material, whereas the upper limit corresponds to a fully structured material. When the upper limit is finite, the model represents a highly shear-thinning, thixotropic, and viscoelastic liquid that possesses an apparent yield stress. When it tends to infinity, the behavior of a true yield-stress material is achieved. Predictions for rheometric flows such as constant shear rate tests, creep tests, SAOS, and large-amplitude oscillatory shear (LAOS) are presented, and it is shown that, in all cases, the trends observed experimentally are faithfully reproduced by the model. Within the framework of the model, simple explanations are given for the avalanche effect and the shear banding phenomenon. The LAOS results obtained are of particular importance because they provide a piece of information that so far is absent in the literature, namely a quantitative link between the Lissajous-Bowditch curve shapes and rheological effects such as elasticity, thixotropy, and yielding.
Plane flow of thixotropic elasto-viscoplastic materials through a 1:4 sudden expansion
Journal of Non-Newtonian Fluid Mechanics, 2015
A numerical investigation of an elasto-viscoplastic thixotropic fluid flowing through a 1:4 plane expansion is performed, using a recently proposed constitutive equation. The conservation equations are solved using a four-field Galerkin least-squares formulation in terms of the extra stress, pressure, velocity, and structure parameter-a scalar quantity that represents the structuring level of the material microstructure. The focus is on determining the effect of thixotropy, elasticity and viscoplasticity on the topology of yielded and unyielded regions of the expansion, on the field of structuring level, and on the field of elastic strain. Relevant ranges of the relaxation time, yield stress, and thixotropy characteristic time are investigated. The numerical results reveal significant effects of these parameters. The trends observed are physically sound and in accordance with the related literature.
A critical overview of elasto-viscoplastic thixotropic modeling
Journal of Non-Newtonian Fluid Mechanics, 2012
The literature on thixotropy modeling is reviewed, with particular emphasis on models for yield stress materials that possess elasticity. The various possible approaches that have been adopted to model the different facets of the mechanical behavior of this kind of materials are compared and discussed in detail. An appraisal is given of the advantages and disadvantages of algebraic versus differential stress equations. The thixotropy phenomenon is described as a dynamical system whose equilibrium locus is the flow curve, and the importance of using the flow curve as an input of the model is emphasized. Different forms for the evolution equation for the structure parameter are analyzed, and appropriate choices are indicated to ensure a truthful description of the thixotropy phenomenon.
Numerical Simulation of a Elasto-Viscoplastic Fluid Flow Inside a Cavity
Revista de Engenharia Térmica, 2018
This article addresses finite element approximations for elasto-viscoplastic flows. Numerical simulations aiming at investigating the role of elasticity for inertialess flows of viscoplastic materials within lid-driven cavity.The mechanical model is made up of the usual governing equations for incompressible fluids coupled with a Oldroyd-B type equation (de Souza Mendes, 2011) modified to incorporate the dependency both of relaxation and retardation time as the viscoplastic viscosity on the strain rate. These parameters depend on the material microstructure, which level is described by an structure parameter . This model is approximated by a multi-field Galerkin least-squares formulation (Behr et al., 1993) in terms of extra-stress tensor, the pressure field and the velocity vector. Results, focused on the determination of yield surface topology, investigate the influence of elastic and viscous governing parameters on the flow pattern.
Modeling the rheology of thixotropic elasto-visco-plastic materials
Journal of Rheology, 2019
To describe the macroscopic rheological behavior of thixotropic elasto-visco-plastic (TEVP) materials, phenomena that take place in their microstructure must be accounted for. To this end, we couple the tensorial constitutive model by Saramito for EVP materials with thixotropy, extending the ideas of isotropic hardening, and with kinematic hardening (KH), to account for back stresses. We use a scalar variable that describes the level of structure at any instance and a modified Armstrong–Frederick KH equation, thus providing rules governing the dynamics of the apparent yield stress. The material viscosity, yield stress, and back stress modulus feature a nonlinear dependence on the structural parameter, enabling the model to make accurate predictions with a single structural parameter. To avoid unphysical stress evolution in both shear and extensional flows, we propose a modified back stress constitutive equation that keeps the components of the stress tensor bounded. The predictions ...
Flow of elasto-viscoplastic thixotropic liquids past a confined cylinder
Journal of Non-Newtonian Fluid Mechanics, 2013
A numerical investigation of elasto-viscoplastic thixotropic liquids flowing past a cylinder confined in a parallel-plate channel is performed, using a recently proposed constitutive equation. The conservation equations are solved using a four-field Galerkin least-squares formulation in terms of the extra-stress, pressure, velocity, and structure parameter -a scalar quantity that represents the structuring level of the material microstructure. The focus is on determining the effect of both thixotropy and elasticity on the topology of yielded and unyielded regions of the channel. The effect on the cylinder drag coefficient is also studied. Relevant ranges of the dimensionless relaxation time and equilibrium time of the material structure are investigated. The numerical results reveal striking effects of thixotropy and elasticity. The trends observed are physically sound and in accordance with the related literature.
International Journal of Engineering Science
In the present work, we present an approach to handle transient flows of elastoviscoplastic thixotropic (EVPT) materials under the action of the gravity force field and subjected to free-surface boundary conditions that are stress-based. This kind of conditions are common in problems where the motion is unknown a priori , i.e. the motion is treated as a consequence while the forces are the cause. The model for the EVPT material employed is within the scope of a recently developed thermodynamic backbone for elastoviscoplastic thixotropic materials. The finite difference Marker and Cell method is used to investigate effects of elasticity, thixotropy, and plasticity varying the Weissenberg number, the dimensionless thixotropic equilibrium time, and the yield number, respectively. The Cartesian Poiseuille flow is used to test the main features of the numerical scheme. The evolution in time of an initially square and fully-structured block is captured. The structure level and shape evolutions of the block reveal the capability of the present numerical approach to handle the complexity of the material and the free-surface motion.
Elastic and viscous effects on flow pattern of elasto-viscoplastic fluids in a cavity
Mechanics Research Communications, 2013
Inertialess flows of elasto-viscoplastic fluids inside a leaky cavity are numerically analyzed using the finite element technique, with the goal of understanding the influence of both the elastic and viscous effects on the topology of the yield surfaces of an elasto-viscoplastic material. Assuming that the collapse of the material microstructure is instantaneous, a mechanical model is composed of the governing equations of mass and momentum for incompressible fluids, and associated with a hyperbolic equation for the extra-stress tensor based on the Oldroyd-B model . The main feature of the model is the consideration of the viscosity and relaxation time as functions of the strain rate to allow the shearthinning of the viscosity and to restrict the elastic effects to the unyielded regions of the material. The numerical simulations are performed through a three-field Galerkin least-squares-type method in terms of the extra-stress tensor and the pressure and velocity fields. The results indicate that the material yield surfaces are strongly influenced by the interplay between the elastic and viscous effects, in accordance with recent experimental visualization of elasto-viscoplastic flows.