Modeling the rheology of thixotropic elasto-visco-plastic materials

Abstract

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 of the new model are compared to experimental data and predictions of previously proposed TEVP models in simple rheometric flows, including steady and step-shear tests, flow reversal, intermittent step tests, small amplitude oscillatory shear (SAOS) and large amplitude oscillatory shear. In most cases, the proposed model reproduces more accurately these experimental data than the other models, highlighting its predictive capabilities. Moreover, SAOS illustrates that introducing viscoplasticity via the Saramito model necessarily reduces G″ to zero in the linear strain regime. This calls for model adjustments in the solid state. Finally, we examined the proposed model in uniaxial elongation and concluded that it is important to include this flow in the rheological characterization and modeling of such systems.

Transition between solid and liquid state of yield-stress fluids under purely extensional deformations

“…Thus, the yield strain of the Pluronic solution is found to be « y = 0.016. As shown by Varchanis et al (21) and can be seen in Fig. 1 D and E, the SRM/HB model predicts a linear elastic solid response in the linear regime (γ 0 → 0), something that does not hold for the Pluronic solution.…”

Advanced Constitutive Modeling of the Thixotropic Elasto-Visco-Plastic Behavior of Blood: Description of the Model and Rheological Predictions

“…Most of the blood constitutive modelling investigations do not present the normal stress prediction, and hence we are not able to make a comparison with other findings. Varchanis et al [62] in their work reported a significant contribution of normal stress in simple shear tests and compared their findings with those predicted by the ML-IKH model, which was found to have similar behavior. The presence of normal stresses is suspensions is attributed the intense interaction between the particles.…”

“…In this work, we modified the constitutive law for blood flow modeling, introducing a thixotropic elasto-viscoplastic formulation. The proposed model was based on the formulation of Varchanis et al [62], which incorporated thixotropy, elasticity and viscoplasticity following an additive elastoplastic decomposition. It was able to capture all the essential steady and transient experimental data.…”

“…∆t is the critical factor for this test since it controls the dynamics of rouleaux formation and consequently the maximum values of stresses. The rectangular shear-step test, also known as intermittent steps test, is composed of two consecutive shear cessation steps with a varied duration, [59,62]. This is another rheological test that has been reported in various investigations to evaluate the thixotropic response as well as the elastic aspect of the material.…”

“…The coupled appearance of several elastic, plastic and thixotropic phenomena and the underlying mechanisms and internal variables in thixotropic elasto-visco-plastic (TEVP) materials necessitates the introduction of a large number of adjustable parameters to describe their rheology. The model proposed by Varchanis et al [62] was suitable for highly concentrated suspensions, which exhibit shear thinning, thixotropy, plasticity and viscoelasticity. It is adequately modified in order to have a stress-controlled dynamic configuration of the structure parameter, accompanied by a reduction in fitting parameters.…”