Rheological Representation Research Articles

Micromechanical modeling of the visco-hyperelastic–viscoplastic​ behavior and fracture of aged semicrystalline polymers

This work presents a micromechanical-based visco-hyperelastic–viscoplastic constitutive model for low-density polyethylene (LDPE) films subjected to accelerated ultraviolet (UV) aging. The model captures the evolution of the mechanical and fracture properties of the material. Our proposed framework assumes that the semicrystalline polymer’s macromechanical behavior is the sum of the intermolecular and macromolecular network contributions. The intermolecular part of the model follows a nonlinear composite mixture rule, combining the contribution of the crystalline and amorphous phases, each represented rheologically by a linear elastic spring in series with a nonlinear viscous dashpot. The rheological representation of the macromolecular network consists of a series of two Langevin springs capturing deformation-induced conformation change and interatomic bond deformation between Kuhn segments, as well as a viscous dashpot for chain relaxation. We have developed a novel framework that reformulates the eight chain model to include the energy densities associated with both conformation change and interatomic bond deformation, providing a more accurate description of macromolecular network mechanical and fracture behavior. The aging of semicrystalline polymers results from two competing mechanisms: oxidation-induced strengthening resulting from chemicrystallization and crosslinking, and oxidation-induced softening resulting from chain scissions and chemicavitation. Our proposed model accurately captures the effect of UV aging on the mechanical behavior of the semicrystalline material. Additionally, we introduce the novel concept of a ”healthy network” to predict the evolution of the strain to fracture. The model accurately predicts the evolution of the mechanical behavior and elongation at break over a wide range of UV irradiation doses.

Swimming of microbes in blood flow of nano-bioconvective Williamson fluid

As blood flow patterns are employed in the diagnosis of circulatory disorders such as arteriosclerotic disease, bioengineers and medical scientists are interested in blood flow identification via the circulatory system. Researchers used non-Newtonian fluid models to measure blood flow cardiovascular system (e.g., hyperbolic tangent fluid, Powell Erying fluid, Casson fluid, Williamson fluid, etc.) as these fluids provide a rheological representation of blood with a more detailed thinning component. In this study, blood is taken as Williamson's fluid, and flow velocity is unsteady towards the stretching/shrinking surface in consonance with exothermic/endothermic function. The theology of gyrotactic microorganisms (GM) is addressed to nanofluid to stabilise nanoparticles due to bioconvection. A finite-difference computational approach evaluates the mathematical model followed by a stability and convergence analysis. The nanofluid blood velocity characteristics, temperature, concentration, and microorganisms are discussed following the diagrams. The skin friction, Nusselt number, Sherwood number and the microorganisms density are evaluated and clarified in detail. Besides, iso-concentrations and iso-microorganisms are configured for various factors to assess the nanofluid blood flows' boundary line thickness. The present analysis may be useful for many hyperthermia therapies, such as cancer treatment, tumour therapy and cardiac surgery, and applications in microbial fuel cells, microfluidic systems, and heat transfer contrivances.

Evaluating numerical and free-drift forecasts of sea ice drift during a Southern Ocean research expedition: An operational perspective

ABSTRACT Antarctic sea ice is prevalently seen as a major player in the climate system, but it is also an important factor in polar maritime safety. Remote sensing and forecasting of Southern Ocean sea ice at time scales suitable for navigation and research planning remain challenging. In this study, numerical sea ice drift forecasts are assessed from the perspective of informing shipping operations. A series of tests is performed to ascertain whether an operational global ocean and sea ice model and a simple free-drift model can provide accurate drift estimates over short lead times. Both approaches are evaluated against ice drift measurements from buoys deployed during two research cruises in the Southern Ocean marginal ice zone during winter and spring. The numerical forecast model was able to forecast sea ice trajectories over 24 h with an average position error of 16.6 km during winter and 9.2 km during spring. The simpler free-drift model, using empirically optimised wind scaling, returned an average position error of 15.9 and 9.3 km during winter and spring respectively. Model skill for both the dynamical and free-drift models is lower in winter than in spring. Free-drift model skill appears linked with sea ice consolidation, which may assist in determining when and where this approach is fit for purpose. Lingering uncertainties regarding the rheological representation of sea ice in the dynamical model and the quality of the wind and ocean forcing remain, potentially affecting model skill over tactical navigation time frames.

Formulation of thermodynamically consistent fractional Burgers models

The approach of viscoelastic body constitutive equation fractionalization using rheological representation of the classical Burgers model and considering the Scott–Blair (fractional) elements instead of the dash-pot elements is adopted. The obtained fractional Burgers model is further generalized by considering arbitrary model parameters: multiplicative constants and orders of fractional differentiation. Thermodynamical consistency of the fractional Burgers model is analyzed, resulting in formulation of eight thermodynamically consistent fractional Burgers models.

Micro-sphere based viscoplastic constitutive model for uncured green rubber

Uncured rubber exhibits strong viscoplastic flow without a distinct yield point accompanied by hardening. Classical hyperelastic models developed for crosslinked rubber do not apply to uncured rubber due to the lack of crosslinks which endow the material its elasticity. This paper presents a new constitutive model for the isothermal response of uncured green rubber. The kinematic structure of the proposed approach is based on the affine micro-sphere model. The computation of the stretch in the orientation direction follows the Cauchy-Born rule. The micro-sphere enables numerical integration over the unit sphere via finite summation over the orientation directions corresponding to the integration points over the sphere. This structure replaces the complex three-dimensional formulations of finite inelasticity based on the multiplicative split of the deformation gradient by a simpler and more attractive one-dimensional rheological representation at the orientation directions. The rheology of the model consists of two parts: (i) a part responsible for the rate-independent reponse and (ii) a part responsible for the rate-dependent response, respectively. The first branch consists of a spring connected to a modified Kelvin element, where the latter spring models the kinematic hardening. The dashpot describes a time-independent endochronic flow rule based solely on the deformation history. The second branch consists of a spring connected to a Maxwell element in parallel to a dashpot. The two dashpots in the latter branch model the ground-state viscoelasticity and rate-dependent hardening phenomenon. Albeit its apparent complexity, the proposed rheology and its numerical implementation are straightforward. The proposed model shows favorable results suitable for large scale finite element based simulations for forming process of uncured rubber components.

Temperature-dependent viscoelastic model for asphalt concrete using discrete rheological representation

The modified viscoelastic model is proposed for asphalt concrete according to a new viscoelastic model, which has four materials parameters. By Fourier transform, the model is able to provide a frequency independent response over a wide range of frequencies. The rheological representation of model is provided by an internal variable description and is processed using the discrete element method. Furthermore, the model has been appropriately enhanced in order that the important temperature effects are taken into account. Asphalt being a thermos-rheologically simple material, the temperature dependence is modeled by the time–temperature superposition principle. The model is applied for the description and prediction of asphalt behavior. The response of the different asphalt materials for frequency sweep test is captured and the model predicts the loss tangent and complex shear modulus for asphalt concrete very well.

A photoviscoplastic model for photoactivated covalent adaptive networks

Light activated polymers (LAPs) are a class of contemporary materials that when irradiated with light respond with mechanical deformation. Among the different molecular mechanisms of photoactuation, here we study radical induced bond exchange reactions (BERs) that alter macromolecular chains through an addition-fragmentation process where a free chain whose active end group attaches then breaks a network chain. Thus the BER yields a polymer with a covalently adaptable network. When a LAP sample is loaded, the macroscopic consequence of BERs is stress relaxation and plastic deformation. Furthermore, if light penetration through the sample is nonuniform, resulting in nonuniform stress relaxation, the sample will deform after unloading in order to achieve equilibrium. In the past, this light activation mechanism was modeled as a phase evolution process where chain addition-fragmentation process was considered as a phase transformation between stressed phases and newly-born phases that are undeformed and stress free at birth. Such a modeling scheme describes the underlying physics with reasonable fidelity but is computationally expensive. In this paper, we propose a new approach where the BER induced macromolecular network alteration is modeled as a viscoplastic deformation process, based on the observation that stress relaxation due to light irradiation is a time-dependent process similar to that in viscoelastic solids with an irrecoverable deformation after light irradiation. This modeling concept is further translated into a finite deformation photomechanical constitutive model. The rheological representation of this model is a photoviscoplastic element placed in series with a standard linear solid model in viscoelasticity. A two-step iterative implicit scheme is developed for time integration of the two time-dependent elements. We carry out a series of experiments to determine material parameters in our model as well as to validate the performance of the model in complex geometrical and loading configurations. The comparison between the finite element simulations and experiments shows that the model can accurately capture the response of the LAP under a wide range of coupled photo-mechanical loading conditions, such as light induced stress relaxation, creep in tension, and bending. Furthermore, we demonstrate the versatility of the model by simulating a series of examples that exhibit complex three-dimensional, time-dependent photodeformation, including photoorigami, photoforming, and photobulge tests.

A finite strain thermo-viscoelastic constitutive model to describe the self-heating in elastomeric materials during low-cycle fatigue

A thermo-visco-hyperelastic constitutive model, in accordance with the second thermodynamics principle, is formulated to describe the self-heating evolution in elastomeric materials under cyclic loading. The mechanical part of the model is based upon a Zener rheological representation in which the specific free energy potential is dependent on an added internal variable, allowing the description of the time-dependent mechanical response. The large strain mechanical behavior is described using a Langevin spring, while the continuous stress-softening under cyclic loading is taken into account by means of a network alteration kinetics. The thermo-mechanical coupling is defined by postulating the existence of a dissipation pseudo-potential, function of the viscous dilatation tensor. The proposed model is fully three-dimensional and is implemented into a finite element code. The model parameters are identified using experimental data obtained on a styrene-butadiene rubber under a given strain rate for different strain conditions. Predicted evolutions given by the model for other strain rates are found in good agreement with the experimental data.

Blood viscoelasticity measurement using steady and transient flow controls of blood in a microfluidic analogue of Wheastone-bridge channel

Accurate measurement of blood viscoelasticity including viscosity and elasticity is essential in estimating blood flows in arteries, arterials, and capillaries and in investigating sub-lethal damage of RBCs. Furthermore, the blood viscoelasticity could be clinically used as key indices in monitoring patients with cardiovascular diseases. In this study, we propose a new method to simultaneously measure the viscosity and elasticity of blood by simply controlling the steady and transient blood flows in a microfluidic analogue of Wheastone-bridge channel, without fully integrated sensors and labelling operations. The microfluidic device is designed to have two inlets and outlets, two side channels, and one bridge channel connecting the two side channels. Blood and PBS solution are simultaneously delivered into the microfluidic device as test fluid and reference fluid, respectively. Using a fluidic-circuit model for the microfluidic device, the analytical formula is derived by applying the linear viscoelasticity model for rheological representation of blood. First, in the steady blood flow, the relationship between the viscosity of blood and that of PBS solution (μBlood /μPBS ) is obtained by monitoring the reverse flows in the bridge channel at a specific flow-rate rate (QPBS (SS) /QBlood (L) ). Next, in the transient blood flow, a sudden increase in the blood flow-rate induces the transient behaviors of the blood flow in the bridge channel. Here, the elasticity (or characteristic time) of blood can be quantitatively measured by analyzing the dynamic movement of blood in the bridge channel. The regression formula (ABlood (t) = A α + A β exp [-(t - t 0 )/λBlood ]) is selected based on the pressure difference (ΔP = PA - PB ) at each junction (A, B) of both side channels. The characteristic time of blood (λBlood ) is measured by analyzing the area (ABlood ) filled with blood in the bridge channel by selecting an appropriate detection window in the microscopic images captured by a high-speed camera (frame rate = 200 Hz, total measurement time = 7 s). The elasticity of blood (GBlood ) is identified using the relationship between the characteristic time and the viscosity of blood. For practical demonstrations, the proposed method is successfully applied to evaluate the variations in viscosity and elasticity of various blood samples: (a) various hematocrits form 20% to 50%, (b) thermal-induced treatment (50 °C for 30 min), (c) flow-induced shear stress (53 ± 0.5 mL/h for 120 min), and (d) normal rat versus spontaneously hypertensive rat. Based on these experimental demonstrations, the proposed method can be effectively used to monitor variations in viscosity and elasticity of bloods, even with the absence of fully integrated sensors, tedious labeling and calibrations.

Generalized self-consistent scheme for the effective behavior of viscoelastic heterogeneous media: A simple approximate solution

This paper gives a simple approximate solution for obtaining the effective behavior of linear viscoelastic heterogeneous media for the case of elastic inclusions immersed within a viscoelastic matrix. The solution in the Laplace–Carson space is obtained by the Generalized self-consistent model and the simplification is in an explicit expression of the inverse Laplace transform. It is shown that the solution in Laplace–Carson space can be approximated by a convenient rational fraction which is given explicitly as a function of viscoelastic parameters. This provides an easy way to perform the inverse Laplace transform. Examples of typical composites, including possibly void and rigid inclusions, are provided and show that the procedure provides reasonably accurate results. In addition, a complete rheological representation can be provided in some cases for describing the behavior of the effective medium.

Rheological representation of fractional order viscoelastic material models

We develop rheological representations, i.e., discrete spectrum models, for the fractional derivative viscoelastic element (fractional dashpot or springpot). Our representations are generalized Maxwell models or series of Kelvin-Voigt units, which, however, maintain the number of parameters of the corresponding fractional order model. Accordingly, the number of parameters of the rheological representation is independent of the number of rheological units. We prove that the representations converge to the corresponding fractional model in the limit as the number of units tends to infinity. The representations extend to compound fractional derivative models such as the fractional Maxwell model, fractional Kelvin-Voigt model, and fractional standard linear solid. Computational experiments show that the rheological representations are accurate approximations of the fractional order models even for a small number of units.

The generalized Kuhn model of linear viscoelasticity

We propose a generalization of the Kuhn model of linear viscoelasticity. This generalization, which has four material parameters, is able to provide a near frequency independent response over a wide range of frequencies. It is useful for highly dissipative materials such as asphalt concrete. It is derived by generalizing Lubliner and Panoskaltsis’s modified Kuhn model, but we also show that it is closely related to fractional derivative models. We show that the model admits a rheological approximation, that is, an approximation by classical springs and dashpots. The model and rheological representation are compared to experimental data.

Viscoelastic crack growth process in wood timbers: An approach by the finite element method for mode I fracture

In this paper the effects of viscoelastic characteristics in wood timbers, on the creep crack growth process are studied through a new finite element approach in the time domain. In order to take into account the linear viscoelastic orthotropic behavior, we present an incremental formulation based on a rheological representation of creep tensor components. By using a relationship between stress and crack opening intensity factors, the general approach of path independent integrals is extended in order to calculate energy release rate and local fracture characteristics. Afterwards, fracture parameters are computed through a coupling process with the incremental viscoelastic behavior. The numerical algorithm is presented and validated through numerical as well as experimental examples.

A combined finite/discrete element simulation of shot peening processes – Part I: studies on 2D interaction laws

In the first part of this series of papers on the combined finite/discrete element simulation of shot peening processes, different contact interaction laws for 2D cases are extensively studied with special attention given to the proper selection of the parameter values involved, which is one of the key issues for successful direct simulation. In addition, computational issues including contact forces, partial contact, energy dissipation, and rheological representation are addressed. Numerical examples for a single shot impact system simulated by the coupled finite/discrete element method using different interaction laws are provided to verify the proposed approaches. The results are also compared with those obtained by using only finite element methods. Findings obtained by performing 2D simulations will, in the subsequent article, be used in realistic computational simulations of 3D shot peening processes.