The Coupling Model: A Fundamental Mechanism Governing Time Dependent Properties of Relaxations, Structural Recovery and Nonlinear Viscoelasticity

1986 ◽  
Vol 79 ◽  
Author(s):  
R. W. Rendell ◽  
K. L. Ngai ◽  
A. F. Yee
Keyword(s):  
Response Function ◽  
Physical Aging ◽  
Nonlinear Viscoelasticity ◽  
Relaxation Times ◽  
Coupling Model ◽  
Time Dependent ◽  
Material Structure ◽  
Strain History ◽  
Structural Recovery ◽  
Model Response

AbstractThe recent renewal of interest in the time dependent response of complex material systems stems both from their increasing importance and from recent advances in theoretical tools and concepts. This paper describes one of these advances, the coupling model of relaxation. The coupling model proposes a view of how relaxation proceeds in time in which a primitive relaxation mode is coupled to its complex surroundings. Examples of the coupling model predictions for terminal relaxations, primary-segmental relaxations including physical aging, and secondary relaxations in polymers are described. It is able to confront and quantitatively explain several long-standing problems and anomalies for which traditional approaches, in their present form, such as distributions of relaxation times, free volume, configuration entropy and reptation are not successful. The coupling model response function is also appropriate for structural nonequilibrium and its predictions for volume recovery are described. The same coupling model response function is used as a timedependent kernal in a constitutive equation to discuss nonlinear viscoelasticity. The model incorporates the strain history dependence and allows for the evolution of material structure. Using information from strain-tickle experiments on polycarbonate and polyetherimide, we show that the coupling model reproduces the essential features observed experimentally for a variety of strain histories.

QUASI-LINEAR VISCOELASTIC MODELLING OF UNCURED PREPREGS UNDER COMPACTION

2021 ◽  
Author(s):  
SIDDHESH S. KULKARNI ◽  
KAMRAN A. KHAN ◽  
REHAN UMER
Keyword(s):  
Stress Relaxation ◽  
Relaxation Function ◽  
Soft Tissues ◽  
Volume Fraction ◽  
Time Dependent ◽  
Strain History ◽  
Manufacturing Processes ◽  
Fiber Volume ◽  
Consolidation Process ◽  
Thermoset Resin

Reinforcement compaction sometimes referred as consolidation process and is one of the key steps in various composite manufacturing processes such as autoclave and out-of-autoclave processing. The prepregs consist of semi-cured thermoset resin system impregnating the fibers. hence, the prepreg shows strong viscoelastic compaction response, which strongly depends on compaction speed and stress relaxation. modeling of time-dependent response is of utmost importance to understand the behavior of prepregs during different stages of composites manufacturing processes. The quasilinear viscoelastic (QLV) theory has been extensively used for the modeling of viscoelastic response of soft tissues in biomedical applications. In QLV approach, the stress relaxation can be expressed in terms of the nonlinear elastic function and the reduced relaxation function. The constitutive equation can be represented by a convolution integral of the nonlinear strain history, and reduced relaxation function. This study adopted a quasilinear viscoelastic modeling approach to describe the time dependent behavior of uncured-prepregs under compression. The model was modified to account for the compaction behavior of the prepreg under a compressive load. The deformation behavior of the prepreg is usually characterized by the fiber volume fraction, V . In this study, the material used was a 2/2 Twill weave glass prepreg (M26T) supplied by Hexcel® Industries USA. We performed a compaction experiment of the uncured prepreg at room temperature at different displacement rate and subsequent relaxation to describe the viscoelastic behavior of the prepreg. The model parameter calibration was performed using the trust-region-reflective algorithm in matlab to a selected number of test data. The calibrated model was then used to predict the rate dependent compaction and relaxation response of prepregs for different fiber volume fractions and strain rates.

Compartmental-model response function for dendritic trees

1993 ◽  
Vol 70 (2) ◽  
pp. 199-207 ◽  
Author(s):  
Paul C. Bressloff ◽  
John G. Taylor
Keyword(s):  
Response Function ◽  
Compartmental Model ◽  
Dendritic Trees ◽  
Model Response

Time-dependent lateral transmission of force in skeletal muscle

2009 ◽  
Vol 465 (2108) ◽  
pp. 2441-2460 ◽  
Author(s):  
Yingxin Gao ◽  
Alan S. Wineman ◽  
Anthony M. Waas
Keyword(s):  
Skeletal Muscle ◽  
Relaxation Time ◽  
Muscle Fibre ◽  
Composite System ◽  
Stress Transfer ◽  
Time Dependent ◽  
Muscle Fibres ◽  
Strain History ◽  
Shear Stresses ◽  
Lateral Stress

There is experimental evidence to suggest that extensible connective tissues are mechanically time-dependent. In view of this, the mechanics of time-dependent lateral stress transfer in skeletal muscle is investigated by employing a viscoelastic shear lag model for the transfer of tensile stress between muscle fibres and the surrounding extracellular matrix (ECM) by means of shear stresses at the interface between the muscle fibre and the ECM. The model allows for both mechanical strains in the muscle as well as the strain owing to muscle contraction. Both the ECM and the muscle fibre are modelled as viscoelastic solids. As a result, time-dependent lateral stress transfer can be studied under a variety of loading and muscle stimulation conditions. The results show that the larger the muscle fibre creep time relative to the ECM relaxation time, the longer it takes for the muscle fibre stress to relax. It also shows that the response of the muscle–ECM composite system also depends on the characteristic time of a strain history relative to the characteristic relaxation time of the ECM. The results from the present model provide significant insight into the role of the parameters that characterize the response of the muscle composite system.

scholarly journals Centre-of-mass like superposition of Ornstein–Uhlenbeck processes: A pathway to non-autonomous stochastic differential equations and to fractional diffusion

2018 ◽  
Vol 21 (5) ◽  
pp. 1420-1435 ◽  
Author(s):  
Mirko D’Ovidio ◽  
Silvia Vitali ◽  
Vittoria Sposini ◽  
Oleksii Sliusarenko ◽  
Paolo Paradisi ◽  
...  
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Gaussian Process ◽  
Relaxation Times ◽  
Random Variable ◽  
Fractional Diffusion ◽  
Time Dependent ◽  
Centre Of Mass ◽  
Time Scaling

Abstract We consider an ensemble of Ornstein–Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centre-of-mass like variable corresponding to this ensemble is statistically equivalent to a process driven by a non-autonomous stochastic differential equation with time-dependent drift and a white noise. In particular, the time scaling and the density function of such variable are driven by the population of timescales and of noise amplitudes, respectively. Moreover, we show that this variable is equivalent in distribution to a randomly-scaled Gaussian process, i.e., a process built by the product of a Gaussian process times a non-negative independent random variable. This last result establishes a connection with the so-called generalized grey Brownian motion and suggests application to model fractional anomalous diffusion in biological systems.

The Effect of Physical Aging on the Time-Dependent Properties of Carbon-Fiber-Reinforced Epoxy Composites

1982 ◽  
Vol 4 (3) ◽  
pp. 97 ◽  
Author(s):  
TT Chiao ◽  
KL Reifsnider ◽  
GP Sendeckyj ◽  
RJ Morgan ◽  
PL Lien ◽  
...  
Keyword(s):  
Carbon Fiber ◽  
Physical Aging ◽  
Time Dependent ◽  
Epoxy Composites ◽  
Fiber Reinforced ◽  
Carbon Fiber Reinforced

Dependence of the dynamic properties of elastohydrodynamic liquids on temperature and pressure (volume)

2010 ◽  
Vol 224 (12) ◽  
pp. 2568-2576 ◽  
Author(s):  
S Bair
Keyword(s):  
Shear Viscosity ◽  
Scaling Function ◽  
Dynamic Properties ◽  
Relaxation Times ◽  
Elastohydrodynamic Lubrication ◽  
Time Dependent ◽  
Essential Property ◽  
Scaling Parameters ◽  
Temperature And Pressure ◽  
Low Shear

Shear viscosity is an essential property of elastohydrodynamic lubrication (EHL) liquids. Relaxation times that govern shear dependence of viscosity, time-dependent shear response, and time-dependent bulk behaviour all scale with temperature and pressure in the same way as does the low-shear viscosity. An accurate description of the temperature, pressure, and shear dependence of viscosity has, however, been missing from EHL analysis since the very beginning of the field resulting in many invalid conclusions. In this article, a generalized version of the Stickel plot is introduced and many empirical models are placed in their relevant region of the temperature and pressure domains by showing where they belong on the Stickel plot. The models that are capable of predicting both temperature and pressure responses are discussed in terms of scaling parameters and an example of a mineral oil from the 1953 ASME viscosity report is used to demonstrate the utility of the scaling parameter models. The Stickel analysis is shown to be extremely useful in identifying the appropriate scaling function.

Predicting the α-relaxation time of glycerol confined in 1.16 nm pores of zeolitic imidazolate frameworks

2020 ◽  
Vol 22 (2) ◽  
pp. 507-511 ◽  
Author(s):  
K. L. Ngai ◽  
P. Lunkenheimer ◽  
A. Loidl
Keyword(s):  
Relaxation Time ◽  
Relaxation Times ◽  
Coupling Model ◽  
Chem Phys ◽  
Zeolitic Imidazolate Frameworks

Relaxation times of glycerol confined in 1.16 nm ZIF pores found by Uhl et al. [J. Chem. Phys., 2019, 150, 024504] are explained quantitatively by the Coupling Model.

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