Modeling of Stress Relaxation Modulus for a Nanocomposite Biosensor by Relaxation Time, Yield Stress, and Zero Complex Viscosity

JOM ◽  
2021 ◽  
Author(s):  
Yasser Zare ◽  
Kyong Yop Rhee
Author(s):  
М.С. Воронин

Приводится метод расчета параметров функции времени релаксации касательных напряжений, являющейся одним из замыкающих соотношений для модели вязкоупругого тела максвелловского типа. Метод основан на упрощении системы уравнений, описывающей деформирование тонкого стержня в рамках модели, если рассматривать эту систему в точке начала пластической деформации. Метод позволяет отыскать те параметры времени релаксации, которые ответственны за описание предела упругости материала в широком диапазоне температур и скоростей деформации. Результаты применения метода демонстрируются сравнением с экспериментальными данными для трeх полимерных материалов: ПММА (полиметилметакрилат), ПТФЭ (политетрафторэтилен) и эпоксидной смолы. A numerical method to determine the parameters of the shear stress relaxation time is discussed. This function is one of the constitutive equations of a Maxwellian viscoelastic model. The method is based on a simplification of the system of equations describing the deformation of a thin rod when this system is considered at the yield stress point. The method allows one to find the relaxation time parameters responsible for the yield stress description in a wide range of temperatures and strain rates. The numerical results obtained by the method are compared with experimental data for polymethylmethacrylate, polytetrafluoroethylene, and epoxy resin.


2011 ◽  
Vol 287-290 ◽  
pp. 1517-1520 ◽  
Author(s):  
Wen Jie Luo ◽  
Si Dong Li ◽  
Shuang Quan Liao ◽  
Lin Fang ◽  
Zhi Fen Wang

The characterization of the aging behavior of raw natural rubber (NR) coagulated by microorganisms (NR-m) was performed on a rubber processing analyzer (RPA) by tests of frequency sweep, strain sweep and stress relaxation, respectively. With the prolongation of the aging time, the storage modulus (G'), storage torque (S'), complex viscosity (η*) and stress relaxation time of raw NR-m decreased while the damping factor (tanδ) were increased. As the oscillation frequency was increasing, the G' rose gradually but the tanδ decreased. The η*diminished over the whole range of frequency shear rate (γƒ) values. Its change remained all almost the same at low strain shear rate (γs) but began to decrease sharply when the rate reached a higher value. The S' soared up in the region of less than 10°, but began to slow down after that point.


2002 ◽  
Vol 16 (17n18) ◽  
pp. 2655-2661
Author(s):  
W. H. LI ◽  
G. CHEN ◽  
S. H. YEO ◽  
H. DU

In this paper, the experimental and modeling study and analysis of the stress relaxation characteristics of magnetorheological (MR) fluids under step shear are presented. The experiments are carried out using a rheometer with parallel-plate geometry. The applied strain varies from 0.01% to 100%, covering both the pre-yield and post-yield regimes. The effects of step strain, field strength, and temperature on the stress modulus are addressed. For small step strain ranges, the stress relaxation modulus G(t,γ) is independent of step strain, where MR fluids behave as linear viscoelastic solids. For large step strain ranges, the stress relaxation modulus decreases gradually with increasing step strain. Morever, the stress relaxation modulus G(t,γ) was found to obey time-strain factorability. That is, G(t,γ) can be represented as the product of a linear stress relaxation G(t) and a strain-dependent damping function h(γ). The linear stress relaxation modulus is represented as a three-parameter solid viscoelastic model, and the damping function h(γ) has a sigmoidal form with two parameters. The comparison between the experimental results and the model-predicted values indicates that this model can accurately describe the relaxation behavior of MR fluids under step strains.


1997 ◽  
Vol 119 (3) ◽  
pp. 262-265 ◽  
Author(s):  
S. R. White ◽  
A. B. Hartman

Little experimental work has been done to characterize how the viscoelastic properties of composite material matrix resins develop during cure. In this paper, the results of a series of creep tests carried out on 3501–6 epoxy resin, a common epoxy matrix material for graphite/epoxy composites, at several different cure states is reported. Beam specimens were isothermally cured at increasing cure temperatures to obtain a range of degrees of cure from 0.66 to 0.99. These specimens were then tested in three-point bending to obtain creep compliance over a wide temperature range. The master curves and shift functions for each degree of cure case were obtained by time-temperature superposition. A numerical technique and direct inversion were used to calculate the stress relaxation modulus master curves from the creep compliance master curves. Direct inversion was shown to be adequate for fully cured specimens, however it underpredicts the relaxation modulus and the transition for partially cured specimens. Correlations with experimental stress relaxation data from Kim and White (1996) showed that reasonably accurate results can be obtained by creep testing followed by numerical conversion using the Hopkins-Hamming method.


2012 ◽  
Vol 11 (5) ◽  
pp. 1525-1546 ◽  
Author(s):  
Philip Barton ◽  
Evgeniy Romenski

AbstractIn this paper we show that entropy can be used within a functional for the stress relaxation time of solid materials to parametrise finite viscoplastic strain-hardening deformations. Through doing so the classical empirical recovery of a suitable irreversible scalar measure of work-hardening from the three-dimensional state parameters is avoided. The success of the proposed approach centres on determination of a rate-independent relation between plastic strain and entropy, which is found to be suitably simplistic such to not add any significant complexity to the final model. The result is sufficiently general to be used in combination with existing constitutive models for inelastic deformations parametrised by one-dimensional plastic strain provided the constitutive models are thermodynamically consistent. Here a model for the tangential stress relaxation time based upon established dislocation mechanics theory is calibrated for OFHC copper and subsequently integrated within a two-dimensional moving-mesh scheme. We address some of the numerical challenges that are faced in order to ensure successful implementation of the proposedmodel within a hydrocode. The approach is demonstrated through simulations of flyer-plate and cylinder impacts.


1982 ◽  
Vol 55 (1) ◽  
pp. 62-65
Author(s):  
W. Batsberg ◽  
O. Kramer

Abstract The experimental result, that the equilibrium force is nearly equal to the pseudoequilibrium force immediately prior to quenching and irradiation, allows the following conclusions: (1) Chain scission during crosslinking is not a serious problem. (2) The network of highly entangled linear chains is effectively at elastic equilibrium immediately prior to crosslinking in the strained state. This would not be the case if the entangled structure remained untrapped. (3) The effect of chain entangling in tightly crosslinked elastomers is large, also at elastic equilibrium. In fact, it is almost quantitatively equal to the pseudo-equilibrium stress relaxation modulus of the uncrosslinked linear polymer. This result is in agreement with the results from the Langley and the two-network methods.


mBio ◽  
2013 ◽  
Vol 4 (5) ◽  
Author(s):  
Brandon W. Peterson ◽  
Henny C. van der Mei ◽  
Jelmer Sjollema ◽  
Henk J. Busscher ◽  
Prashant K. Sharma

ABSTRACTBacteria in the biofilm mode of growth are protected against chemical and mechanical stresses. Biofilms are composed, for the most part, of extracellular polymeric substances (EPSs). The extracellular matrix is composed of different chemical constituents, such as proteins, polysaccharides, and extracellular DNA (eDNA). Here we aimed to identify the roles of different matrix constituents in the viscoelastic response of biofilms.Staphylococcus aureus,Staphylococcus epidermidis,Streptococcus mutans, andPseudomonas aeruginosabiofilms were grown under different conditions yielding distinct matrix chemistries. Next, biofilms were subjected to mechanical deformation and stress relaxation was monitored over time. A Maxwell model possessing an average of four elements for an individual biofilm was used to fit the data. Maxwell elements were defined by a relaxation time constant and their relative importance. Relaxation time constants varied widely over the 104 biofilms included and were divided into seven ranges (<1, 1 to 5, 5 to 10, 10 to 50, 50 to 100, 100 to 500, and >500 s). Principal-component analysis was carried out to eliminate related time constant ranges, yielding three principal components that could be related to the known matrix chemistries. The fastest relaxation component (<3 s) was due to the presence of water and soluble polysaccharides, combined with the absence of bacteria, i.e., the heaviest masses in a biofilm. An intermediate component (3 to 70 s) was related to other EPSs, while a distinguishable role was assigned to intact eDNA, which possesses a unique principal component with a time constant range (10 to 25 s) between those of EPS constituents. This implies that eDNA modulates its interaction with other matrix constituents to control its contribution to viscoelastic relaxation under mechanical stress.IMPORTANCEThe protection offered by biofilms to organisms that inhabit it against chemical and mechanical stresses is due in part to its matrix of extracellular polymeric substances (EPSs) in which biofilm organisms embed themselves. Mechanical stresses lead to deformation and possible detachment of biofilm organisms, and hence, rearrangement processes occur in a biofilm to relieve it from these stresses. Maxwell analysis of stress relaxation allows the determination of characteristic relaxation time constants, but the biofilm components and matrix constituents associated with different stress relaxation processes have never been identified. Here we grew biofilms with different matrix constituents and used principal-component analysis to reveal that the presence of water and soluble polysaccharides, together with the absence of bacteria, is associated with the fastest relaxation, while other EPSs control a second, slower relaxation. Extracellular DNA, as a matrix constituent, had a distinguishable role with its own unique principal component in stress relaxation with a time constant range between those of other EPSs.


2021 ◽  
Vol 1965 (1) ◽  
pp. 012023
Author(s):  
Zhang Jian-bin ◽  
Guo Lei ◽  
Li Guang-hua ◽  
Lu Bing-ju ◽  
Cheng Dong

2020 ◽  
Author(s):  
Emilia M. Grad ◽  
Isabell Tunn ◽  
Dion Voerman ◽  
Alberto S. de Léon ◽  
Roel Hammink ◽  
...  

Biological materials combine stress relaxation and self-healing with non-linear stress-strain responses. These characteristic features are a direct result of hierarchical self-assembly, which often results in fiber-like architectures. Even though structural knowledge is rapidly increasing, it has remained a challenge to establish relationships between microscopic and macroscopic structure and function. Here, we focus on understanding how network topology determines the viscoelastic properties, i.e. stress relaxation, of biomimetic hydrogels. We have dynamically crosslinked two different synthetic polymers with one and the same crosslink. The first polymer, a polyisocyanopeptide (PIC), self-assembles into semi-flexible, fiber-like bundles and thus displays stress-stiffening, similar to many biopolymer networks. The second polymer, 4-arm poly(ethylene glycol) (starPEG), serves as a reference network with well-characterized structural and viscoelastic properties. Using one and the same coiled coil crosslink allows us to decouple the effects of crosslink kinetics and network topology on the stress relaxation behavior of the resulting hydrogel networks. We show that the fiber-containing PIC network displays a relaxation time approximately two orders of magnitude slower than the starPEG network. This reveals that crosslink kinetics is not the only determinant for stress relaxation. Instead, we propose that the different network topologies determine the ability of elastically active network chains to relax stress. In the starPEG network, each elastically active chain contains exactly one crosslink. In the absence of entanglements, crosslink dissociation thus relaxes the entire chain. In contrast, each polymer is crosslinked to the fiber bundle in multiple positions in the PIC hydrogel. The dissociation of a single crosslink is thus not sufficient for chain relaxation. This suggests that tuning the number of crosslinks per elastically active chain in combination with crosslink kinetics is a powerful design principle for tuning stress relaxation in polymeric materials. The presence of a higher number of crosslinks per elastically active chain thus yields materials with a slow macroscopic relaxation time but fast dynamics at the microscopic level. Using this principle for the design of synthetic cell culture matrices will yield materials with excellent long-term stability combined with the ability to locally reorganize, thus facilitating cell motility, spreading and growth.


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