The Comparison of Fractional Derivative Model and Classical Spring-Dashpot Model in the Identification of Viscoelastic Characteristics of a Rubber Material

In the design of viscoelastic materials used in rubber products, not theoretical approaches but experimental approaches have been usually employed. This is due to the difficulties in mathematical procedures of the dynamic material characteristics such as the dependencies of strain amplitude, frequency and/or environmental temperature in deformation. In mathematical approach there are two kind of analytical models for a complex module of the material, which are a fractional derivative model and a spring-dashpot model. However there are few papers dealing with the study of the identifications of parameters for the experimental modulus actually obtained not only by using the fractional derivative model but also by using the spring-dashpot model and the discussion of the comparisons of the two models. In the present paper, the complex elastic modulus for a rubber material are obtained experimentally for a wide range of excitation frequency, and the modulus-frequency relations are derived analytically by using the two models, respectively. Finally, the applicability of the models are discussed from the numerical results.

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Predicting the high strain rate response of plasticised poly(vinyl chloride) using a fractional derivative model

EPJ Web of Conferences ◽

10.1051/epjconf/201818301013 ◽

2018 ◽

Vol 183 ◽

pp. 01013 ◽

Cited By ~ 1

Author(s):

Akash Trivedi ◽

Clive Siviour

Keyword(s):

Fractional Derivative ◽

High Strain Rate ◽

Strain Rate ◽

Vinyl Chloride ◽

High Strain ◽

Mechanical Analysis ◽

High Rate ◽

Poly Vinyl Chloride ◽

Fractional Derivative Model ◽

Wide Range

Polymers are frequently used in fields as diverse as aerospace, biomedicine, automotive and in-dustrial vibration damping, where they are often subjected to high strain rate or impact loading. Poly(vinyl chloride) (PVC), and its plasticised variants (PPVC), are just two examples of this broad category of materi-als. Since many polymers exhibit strong rate and temperature dependence, including a low temperature brittle transition, it is extremely important to understand their mechanical responses over a wide range of loading con-ditions.PVC with 60 wt% plasticiser is used in this study, as its highly rubbery nature lends itself well to being used in various load mitigation and energy absorption applications. It is challenging to obtain high strain rate data on rubbery materials using conventional techniques such as the split-Hopkinson (Kolsky) bar. Therefore, alternative approaches are required. Based on previous work developing a framework to predict high rate re-sponseusing a fractional derivative model, Dynamic Mechanical Analysis (DMA) experiments are conducted on the PPVC to construct a master curve of storage modulus. These data are used to part-calibrate a modified Mulliken-Boyce model which also takes into account specimen heating to derive stress-strain relationships at strain rates varying from 0.001 s_1 to 13 500 s_1. This model is further calibrated against experiments conducted in a previous study and shown to provide an excellent description of the behaviour at these rates.

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Bio-Based Alternatives to Phenol and Formaldehyde for the Production of Resins

Polymers ◽

10.3390/polym12102237 ◽

2020 ◽

Vol 12 (10) ◽

pp. 2237 ◽

Cited By ~ 2

Author(s):

P. R. Sarika ◽

Paul Nancarrow ◽

Abdulrahman Khansaheb ◽

Taleb Ibrahim

Keyword(s):

Raw Materials ◽

Phenol Formaldehyde ◽

Raw Material ◽

Wood Industry ◽

Suitable Material ◽

The Past ◽

Wide Range ◽

Recent Developments ◽

Sustainable Materials ◽

Materials Used

Phenol–formaldehyde (PF) resin continues to dominate the resin industry more than 100 years after its first synthesis. Its versatile properties such as thermal stability, chemical resistance, fire resistance, and dimensional stability make it a suitable material for a wide range of applications. PF resins have been used in the wood industry as adhesives, in paints and coatings, and in the aerospace, construction, and building industries as composites and foams. Currently, petroleum is the key source of raw materials used in manufacturing PF resin. However, increasing environmental pollution and fossil fuel depletion have driven industries to seek sustainable alternatives to petroleum based raw materials. Over the past decade, researchers have replaced phenol and formaldehyde with sustainable materials such as lignin, tannin, cardanol, hydroxymethylfurfural, and glyoxal to produce bio-based PF resin. Several synthesis modifications are currently under investigation towards improving the properties of bio-based phenolic resin. This review discusses recent developments in the synthesis of PF resins, particularly those created from sustainable raw material substitutes, and modifications applied to the synthetic route in order to improve the mechanical properties.

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Active control of liquid film flows: beyond reduced-order models

Nonlinear Dynamics ◽

10.1007/s11071-021-06287-5 ◽

2021 ◽

Vol 104 (1) ◽

pp. 267-287

Author(s):

Radu Cimpeanu ◽

Susana N. Gomes ◽

Demetrios T. Papageorgiou

Keyword(s):

Liquid Film ◽

Information Transfer ◽

Analytical Models ◽

Feedback Controls ◽

Reduced Order ◽

Modelling Framework ◽

Theoretical Approaches ◽

Active Feedback ◽

Feedback Strategies ◽

Set Up

AbstractThe ability to robustly and efficiently control the dynamics of nonlinear systems lies at the heart of many current technological challenges, ranging from drug delivery systems to ensuring flight safety. Most such scenarios are too complex to tackle directly, and reduced-order modelling is used in order to create viable representations of the target systems. The simplified setting allows for the development of rigorous control theoretical approaches, but the propagation of their effects back up the hierarchy and into real-world systems remains a significant challenge. Using the canonical set-up of a liquid film falling down an inclined plane under the action of active feedback controls in the form of blowing and suction, we develop a multi-level modelling framework containing both analytical models and direct numerical simulations acting as an in silico experimental platform. Constructing strategies at the inexpensive lower levels in the hierarchy, we find that offline control transfer is not viable; however, analytically informed feedback strategies show excellent potential, even far beyond the anticipated range of applicability of the models. The detailed effects of the controls in terms of stability and treatment of nonlinearity are examined in detail in order to gain understanding of the information transfer inside the flows, which can aid transition towards other control-rich frameworks and applications.

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Analysis of the Impact on the Mechanical Properties of Modification of Oligohydroxyethers in Organic Solvent Solution with Rubbers

Polymers ◽

10.3390/polym13040519 ◽

2021 ◽

Vol 13 (4) ◽

pp. 519

Author(s):

Vitalii Bezgin ◽

Agata Dudek ◽

Adam Gnatowski

Keyword(s):

Mechanical Properties ◽

Scientific Paper ◽

Styrene Butadiene Rubber ◽

Butadiene Rubber ◽

Molecular Weights ◽

Wide Range ◽

Strength Tests ◽

Materials Used ◽

Styrene Butadiene ◽

The Impact

This paper proposes and presents the chemical modification of linear hydroxyethers (LHE) with different molecular weights (380, 640, and 1830 g/mol) with the addition of three types of rubbers (polysulfide rubber (PSR), polychloroprene rubber (PCR), and styrene-butadiene rubber (SBR)). The main purpose of choosing this type of modification and the materials used was the possibility to use it in industrial settings. The modification process was conducted for a very wide range of modifier additions (rubber) per 100 g LHE. The materials obtained in the study were subjected to strength tests in order to determine the effect of the modification on functional properties. Mechanical properties of the modified materials were improved after the application of the modifier (rubber) to polyhydroxyether (up to certain modifier content). The most favorable changes in the tested materials were registered in the modification of LHE-1830 with PSR. In the case of LHE-380 and LHE-640 modified in cyclohexanol (CH) and chloroform (CF) solutions, an increase in the values of the tested properties was also obtained, but to a lesser extent than for LHE-1830. The largest changes were registered for LHE-1830 with PSR in CH solution: from 12.1 to 15.3 MPa for compressive strength tests, from 0.8 to 1.5 MPa for tensile testing, from 0.8 to 14.7 MPa for shear strength, and from 1% to 6.5% for the maximum elongation. The analysis of the available literature showed that the modification proposed by the authors has not yet been presented in any previous scientific paper.

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Universal mobility characteristics of graphene originating from charge scattering by ionised impurities

Communications Physics ◽

10.1038/s42005-021-00518-2 ◽

2021 ◽

Vol 4 (1) ◽

Author(s):

Jonathan H. Gosling ◽

Oleg Makarovsky ◽

Feiran Wang ◽

Nathan D. Cottam ◽

Mark T. Greenaway ◽

...

Keyword(s):

Electrical Conductivity ◽

Carrier Density ◽

Carrier Mobility ◽

Carrier Transport ◽

Analytical Models ◽

Pristine Graphene ◽

High Electron ◽

Boltzmann Transport ◽

Transport Parameters ◽

Wide Range

AbstractPristine graphene and graphene-based heterostructures can exhibit exceptionally high electron mobility if their surface contains few electron-scattering impurities. Mobility directly influences electrical conductivity and its dependence on the carrier density. But linking these key transport parameters remains a challenging task for both theorists and experimentalists. Here, we report numerical and analytical models of carrier transport in graphene, which reveal a universal connection between graphene’s carrier mobility and the variation of its electrical conductivity with carrier density. Our model of graphene conductivity is based on a convolution of carrier density and its uncertainty, which is verified by numerical solution of the Boltzmann transport equation including the effects of charged impurity scattering and optical phonons on the carrier mobility. This model reproduces, explains, and unifies experimental mobility and conductivity data from a wide range of samples and provides a way to predict a priori all key transport parameters of graphene devices. Our results open a route for controlling the transport properties of graphene by doping and for engineering the properties of 2D materials and heterostructures.

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Development of Permeability Models for Saturated Fluid Flow across Arrays of Fibre Clusters

Advanced Composites Letters ◽

10.1177/096369350201100303 ◽

2002 ◽

Vol 11 (3) ◽

pp. 096369350201100

Author(s):

E.M. Gravel ◽

T.D. Papathanasiou

Keyword(s):

Analytical Models ◽

Dual Porosity ◽

Hydraulic Permeability ◽

Fibrous Media ◽

Fibre Bundles ◽

Hexagonal Packing ◽

Composites Manufacturing ◽

Starting Point ◽

Wide Range ◽

Flow Through

Dual porosity fibrous media are important in a number of applications, ranging from bioreactor design and transport in living systems to composites manufacturing. In the present study we are concerned with the development of predictive models for the hydraulic permeability ( Kp) of various arrays of fibre bundles. For this we carry out extensive computations for viscous flow through arrays of fibre bundles using the Boundary Element Method (BEM) implemented on a multi-processor computer. Up to 350 individual filaments, arranged in square or hexagonal packing within bundles, which are also arranged in square of hexagonal packing, are included in each simulation. These are simple but not trivial models for fibrous preforms used in composites manufacturing – dual porosity systems characterised by different inter- and intra-tow porosities. The way these porosities affect the hydraulic permeability of such media is currently unknown and is elucidated through our simulations. Following numerical solution of the governing equations, ( Kp) is calculated from the computed flowrate through Darcy's law and is expressed as function of the inter- and intra-tow porosities (φ, φt) and of the filament radius ( Rf). Numerical results are also compared to analytical models. The latter form the starting point in the development of a dimensionless correlation for the permeability of such dual porosity media. It is found that the numerically computed permeabilities follow that correlation for a wide range of φ i, φt and Rf.

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