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Constitutive modelling of the amplitude and frequency dependency of filled elastomers utilizing a modified Boundary Surface Model
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics. KTH, School of Engineering Sciences (SCI), Centres, VinnExcellence Center for ECO2 Vehicle design. Scania, Södertälje, Sweden .ORCID iD: 0000-0002-1036-6837
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics. KTH, School of Engineering Sciences (SCI), Centres, VinnExcellence Center for ECO2 Vehicle design.ORCID iD: 0000-0001-5760-3919
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2014 (English)In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 51, no 19-20, 3431-3438 p.Article in journal (Refereed) Published
Abstract [en]

A phenomenological uniaxial model is derived for implementation in the time domain, which captures the amplitude and frequency dependency of filled elastomers. Motivated by the experimental observation that the frequency dependency is stronger for smaller strain amplitudes than for large ones, a novel material model is presented. It utilizes a split of deformation between a generalized Maxwell chain in series with a bounding surface plasticity model with a vanishing elastic region. Many attempts to capture the behaviour of filled elastomers are found in the literature, which often utilize an additive split between an elastic and a history dependent element, in parallel. Even though some models capture the storage and loss modulus during sinusoidal excitations, they often fail to do so for more complex load histories. Simulations with the derived model are compared to measurements in simple shear on a compound of carbon black filled natural rubber used in driveline isolators in the heavy truck industry. The storage and loss modulus from simulations agree very well with measurements, using only 7 material parameters to capture 2 decades of strain (0.5-50% shear strain) and frequency (0.2-20 Hz). More importantly, with material parameters extracted from the measured storage and loss modulus, measurements of a dual sine excitation are well replicated. This enables realistic operating conditions to be simulated early in the development process, before an actual prototype is available for testing, since the loads in real life operating conditions frequently are a combination of many harmonics.

Place, publisher, year, edition, pages
2014. Vol. 51, no 19-20, 3431-3438 p.
Keyword [en]
Amplitude dependency, Boundary Surface Model, Carbon black, Filled elastomers, Fletcher-Gent Effect, Natural rubber
National Category
Vehicle Engineering
Identifiers
URN: urn:nbn:se:kth:diva-151310DOI: 10.1016/j.ijsolstr.2014.06.003ISI: 000341469900012Scopus ID: 2-s2.0-84906245570OAI: oai:DiVA.org:kth-151310DiVA: diva2:747787
Note

QC 20140917

Available from: 2014-09-17 Created: 2014-09-17 Last updated: 2017-12-05Bibliographically approved
In thesis
1. Modelling of the Fletcher-Gent effect and obtaining hyperelastic parameters for filled elastomers
Open this publication in new window or tab >>Modelling of the Fletcher-Gent effect and obtaining hyperelastic parameters for filled elastomers
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The strain amplitude dependency , i.e. the Fletcher-Gent effect and Payne effect, and the strain rate dependency of rubber with reinforcing fillers is modelled using a modified boundary surface model and implemented uniaxially. In this thesis, a split of strain instead of stress is utilized, and the storage and loss modulus are captured over two decades of both strain amplitudes and frequencies. In addition, experimental results from bimodal excitation are replicated well, even though material parameters were obtained solely from harmonic excitation. These results are encouraging since the superposition principle is not valid for filled rubber, and real-life operational conditions in general contain several harmonics. This means that formulating constitutive equations in the frequency domain is a cumbersome task, and therefore the derived model is implemented in the time domain. Filled rubber is used irreplaceable in several engineering solutions, such as tires, bushings, vibrations isolators, seals and tread belts, to name just a few. In certain applications, it is sufficient to model the elastic properties of a component during finite strains. However, Hooke’s law is inadequate for this task. Instead, hyperelastic material models are used. Finally, the thesis presents a methodology for obtaining the required material parameters utilizing experiments in pure shear, uniaxial tension and the inflation of a rubber membrane. It is argued that the unloading curve rather than the loading curve is more suitable for obtaining these parameters, even at very low strain rates.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. x, 54 p.
Series
TRITA-AVE, ISSN 1651-7660 ; 2014:47
Keyword
filled elastomers, natural rubber, carbon black, Fletcher-Gent effect, Payne-effect, finite strain, hyperelastic
National Category
Other Natural Sciences
Identifiers
urn:nbn:se:kth:diva-151304 (URN)978-91-7595-273-4 (ISBN)
Presentation
2014-10-08, Munin, Teknikringen 8, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20140917

Available from: 2014-09-17 Created: 2014-09-17 Last updated: 2014-09-24Bibliographically approved
2. Modelling the viscoplastic properties of carbon black filled rubber: A finite strain material model suitable for Finite Element Analysis
Open this publication in new window or tab >>Modelling the viscoplastic properties of carbon black filled rubber: A finite strain material model suitable for Finite Element Analysis
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

An increased environmental awareness, legal demands and the large part of total costs attributable to fuel cost are all incentives for the automotive industry to reduce fuel consumption. The optimal driveline to enable this reduction depends on the operational conditions and the available infrastructure. Moreover, special care is needed when developing the driveline isolators, since the demands on noise, vibration and harshness (NVH) are the same regardless of driveline. To this end, computer aided calculations can be used in order to evaluate a large number of configurations. However, these calculations are only, at best, as good as the material models employed. In the foreseeable future, rubber with reinforcing fillers will be used in vibration isolators in order to obtain the desired properties of these components. However, the stiffness and damping of rubber with reinforcing fillers are highly non-linear functions, and the available material models in commercial software and in the literature are often insufficient. Therefore, a finite strain viscoplastic material model is derived in the time domain and implemented as a user defined material model in Abaqus Explicit. The model captures the strain amplitude and frequency dependency of the storage and loss modulus for a carbon black filled natural rubber. The model is accurate over a wide range of shear strain amplitudes and frequencies, 0.2-50 % and 0.5-20 Hz, respectively, using only 5 material parameters. In addition, the model correctly captures the response from bimodal excitations. The implementation in Abaqus Explicit enables component characteristics to be evaluated early in the development phase, with material parameters derived from simple test specimens. The improved accuracy of simulations of these components can aid engineers develop more optimized solutions faster than with conventional methods.

Abstract [sv]

En ökad miljömedvetenhet, juridiska krav och den stora delen av de totala kostnaderna som kan hänföras till bränslekostnader är alla incitament för fordonsindustrin att minska bränsleförbrukningen. Den optimala drivlinan för att möjliggöra denna minskning beror på driftförhållanden och den tillgängliga infrastrukturen. Dessutom ställs höga krav på utvecklingen av drivlineisolatorer, eftersom kraven på buller och vibrationer (NVH) är desamma oavsett drivlina. För detta ändamål kan datorstödda beräkningar användas för att utvärdera ett stort antal konfigurationer. Dessa beräkningar är, i bästa fall, endast så bra som de använda materialmodellerna. Inom en överskådlig framtid kommer gummi med förstärkande fyllmedel användas i vibrationsisolatorer för att erhålla de önskade egenskaperna hos dessa komponenter. Men styvheten och dämpningen i gummi med förstärkande fyllmedel är kraftigt icke-linjära funktioner, och de tillgängliga materialmodellerna i kommersiella programvaror och i litteraturen är ofta otillräckliga. Därför är en viskoplastisk materialmodell för finita deformationer framtagen i tidsdomänen och implementeras som ett användardefinierat material i Abaqus Explicit. Modellen fångar töjningsamplitud- och frekvensberoendet av lagrings- och förlustmodulen för ett kimröksfyllt naturgummi. Den är korrekt över ett brett intervall av skjuvtöjningsamplituder och frekvenser, 0.2-50% respektive 0.5-20 Hz, och kräver endast 5 materialparametrar. Dessutom fångar modeller responsen från bimodala excitationer. Implementeringen i Abaqus Explicit gör att komponentegenskaper kan utvärderas tidigt i utvecklingsfasen, med materialparametrar som härrör från enkla provkroppar. Den förbättrade noggrannheten i simuleringar av dessa komponenter kan hjälpa ingenjörer att utveckla mer optimerade lösningar snabbare än med konventionella metoder.

Place, publisher, year, edition, pages
Stockholm: US-AB, 2016. xii, 55 p.
Series
TRITA-AVE, ISSN 1651-7660 ; 2016:12
Keyword
reinforcing fillers, rubber, finite strain, viscoplastic, förstärkande fyllmedel, gummi, finita töjningar, viskoplastisk
National Category
Vehicle Engineering
Research subject
Vehicle and Maritime Engineering
Identifiers
urn:nbn:se:kth:diva-184879 (URN)978-91-7595-902-3 (ISBN)
Public defence
2016-04-29, D2, Lindstedtsvägen 5, 10044 Stockholm, KTH Campus, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

QC 20160406

Available from: 2016-04-06 Created: 2016-04-06 Last updated: 2016-04-06Bibliographically approved

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Österlöf, RickardKari, Leif

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