1,184 research outputs found

    A comparison of constitutive models for describing the flow of uncured styrene-butadiene rubber

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    Uncured styrene-butadiene rubber (SBR) can be modelled as a viscoelastic material with at least two different relaxation mechanisms. In this paper we compare multi-mode constitutive models combining two viscoelastic modes (linear and/or nonlinear) in three possible ways. Our particular choice of the two modes was inspired by models originally developed to describe the response of asphalt binders. We select the model that best fits the experimental data obtained from a modified stress relaxation experiment in the torsional configuration of the plate-plate rheometer. The optimisation of the five model parameters for each model is achieved by minimising the weighted least-squares distance between experimental observations and the computer model output using a tree-structured Parzen estimator algorithm to find an initial guess, followed by further optimisation using the Nelder-Mead simplex algorithm. The results show that the model combining the linear mode and the nonlinear mode is the most suitable variant to describe the observed behavior of SBR in the given regime. The predictive capabilities of the three models are further examined in changed experimental and numerical configurations. Full data and code to produce the figures in this article are included as supplementary material

    Fractional Calculus via Functional Calculus: Theory and Applications

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    This paper demonstrates the power of the functional-calculus definition of linear fractional (pseudo-)differential operators via generalised Fourier transforms. Firstly, we describe in detail how to get global causal solutions of linear fractional differential equations via this calculus. The solutions are represented as convolutions of the input functions with the related impulse responses. The suggested method via residue calculus separates an impulse response automatically into an exponentially damped (possibly oscillatory) part and a ''slow' relaxation. If an impulse response is stable it becomes automatically causal, otherwise one has to add a homogeneous solution to get causality. Secondly, we present examples and, moreover, verify the approach along experiments on viscolelastic rods. The quality of the method as an effective few-parameter model is impressively demonstrated: the chosen reference example PTFE (Teflon) shows that in contrast to standard classical models our model describes the behaviour in a wide frequency range within the accuracy of the measurement. Even dispersion effects are included. Thirdly, we conclude the paper with a survey of the required theory. There the attention is directed to the extension from the L-2-approach on the space of distributions cal D-

    Seismic reverse-time migration in viscoelastic media

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    Seismic images are key to exploration seismology. They help identify structures in the subsurface and locate potential reservoirs. However, seismic images suffer from the problem of low resolution caused by the viscoelasticity of the medium. The viscoelasticity of the media is caused by the combination of fractured solid rock and fluids, such as water, oil and gas. This viscoelasticity of the medium causes attenuation of seismic waves, which includes energy absorption and velocity dispersion. These two attenuation effects significantly change the seismic data, and thus the seismic imaging. The aim of this thesis is to deepen the understanding of seismic wave propagation in attenuating media and to further investigate the method for high-resolution seismic imaging. My work, presented in this dissertation, comprises the following three parts. First, the determination of the viscoelastic parameters in the generalised viscoelastic wave equation. The viscoelasticity of subsurface media is succinctly represented in the generalised wave equation by a fractional temporal derivative. This generalised viscoelastic wave equation is characterised by the viscoelastic parameter and the viscoelastic velocity, but these parameters are not well formulated and therefore unfavourable for seismic implementation. The causality and stability of the generalised wave equation are proved by deriving the rate-of-relaxation function. On this basis, the viscoelastic parameter is formulated based on the constant Q model, and the viscoelastic velocity is formulated in terms of the reference velocity and the viscoelastic parameter. These two formulations adequately represent the viscoelastic effect in seismic wave propagation. Second, the development of a fractional spatial derivatives wave equation with a spatial filter. This development aims to effectively and efficiently solve the generalised viscoelastic wave equation with fractional temporal derivative, which is numerically challenging. I have transferred the fractional temporal derivative into fractional spatial derivatives, which can be solved using the pseudo-spectral implementation. However, this method is inaccurate in heterogeneous media. I introduced a spatial filter to correct the simulation error caused by the averaging in this implementation. The numerical test shows that the proposed spatial filter can significantly improve the accuracy of the seismic simulation and maintain high efficiency. Moreover, the proposed wave equation with fractional spatial derivatives is applied to compensate for the attenuation effects in reverse-time migration. This allows the dispersion correction and energy compensation to be performed simultaneously, which improves the resolution of the migration results. Finally, the development of reverse-time migration using biaxial wavefield decomposition to reduce migration artefacts and further improve the resolution of seismic images. In reverse-time migration, the cross-correlation of unphysical waves leads to large artefacts. By decomposing the wavefield both horizontally and vertically, and selecting only the causal waves for cross-correlation, the artefacts are greatly reduced, and the delicate structures can be identified. This decomposition method is also suitable for reverse-time migration with attenuation compensation. The migration results show that the resolution of the final seismic image is significantly improved, compared to conventional reverse-time migration.Open Acces

    Dynamic stiffness and damping prediction on rubber material parts, FEA and experimental correlation

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    The final objective of the present work is the accurate prediction of the dynamic stiffness behaviour of complex rubber parts using finite element simulation tools. For this purpose, it becomes necessary to perform a complex rubber compound material characterisation and modelling work; this needs two important previous steps. These steps are detailed in the present document together with a theoretical review of viscoelastic visco-elasto-plastic models for elastomers. Firstly, a new characterisation method is proposed to determine the degree of cure of rubber parts. It is known that the degree of cure of rubbers bears heavily on their mechanical properties. This method consists of the correlation of swelling results to rheometer data achieving a good agreement. Secondly, the influence of the strain rate used in static characterisation tests is studied. In this step, a new characterisation method is proposed. The latter characterisation method will be used to fit extended hyperelastic models in Finite Element Analysis (FEA) software like ANSYS. The proposed method improves the correlation of experimental data to simulation results obtained by the use of standard methods. Finally, the overlay method proposed by Austrell concerning frequency dependence of the dynamic modulus and loss angle that is known to increase more with frequency for small amplitudes than for large amplitudes is developed. The original version of the overlay method yields no difference in frequency dependence with respect to different load amplitudes. However, if the element in the viscoelastic layer of the finite element model are given different stiffness and loss properties depending on the loading amplitude level, frequency dependence is shown to be more accurate compared to experiments. The commercial finite element program Ansys is used to model an industrial metal rubber part using two layers of elements. One layer is a hyper viscoelastic layer and the other layer uses an elasto-plastic model with a multi-linear kinematic hardening rule. The model, being intended for stationary cyclic loading, shows good agreement with measurements on the harmonically loaded industrial rubber part

    Study on the generalized formulations with the aim to reproduce the viscoelastic dynamic behavior of polymers

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    Appropriate modelling of the real behavior of viscoelastic materials is of fundamental importance for correct studies and analyses of structures and components where such materials are employed. In this paper, the potential to employ a generalized Maxwell model and the relative fraction derivative model is studied with the aim to reproduce the experimental behavior of viscoelastic materials. For both models, the advantage of using the pole-zero formulation is demonstrated and a specifically constrained identification procedure to obtain the optimum parameters set is illustrated. Particular emphasis is given on the ability of the models to adequately fit the experimental data with a minimum number of parameters, addressing the possible computational issues. The question arises about the minimum number of experimental data necessary to estimate the material behavior in a wide frequency range, demonstrating that accurate results can be obtained by knowing only the data of the upper and low frequency plateaus plus the ones at the loss tangent peak

    A unified rheological model for cells and cellularised materials.

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    The mechanical response of single cells and tissues exhibits a broad distribution of time-scales that often gives rise to a distinctive power-law rheology. Such complex behaviour cannot be easily captured by traditional rheological approaches, making material characterisation and predictive modelling very challenging. Here, we present a novel model combining conventional viscoelastic elements with fractional calculus that successfully captures the macroscopic relaxation response of epithelial monolayers. The parameters extracted from the fitting of the relaxation modulus allow prediction of the response of the same material to slow stretch and creep, indicating that the model captured intrinsic material properties. Two characteristic times, derived from the model parameters, delimit different regimes in the materials response. We compared the response of tissues with the behaviour of single cells as well as intra and extra-cellular components, and linked the power-law behaviour of the epithelium to the dynamics of the cell cortex. Such a unified model for the mechanical response of biological materials provides a novel and robust mathematical approach to consistently analyse experimental data and uncover similarities and differences in reported behaviour across experimental methods and research groups. It also sets the foundations for more accurate computational models of tissue mechanics

    Dynamics of viscoelastic-magnetorheological sandwich structures: multiphysics analysis

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    A fundamental aim of many industrial sectors is the reduction of structural vibration in order to increase the service life of mechanical components and diminish noise radiation. Viscoelastic sandwiches have been widely applied to attenuate structural vibration as they are cost-effective and simple to employ. However, the constantly increasing requirements for vibration control have made the latest research move towards smart structures able to adapt to random vibrations in real time. Magnetorheological materials are a class of smart materials able to modify their rheological properties in response to magnetic fields. Thus, they offer attractive features for constructing smart sandwich structure with enhanced vibration control. The present thesis studies the dynamics of thin viscoelastic-magnetorheological sandwich structures. These sandwiches are analogous to thin viscoelastic sandwiches in the absence of a magnetic field, whereas when magnetic fields are applied their dynamic behaviour is modified as a result of the coupling of multiple physical phenomena generated in their skins and core. The dynamic behaviour of thin viscoelastic sandwiches was analysed as a way of studying the behaviour of thin viscoelastic-magnetorheological sandwiches in the absence of a magnetic field. To that end, sandwiches of different compositions were characterized and numerical models were defined. From the joint analysis of the experimental and numerical results, the influence of the nature and thickness of both viscoelastic adhesive and metallic skins on the dynamic properties of the sandwich were determined. The phenomenon of eddy currents generated in metallic skins was studied in order to determine its influence on the dynamic behaviour of viscoelasticmagnetorheological sandwiches. To do this, an experimental modal analysis with a metallic beam, with and without induced eddy currents, was carried out. Then, in view of the damping capacity of eddy currents, a new hybrid sandwich structure combining viscoelastic and eddy current damping was proposed. Afterwards, a new inverse method was developed to estimate and model the influence of eddy currents. The phenomena generated in the viscoelastic-magnetorheological core, the magnetorheological effect and magnetic force, were studied. To that end, a magneto-dynamic model of viscoelastic-magnetorheological sandwiches including both phenomena was proposed and validated with experimental results. Finally, the dynamic behaviour of a thin viscoelastic-magnetorheological sandwich was analysed experimentally, and the influence of the magnetic particles and the intensity and position of the magnetic field was studied. The knowledge acquired in the course of this research enables determining the physical phenomena governing the dynamics of thin viscoelastic-magnetorheological sandwiches and explain the experimentally observed magneto-dynamic behaviour.Sektore industrial askoren helburua egiturazko bibrazioak murriztea da, honela, osagai mekanikoen bizitza erabilgarria luzatu eta erradiazio akustikoa murrizten baita. Sandwich biskoelastikoak oso erabiliak izan dira egiturazko bibrazioak moteltzeko, izan ere, inplementatzeko errazak eta kostu baxukoak baitira. Gaur egun, gero eta bibrazio-kontrol efikazagoa eskatzen denez, denbora errealean ausazko bibrazioetara egokitzeko gai diren estruktura adimendunetan ardaztu dira azken ikerketak. Material magnetoerreologikoak material adimendunak dira, zeinen propietate erreologikoak eremu magnetiko baten bidez aldatu daitezkeen. Hortaz, ohiko sandwichen nukleoa material magnetoerreologikoekin ordezkatu daiteke, sandwich estruktura adimenduak sortzeko. Tesi doktoral honen helburu nagusia sandwich biskoelastiko-magnetoerreologiko meheen dinamika aztertzea da. Eremu magnetikorik aplikatu ezean, sandwich hauen izaera dinamikoa sandwich biskoelastikoen bera da. Eremu magnetikoak aplikatzean, berriz, sandwichen izaera dinamikoa aldatu egiten da, beraien azal eta nukleoetan sortzen diren fenomeno ezberdinen akoplamenduagatik. Lehenik, sandwich biskoelastiko meheen jokaera dinamikoa aztertu da, sandwich biskoelastiko-magnetoerreologikoen jokaera eremu magnetikorik gabe analizatzeko asmoz. Horretarako, konposizio ezberdineko sandwich biskoelastikoak karakterizatu eta zenbakizko ereduak definitu dira. Itsasgarri biskoelastikoek eta azal metalikoek sandwicharen propietate dinamikoetan duten eragina zehaztu da emaitza esperimental eta zenbakizkoei esker. Azal metalikoetan sortutako Foucault-en korronteen fenomenoa ere aztertu da, korronte hauek sandwich biskoelastiko-magnetorreologikoen jokaera dinamikoaren gain duten eragina zehazteko. Horretarako, metalezko habe baten analisi modal esperimentala gauzatu da, habeak Foucault-en korronteak induzituta eta induzitu gabe dituelarik. Jarraian Foucault-en korronteen moteltze-gaitasuna ikusirik, sandwich hibrido berria proposatu da, zeinak moteltze biskoelastikoa eta Foucault-ena batzen dituen. Ondoren, metodo alderantzikatu berria garatu da, korronte hauen eragina zenbatetsi eta modelatzeko. Nukleo biskoelastiko-magnetoerreologikoetan sortutako fenomenoak ere aztertu dira, hau da, efektu magnetoerreologikoa eta indar magnetikoa. Horretarako, bi fenomeno hauek kontutan hartzen dituen sandwich biskoelastikomagnetoerreologikoen eredu dinamikoa proposatu eta emaitza esperimentalekin egiaztatu da. Azkenik, sandwich biskoelastiko-magnetoerreologiko meheen jokaera dinamikoa esperimentalki ebaluatu da. Partikula magnetikoek eta eremu magnetikoaren intentsitateak eta posizioak sandwicharen propietate dinamikoetan duten eragina aztertu da. Tesi doktoral honetan zehar sortutako ezagutzak, sandwich hauen erantzun magnetodinamikoa gidatzen duten fenomeno fisikoak ezagutzea ahalbidetu du.En la actualidad, numerosos sectores industriales tienen como objetivo disminuir la amplitud de las vibraciones con el fin de alargar la vida útil de los componentes y reducir la radiación acústica. Con este propósito se utilizan sándwich viscoelasticos, ya que son sencillos de implementar, de bajo coste y eficaces en la atenuación de vibraciones estructurales. Sin embargo, estos sándwich no tienen la capacidad de adaptarse en tiempo real a las condiciones de trabajo, por lo que las últimas investigaciones en control de vibraciones se centran en estructuras inteligentes. Los materiales magnetorreológicos son capaces de modificar sus propiedades reológicas en respuesta a campos magnéticos externos, y por tanto son idóneos para fabricar estructuras sándwich inteligentes. El objetivo principal de la presente tesis doctoral es conocer la respuesta dinámica de sándwich viscoelasticos-magnetorreológicos finos. En ausencia de campo magnético el comportamiento dinámico de estos sándwich es análogo al de los sándwich viscoelasticos, sin embargo al aplicar un campo magnético su comportamiento dinámico se modifica como resultado del acoplamiento de múltiples fenómenos físicos generados en las pieles y en el núcleo. Se ha analizado el comportamiento dinámico de los sándwich viscoelasticos finos para entender la respuesta de los sándwich viscoelasticos-magnetorreológicos en ausencia de campo magnético. Para ello, se han caracterizado sándwich de diferentes composiciones y se han generado modelos numéricos. Con estos análisis se ha establecido la influencia de la composición y del espesor tanto del adhesivo viscoelastico, como de las pieles metálicas en las propiedades dinámicas del sándwich. Se han estudiado las corrientes de Foucault que se generan en las pieles metálicas de los sándwich. Dada la capacidad de amortiguación de estas corrientes, se ha propuesto un nuevo sándwich híbrido que combina el amortiguamiento viscoelastico, con las corrientes de Foucault. Además, se ha desarrollado un nuevo método inverso que estima la influencia de este fenómeno en la respuesta dinámica de los sándwich. En el núcleo viscoelastico-magnetorreológico concurren dos fenómenos: el efecto magnetorreológico, propio de la inteligencia del núcleo, y la fuerza magnética que se origina por el acoplamiento de las vibraciones del núcleo magnetizado con el campo magnético aplicado. Ambos fenómenos se han incluido en un nuevo modelo numérico, que se ha validado con resultados experimentales, y se ha establecido su influencia en la dinámica del sándwich. Por último, se ha estudiado experimentalmente la influencia de las partículas magnéticas, y de la intensidad y posición del campo magnético en el comportamiento dinámico de los sándwich viscoelastico-magnetorreológico finos. El conocimiento adquirido con esta tesis, ha permitido determinar los fenómenos físicos que rigen la dinámica del sándwich viscoelastico-magnetorreológico y explicar el comportamiento magneto-dinámico experimental observado

    Mechanical behaviour of fibre metal laminates based on self-reinforced composites for impact applications

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    Lightness and appropriate mechanical response of materials are currently demanded in many applications related to transportation (automotive, aeronautic). Depending on the component, an appropriate mechanical behaviour may consist in having either damage tolerance or energy dissipation capacity. In this regard, it is essential to understand the mechanical behaviour of the materials in order to succeed in the selection of them and the design of components. Fibre metal laminates (FMLs) are multilayer systems consisting of stacked metal sheets and thin plates of composite material. Among FMLs, the ones based on self-reinforced composites (SRCs) have demonstrated they can offer an excellent response to low and high velocity impact loadings in terms of impact energy dissipating capacity when compared to thermosetting matrix-based systems. The main objective of this thesis is to study the mechanical behaviour of fibre metal laminates based on SRCs. Within this general objective, three partial subobjectives are established: - To select the most appropriate SRC-FML, between an Al-based one and a Mg-based one, in terms of energy dissipation capacity under low-velocity impacts. - To characterise the mechanical behaviour of the plain SRC and to evaluate its influence in the mechanical response of the FML based on the strain rate. - To develop a constitutive model of the mechanical behaviour of the SRC. The results reveal that the Al/SRPP-FML is the most appropriate in terms of energy dissipation capacity under low-velocity impacts. After that, the characterisation of the plain SRPP shows that, when the material is submitted to both tensile and shear stresses solicitations, it presents irreversible strains, hysteresis phenomena under cyclic loads, a rate-dependent behaviour and a stiffness varying with the strain. Besides, its influence in the mechanical response of the FML is considerable. Then, a constitutive model of the mechanical behaviour of the SRC is proposed. The model is based on the combination of a elastoplastic model and a fractional viscoelastic model. The numerical-experimental correlation demonstrates that the model is capable of predicting accurately both the cyclic tensile and shear behaviours of the SRPP
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