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Michele Ciavarella - One of the best experts on this subject based on the ideXlab platform.
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On the existence and uniqueness of steady state solutions in thermoelastic contact with Frictional Heating
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2005Co-Authors: Lars-erik Andersson, Anders Klarbring, James Barber, Michele CiavarellaAbstract:Existence and Uniquness of Steady State Solutions in Thermoelastic Contact with Frictional Heating
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Instability of thermoelastic contact for two half-planes sliding out-of-plane with contact resistance and Frictional Heating
Journal of the Mechanics and Physics of Solids, 2004Co-Authors: Luciano Afferrante, Michele CiavarellaAbstract:Abstract Thermoelastic contact is known to show instabilities when the heat transmitted across the interface depends on the pressure, either because of a pressure-dependent thermal contact resistance R(p) or because of Frictional Heating due to the product of friction coefficient, speed, and pressure, fVp. Recently, the combined effect of pressure-dependent thermal contact resistance and Frictional Heating has been studied in the context of simple rod models or for a more realistic elastic conducting half-plane sliding against a rigid perfect conductor “wall”. Because R(p) introduces a non-linearity even in full contact, the “critical speed” for the uniform pressure solution to be unstable depends not just on material properties, and geometry, but also on the heat flux and on pressure. Here, the case of two different elastic and conducting half-planes is studied, and Frictional Heating is shown to produce significant effects on the stability boundaries with respect to the Zhang and Barber (J. Appl. Mech. 57 (1990) 365) corresponding case with no sliding. In particular, Frictional Heating makes instability possible for a larger range of prescribed temperature drop at the interface including, at sufficiently high speeds, the region of opposite sign of that giving instability in the corresponding static case. The effect of Frictional Heating is particularly relevant for one material combinations of the Zhang and Barber (J. Appl. Mech. 57 (1990) 365) classification (denominated class b here), as above a certain critical speed, the system is unstable regardless of temperature drop at the interface. Finally, if the system has a prescribed heat flow into one of the materials, the results are similar, except that Frictional Heating may also become a stabilizing effect, if the resistance function and the material properties satisfy a certain condition.
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The thermoelastic Aldo contact model with Frictional Heating
Journal of the Mechanics and Physics of Solids, 2004Co-Authors: Luciano Afferrante, Michele CiavarellaAbstract:Abstract In the study of the essential features of thermoelastic contact, Comninou and Dundurs (J. Therm. Stresses 3 (1980) 427) devised a simplified model, the so-called “Aldo model”, where the full 3 D body is replaced by a large number of thin rods normal to the interface and insulated between each other, and the system was further reduced to 2 rods by Barber's Conjecture (ASME J. Appl. Mech. 48 (1981) 555). They studied in particular the case of heat flux at the interface driven by temperature differences of the bodies, and opposed by a contact resistance, finding possible multiple and history dependent solutions, depending on the imposed temperature differences. The Aldo model is here extended to include the presence of Frictional Heating. It is found that the number of solutions of the problem is still always odd, and Barber's graphical construction and the stability analysis of the previous case with no Frictional Heating can be extended. For any given imposed temperature difference, a critical speed is found for which the uniform pressure solution becomes non-unique and/or unstable. For one direction of the temperature difference, the uniform pressure solution is non-unique before it becomes unstable. When multiple solutions occur, outermost solutions (those involving only one rod in contact) are always stable. A full numerical analysis has been performed to explore the transient behaviour of the system, in the case of two rods of different size. In the general case of N rods, Barber's conjecture is shown to hold since there can only be two stable states for all the rods, and the reduction to two rods is always possible, a posteriori.
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interaction of thermal contact resistance and Frictional Heating in thermoelastic instability
International Journal of Solids and Structures, 2003Co-Authors: Michele Ciavarella, Anders Klarbring, Luciano Afferrante, Lars Johansson, J R BarberAbstract:Thermoelastic contact problems can posess non-unique and/or unstable steady-state solutions if there is Frictional Heating or if there is a pressure-dependent thermal contact resistance at the interface. These two effects have been extensively studied in isolation, but their possible interaction has never been investigated. In this paper, we consider an idealized problem in which a thermoelastic rod slides against a rigid plane with both Frictional Heating and a contact resistance. For sufficiently low sliding speeds, the results are qualitatively similar to those with no sliding. In particular, there is always an odd number of steady-state solutions; if the steady-state is unique it is stable and if it is non-unique, stable and unstable solutions alternate, with the outlying solutions being stable. However, we identify a sliding speed V(0) above which the number of steady states is always even (including zero, implying possible non-existence of a steady-state) and again stable and unstable states alternate. A parallel numerical study shows that for V>V(0) there are some initial conditions from which the contact pressure grows without limit in time, whereas for V
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Interaction of thermal contact resistance and Frictional Heating in thermoelastic instability
International Journal of Solids and Structures, 2003Co-Authors: Michele Ciavarella, Anders Klarbring, Luciano Afferrante, Lars Johansson, James BarberAbstract:Thermoelastic contact problems can posess non-unique and/or unstable steady-state solutions if there is Frictional Heating or if there is a pressure-dependent thermal contact resistance at the interface. These two effects have been extensively studied in isolation, but their possible interaction has never been investigated. In this paper, we consider an idealized problem in which a thermoelastic rod slides against a rigid plane with both Frictional Heating and a contact resistance. For sufficiently low sliding speeds, the results are qualitatively similar to those with no sliding. In particular, there is always an odd number of steady-state solutions; if the steady-state is unique it is stable and if it is non-unique, stable and unstable solutions alternate, with the outlying solutions being stable. However, we identify a sliding speed V(0) above which the number of steady states is always even (including zero, implying possible non-existence of a steady-state) and again stable and unstable states alternate. A parallel numerical study shows that for V>V(0) there are some initial conditions from which the contact pressure grows without limit in time, whereas for V
Luciano Afferrante - One of the best experts on this subject based on the ideXlab platform.
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Instability of thermoelastic contact for two half-planes sliding out-of-plane with contact resistance and Frictional Heating
Journal of the Mechanics and Physics of Solids, 2004Co-Authors: Luciano Afferrante, Michele CiavarellaAbstract:Abstract Thermoelastic contact is known to show instabilities when the heat transmitted across the interface depends on the pressure, either because of a pressure-dependent thermal contact resistance R(p) or because of Frictional Heating due to the product of friction coefficient, speed, and pressure, fVp. Recently, the combined effect of pressure-dependent thermal contact resistance and Frictional Heating has been studied in the context of simple rod models or for a more realistic elastic conducting half-plane sliding against a rigid perfect conductor “wall”. Because R(p) introduces a non-linearity even in full contact, the “critical speed” for the uniform pressure solution to be unstable depends not just on material properties, and geometry, but also on the heat flux and on pressure. Here, the case of two different elastic and conducting half-planes is studied, and Frictional Heating is shown to produce significant effects on the stability boundaries with respect to the Zhang and Barber (J. Appl. Mech. 57 (1990) 365) corresponding case with no sliding. In particular, Frictional Heating makes instability possible for a larger range of prescribed temperature drop at the interface including, at sufficiently high speeds, the region of opposite sign of that giving instability in the corresponding static case. The effect of Frictional Heating is particularly relevant for one material combinations of the Zhang and Barber (J. Appl. Mech. 57 (1990) 365) classification (denominated class b here), as above a certain critical speed, the system is unstable regardless of temperature drop at the interface. Finally, if the system has a prescribed heat flow into one of the materials, the results are similar, except that Frictional Heating may also become a stabilizing effect, if the resistance function and the material properties satisfy a certain condition.
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The thermoelastic Aldo contact model with Frictional Heating
Journal of the Mechanics and Physics of Solids, 2004Co-Authors: Luciano Afferrante, Michele CiavarellaAbstract:Abstract In the study of the essential features of thermoelastic contact, Comninou and Dundurs (J. Therm. Stresses 3 (1980) 427) devised a simplified model, the so-called “Aldo model”, where the full 3 D body is replaced by a large number of thin rods normal to the interface and insulated between each other, and the system was further reduced to 2 rods by Barber's Conjecture (ASME J. Appl. Mech. 48 (1981) 555). They studied in particular the case of heat flux at the interface driven by temperature differences of the bodies, and opposed by a contact resistance, finding possible multiple and history dependent solutions, depending on the imposed temperature differences. The Aldo model is here extended to include the presence of Frictional Heating. It is found that the number of solutions of the problem is still always odd, and Barber's graphical construction and the stability analysis of the previous case with no Frictional Heating can be extended. For any given imposed temperature difference, a critical speed is found for which the uniform pressure solution becomes non-unique and/or unstable. For one direction of the temperature difference, the uniform pressure solution is non-unique before it becomes unstable. When multiple solutions occur, outermost solutions (those involving only one rod in contact) are always stable. A full numerical analysis has been performed to explore the transient behaviour of the system, in the case of two rods of different size. In the general case of N rods, Barber's conjecture is shown to hold since there can only be two stable states for all the rods, and the reduction to two rods is always possible, a posteriori.
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interaction of thermal contact resistance and Frictional Heating in thermoelastic instability
International Journal of Solids and Structures, 2003Co-Authors: Michele Ciavarella, Anders Klarbring, Luciano Afferrante, Lars Johansson, J R BarberAbstract:Thermoelastic contact problems can posess non-unique and/or unstable steady-state solutions if there is Frictional Heating or if there is a pressure-dependent thermal contact resistance at the interface. These two effects have been extensively studied in isolation, but their possible interaction has never been investigated. In this paper, we consider an idealized problem in which a thermoelastic rod slides against a rigid plane with both Frictional Heating and a contact resistance. For sufficiently low sliding speeds, the results are qualitatively similar to those with no sliding. In particular, there is always an odd number of steady-state solutions; if the steady-state is unique it is stable and if it is non-unique, stable and unstable solutions alternate, with the outlying solutions being stable. However, we identify a sliding speed V(0) above which the number of steady states is always even (including zero, implying possible non-existence of a steady-state) and again stable and unstable states alternate. A parallel numerical study shows that for V>V(0) there are some initial conditions from which the contact pressure grows without limit in time, whereas for V
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Interaction of thermal contact resistance and Frictional Heating in thermoelastic instability
International Journal of Solids and Structures, 2003Co-Authors: Michele Ciavarella, Anders Klarbring, Luciano Afferrante, Lars Johansson, James BarberAbstract:Thermoelastic contact problems can posess non-unique and/or unstable steady-state solutions if there is Frictional Heating or if there is a pressure-dependent thermal contact resistance at the interface. These two effects have been extensively studied in isolation, but their possible interaction has never been investigated. In this paper, we consider an idealized problem in which a thermoelastic rod slides against a rigid plane with both Frictional Heating and a contact resistance. For sufficiently low sliding speeds, the results are qualitatively similar to those with no sliding. In particular, there is always an odd number of steady-state solutions; if the steady-state is unique it is stable and if it is non-unique, stable and unstable solutions alternate, with the outlying solutions being stable. However, we identify a sliding speed V(0) above which the number of steady states is always even (including zero, implying possible non-existence of a steady-state) and again stable and unstable states alternate. A parallel numerical study shows that for V>V(0) there are some initial conditions from which the contact pressure grows without limit in time, whereas for V
James Barber - One of the best experts on this subject based on the ideXlab platform.
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On the existence and uniqueness of steady state solutions in thermoelastic contact with Frictional Heating
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2005Co-Authors: Lars-erik Andersson, Anders Klarbring, James Barber, Michele CiavarellaAbstract:Existence and Uniquness of Steady State Solutions in Thermoelastic Contact with Frictional Heating
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Interaction of thermal contact resistance and Frictional Heating in thermoelastic instability
International Journal of Solids and Structures, 2003Co-Authors: Michele Ciavarella, Anders Klarbring, Luciano Afferrante, Lars Johansson, James BarberAbstract:Thermoelastic contact problems can posess non-unique and/or unstable steady-state solutions if there is Frictional Heating or if there is a pressure-dependent thermal contact resistance at the interface. These two effects have been extensively studied in isolation, but their possible interaction has never been investigated. In this paper, we consider an idealized problem in which a thermoelastic rod slides against a rigid plane with both Frictional Heating and a contact resistance. For sufficiently low sliding speeds, the results are qualitatively similar to those with no sliding. In particular, there is always an odd number of steady-state solutions; if the steady-state is unique it is stable and if it is non-unique, stable and unstable solutions alternate, with the outlying solutions being stable. However, we identify a sliding speed V(0) above which the number of steady states is always even (including zero, implying possible non-existence of a steady-state) and again stable and unstable states alternate. A parallel numerical study shows that for V>V(0) there are some initial conditions from which the contact pressure grows without limit in time, whereas for V
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Thermoelastic Contact with Frictional Heating
Advances in Mechanics and Mathematics, 1Co-Authors: Lars-erik Andersson, Anders Klarbring, James Barber, Michele CiavarellaAbstract:The paper treats thermoelastic contact problems, where a variable contact heat flow resistance as well as Frictional Heating are considered. Existence and uniqueness of steady state solutions, for both a one-dimensional and a three-dimensional system, are investigated. Existence is guaranteed if the contact heat flow resistance goes to zero as the pressure goes to infinity or if the Frictional Heating is sufficiently small. Uniqueness holds in the vicinity of zero Frictional Heating and thermally insulated contact.
Anders Klarbring - One of the best experts on this subject based on the ideXlab platform.
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On the existence and uniqueness of steady state solutions in thermoelastic contact with Frictional Heating
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2005Co-Authors: Lars-erik Andersson, Anders Klarbring, James Barber, Michele CiavarellaAbstract:Existence and Uniquness of Steady State Solutions in Thermoelastic Contact with Frictional Heating
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interaction of thermal contact resistance and Frictional Heating in thermoelastic instability
International Journal of Solids and Structures, 2003Co-Authors: Michele Ciavarella, Anders Klarbring, Luciano Afferrante, Lars Johansson, J R BarberAbstract:Thermoelastic contact problems can posess non-unique and/or unstable steady-state solutions if there is Frictional Heating or if there is a pressure-dependent thermal contact resistance at the interface. These two effects have been extensively studied in isolation, but their possible interaction has never been investigated. In this paper, we consider an idealized problem in which a thermoelastic rod slides against a rigid plane with both Frictional Heating and a contact resistance. For sufficiently low sliding speeds, the results are qualitatively similar to those with no sliding. In particular, there is always an odd number of steady-state solutions; if the steady-state is unique it is stable and if it is non-unique, stable and unstable solutions alternate, with the outlying solutions being stable. However, we identify a sliding speed V(0) above which the number of steady states is always even (including zero, implying possible non-existence of a steady-state) and again stable and unstable states alternate. A parallel numerical study shows that for V>V(0) there are some initial conditions from which the contact pressure grows without limit in time, whereas for V
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Interaction of thermal contact resistance and Frictional Heating in thermoelastic instability
International Journal of Solids and Structures, 2003Co-Authors: Michele Ciavarella, Anders Klarbring, Luciano Afferrante, Lars Johansson, James BarberAbstract:Thermoelastic contact problems can posess non-unique and/or unstable steady-state solutions if there is Frictional Heating or if there is a pressure-dependent thermal contact resistance at the interface. These two effects have been extensively studied in isolation, but their possible interaction has never been investigated. In this paper, we consider an idealized problem in which a thermoelastic rod slides against a rigid plane with both Frictional Heating and a contact resistance. For sufficiently low sliding speeds, the results are qualitatively similar to those with no sliding. In particular, there is always an odd number of steady-state solutions; if the steady-state is unique it is stable and if it is non-unique, stable and unstable solutions alternate, with the outlying solutions being stable. However, we identify a sliding speed V(0) above which the number of steady states is always even (including zero, implying possible non-existence of a steady-state) and again stable and unstable states alternate. A parallel numerical study shows that for V>V(0) there are some initial conditions from which the contact pressure grows without limit in time, whereas for V
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Thermoelastic Contact with Frictional Heating
Advances in Mechanics and Mathematics, 1Co-Authors: Lars-erik Andersson, Anders Klarbring, James Barber, Michele CiavarellaAbstract:The paper treats thermoelastic contact problems, where a variable contact heat flow resistance as well as Frictional Heating are considered. Existence and uniqueness of steady state solutions, for both a one-dimensional and a three-dimensional system, are investigated. Existence is guaranteed if the contact heat flow resistance goes to zero as the pressure goes to infinity or if the Frictional Heating is sufficiently small. Uniqueness holds in the vicinity of zero Frictional Heating and thermally insulated contact.
Davy Guillarme - One of the best experts on this subject based on the ideXlab platform.
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Estimation of pressure-, temperature- and Frictional Heating-related effects on proteins’ retention under ultra-high-pressure liquid chromatographic conditions
Journal of chromatography. A, 2015Co-Authors: Szabolcs Fekete, Davy GuillarmeAbstract:The goal of this work was to evaluate the changes in retention induced by Frictional Heating, pressure and temperature under ultra high pressure liquid chromatography (UHPLC) conditions, for four model proteins (i.e. lysozyme, myoglobin, fligrastim and interferon alpha-2A) possessing molecular weights between 14 and 20kDa. First of all, because the decrease of the molar volume upon adsorption onto a hydrophobic surface was more pronounced for large molecules such as proteins, the impact of pressure appears to overcome the Frictional Heating effects. Nevertheless, we have also demonstrated that the retention decrease due to Frictional Heating was not negligible with such large biomolecules in the variable inlet pressure mode. Secondly, it is clearly shown that the modification of retention under various pressure and temperature conditions cannot be explained solely by the Frictional Heating and pressure effects. Indeed, some very uncommon van't Hoff plots (concave plots with a maximum) were recorded for our model/therapeutic proteins. These maximum retention factors values on the van't Hoff plots indicate a probable change of secondary structure/conformation with pressure and temperature. Based on these observations, it seems that the combination of pressure and temperature causes the protein denaturation and this folding-unfolding procedure is clearly protein dependent.
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Estimation of the effects of longitudinal temperature gradients caused by Frictional Heating on the solute retention using fully porous and superficially porous sub-2μm materials.
Journal of chromatography. A, 2014Co-Authors: Szabolcs Fekete, Jenő Fekete, Davy GuillarmeAbstract:Abstract In this study, the retention changes induced by Frictional Heating were evaluated for model small compounds (150–190 Da) and a small protein, namely insulin (5.7 kDa). For this purpose, the effect of longitudinal temperature gradient caused by Frictional Heating was experimentally dissociated from the combined effect of pressure and Frictional Heating, by working either in constant and variable inlet pressure modes. Various columns packed with core–shell and fully porous sub-2 μm particles were tested. It appears that Frictional Heating was less pronounced on the column packed with smallest core–shell particles (1.3 μm), compared to the ones packed with core–shell and fully porous particles of 1.7–1.8 μm. This observation was attributed to the low permeability of this material and the fact that it can only be employed in a restricted flow rate range, thus limiting the generated heat power. In addition, the thermal conductivity of the solid silica core of superficially porous particles (1.4 W/m/K) is known to be much larger than that of fully porous silica. Then, the heat dissipation is improved. However, if systems with higher pressure capability would be available and the mechanical stability of 1.3 μm core–shell material was extended to e.g. 2000 bar, the retention would be more severely impacted. At 2000 bar, ∼4.4 W heat power and +30 °C increase at column outlet temperature is expected. Last but not least, when analyzing large molecules, the impact of pressure overcomes the Frictional Heating effects. This was demonstrated in this study with insulin (∼5.7 kDa).
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Practical method transfer from high performance liquid chromatography to ultra-high performance liquid chromatography: the importance of Frictional Heating.
Journal of chromatography. A, 2011Co-Authors: Lucie Nováková, Jean-luc Veuthey, Davy GuillarmeAbstract:Abstract In theory, with identical stationary phase chemistry, the transfer of an HPLC method to UHPLC conditions is straightforward and necessitates the calculation of new conditions based on column and instrument geometries. Occasionally, undesirable changes in selectivity, retention or efficiency have been reported and have been attributed to a Frictional Heating phenomenon that is due to the elevated generated pressure drop. In the present study, the Frictional Heating in a UHPLC system was evaluated experimentally under gradient elution conditions (acetonitrile/buffer at pH 3 and 9) with generated pressure drops in the range of 100–1000 bar on both 1.0 mm and 2.1 mm I.D. columns using a mixture of 10 representative basic, acidic and neutral pharmaceutical compounds. Under adiabatic conditions (i.e., still-air oven), the longitudinal temperature gradient was estimated at +4 °C, +8 °C and +16 °C at 300, 600 and 1000 bar, respectively, on a 2.1 mm I.D. column using an empirical measurement procedure. With the 1.0 mm I.D. column, these values were reduced to +3 °C, +6 °C and +12 °C, respectively. Finally, various approaches to eliminate or at least to reduce the effect of Frictional Heating are briefly discussed.
