The Compression of Bonded Rubber Blocks

Gent, A. N.; Lindley, P. B.

doi:10.1243/pime_proc_1959_173_022_02

Cited by 262 publications

(143 citation statements)

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“…The transition to an apparently higher modulus is well known in compression testing of thin compliant materials and is related to the friction between the platens and the sample preventing the lateral (Poisson's) expansion. The form of the compressive stress-strain curve has been shown to depend on the sample aspect ratio 20 , surface roughness 21 , sample-platen friction and the nature of lubricating films 19,21 . The sharp transition from low to high modulus has been previously investigated and found to shift to higher strains when the platen-sample friction was reduced (for example, by using frictionless air bearings).…”

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confidence: 99%

Surprising shrinkage of expanding gels under an external load

et al. 2005

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H ydrogels are fascinating and useful in that they can show large volume changes in response to various stimuli, such as temperature or chemical environment 1 . Here we report the peculiar observation that chemically crosslinked hydrogels that normally expand owing to a change in electrolyte pH can be made to shrink in certain circumstances. Specifically, these hydrogels contract when tested at a constant compressive force and subjected to a pH change that causes expansion in the absence of the applied load. When tested under tension, the gels always expand. Although the effects of external stress on the swelling of gels is known 2-4 , the concomitant change in gel mechanical properties during pH switching was found to be a more dominant effect in our studies. However, existing mechanical models 5,6 used to predict dimensional changes in actuator materials could not explain both the tensile and compression results. In addition, we show that the friction between metal plates of the apparatus and the gel is a key factor in explaining the contractile actuation under compressive loads. The observations reported in this paper are important for the successful design and use of hydrogel actuators in devices such as valves for microfluidics.Volume changes occur in polyelectrolyte hydrogels when the thermodynamic balance between expansion forces (electrostatic repulsion and osmotic pressure of counterions) and contractile forces (stretching of elastically active network chains) is shifted by changes in the chemical environment. Hydrogel 'artificial muscles' 7 can generate huge dimensional changes in response to changes in temperature 8 , pH 9 , solvent 10 and electric fields 11 . Polymer conformation changes are also accompanied by large changes in equilibrium water content (EWC) of the gel, which can conveniently be measured gravimetrically. Many examples of changes in EWC with changes in pH are available in the literature, for example in the gels based on chitosan 12 .Various applications for actuating gels have been proposed, with the microscopic devices seeming most promising owing to their reasonable response times 13 . In practical applications, the influence of the external stresses on the operation of actuators cannot be neglected. Changes in mechanical properties such as

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confidence: 99%

Surprising shrinkage of expanding gels under an external load

et al. 2005

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“…A linear elastic theory is the most common method used to predict the compression and the bending stiffness of a thin elastomeric pad. The first analysis of the compression stiffness was done using an energy approach by Rocard [1937]; further developments were made by Gent and Lindley [1959] and Gent and Meinecke [1970]. A very detailed description of the theory is given by Kelly [1996] and need not be repeated here.…”

Section: Vertical Stiffness Of Fiber-reinforced Bearingsmentioning

confidence: 99%

Analysis of the run-in effect in fiber-reinforced isolators under vertical load

Kelly

2008

JOMMS

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Previous work on experimental and theoretical studies on fiber-reinforced bearings has shown the feasibility of using them as lightweight low-cost elastomeric isolators for application to housing, schools and other public buildings in highly seismic areas of the developing world. The theoretical analysis covered the mechanical characteristics of these bearings where the reinforcing elements, normally steel plates, are replaced by fiber reinforcement. The fiber in the fiber-reinforced isolator, in contrast to the steel in the conventional isolator (which is assumed to be rigid both in extension and flexure), is assumed to be flexible in extension, but completely without flexural rigidity. This leads to an extension of the theoretical analysis on which the design of steel-reinforced isolators is based that accommodates the stretching of the fiber-reinforcement. Several examples of isolators in the form of long strips were tested at the Earthquake Engineering Research Center Laboratory.The theoretical analysis suggests, and the test results confirmed, that it is possible to produce a fiberreinforced strip isolator that matches the behavior of a steel-reinforced isolator. The fiber-reinforced isolator is significantly lighter and can be made by a much less labor-intensive manufacturing process. The advantage of the strip isolator is that it can be easily used in buildings with masonry walls.The main difference between the behavior of a fiber-reinforced and a steel-reinforced bearing is the degree of run-in under vertical loading. In this context we mean by run-in that a certain amount of vertical load must be applied to the bearing before its vertical stiffness can be developed.The most likely source of the run-in is that the fibers are initially not straight and as they have no bending stiffness, the vertical stiffness cannot be developed until they have been straightened by the action of the applied vertical load. Straightening the fibers requires them to push against the surrounding rubber. This causes an increasing force in the fiber, and as it is straightening, there will be a transition to the stretching of the fiber and to the consequent stiffness of the composite system. These bearings can be used in a wide range of applications in addition to seismic protection of buildings including bridge bearings and vibration isolation bearings, so there is a need to be able to predict how much vertical load or vertical displacement is needed before the full vertical stiffness can be achieved. In this paper a theoretical analysis of the effect has been developed in an attempt to formulate a prediction for the transition from the initially bent to the finally straight fiber.The method takes the already formulated analysis for the straight fiber and modifies it by treating the fiber as a curved string on an elastic foundation, adds to this an estimate of the subgrade reaction of this foundation, and, using the basic equations of the fiber-rubber composite, calculates the effective compression modulus as a function of the ...

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“…Beside the expansion, the apparent Young modulus of the constrained polymer E app and the modulus of the siliconpolymer stack E stack are also important parameters of the actuator. 6 They are given by…”

Section: ͑6͒mentioning

confidence: 99%

Polymer constraint effect for electrothermal bimorph microactuators

Duc

Lau

Sarro

2007

Applied Physics Letters

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The authors report on the analysis of the polymer constraint effect and its use for a micromachined electrothermal bimorph actuator. The actuated displacement is enhanced due to the polymer constraint effect. Both the thermal expansion and apparent Young's modulus of the constrained polymer blocks are significantly improved, compared with the no constraint case. The calculation that agrees well with experimental results provides the means to optimize the design of the constrained polymer stack electrothermal microactuator. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2779929͔ Thermal expansion of polymer is currently widely used in microactuators to produce large motion at low temperature. In most of the polymeric electrothermal actuators reported in literature, a thin metal layer deposited on the top surface of the polymer structures is employed as heater. 1,2 Hence, the heat transfer interface between the heater and the polymer is rather limited. Since the polymer layers have low heat conduction rate, the actuator dimensions need to be small enough to get a good vertical temperature profile in the structure. Consequently, the resulting motion is quite limited. Moreover, the unintended vertical movement couples and interferes with the desired lateral movement of the structures.In this letter, we report on a silicon-polymer electrothermal bimorph actuator with a large motion range. This actuator has a silicon comb finger structure with a metal heater on top. The gaps between comb fingers are filled with polymer ͓see Fig. 1͑a͔͒. When the heater is activated, the generated heat is efficiently transferred to the surrounding polymer through the deep silicon comb finger structures that have a large heat transfer interface area with the polymer layers. The polymer layers expand along the lateral direction causing bending displacement of the bimorph cantilever actuator. Moreover, the thermal expansion of this actuator is enhanced due to the constraint effect of polymer layers between rigid silicon plates. 3 A calculation of compressed displacement of a constrained rubber between two rigid surfaces based on the hydrostatic pressure is reported in Ref. 4. The hydrostatic pressure theory is expanded here by taking into account the thermal expansion of constrained polymer as a function of the ratio between the dimensions of the rigid plate and the thickness of the polymer block. Finally, the thermal displacement of the actuator is then calculated using bimorph bending theory.It is assumed that the plates have infinite length, the thickness of the polymer block h is much smaller than the width w of the plate ͑h Ӷ w͒, and the polymer is incompressible ͑Poisson's ratio S = 0.5͒. When the temperature of the structure changes by ⌬T degree, the volume thermal expansion of a polymer block is given by 5where V is the initial volume of the polymer block and ␣ T is the thermal expansion coefficient ͑CTE͒ of the polymer. In the case of no constraint, the volume of the polymer block expands in three dimensions, as indicated b...

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The Compression of Bonded Rubber Blocks

Cited by 262 publications

References 14 publications

Surprising shrinkage of expanding gels under an external load

Surprising shrinkage of expanding gels under an external load

Analysis of the run-in effect in fiber-reinforced isolators under vertical load

Polymer constraint effect for electrothermal bimorph microactuators

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