Axial Loading of Bonded Rubber Blocks

a b s t r a c tCompression of elastic layers bonded between parallel plates often find applications in the mechanical characterization of soft materials or the transfer-printing of nanomembranes with polymeric stamps. In addition, annular rubbery gaskets and sealers are often under uniaxial compression during service. Analysis of elastic layers under compression has been focused on nearly incompressible materials such as rubbers, and empirical assumptions of displacements were adopted for simplicity. For compressible materials, solutions obtained by the method of averaged equilibrium are sufficient for effective compression modulus but inaccurate for the displacement or stress fields whereas solutions obtained by the method of series expansion are considerably complicated. In this paper, we report full field, closed-form solutions for bonded elastic layers (disks, annuli, annuli with rigid shafts, infinitely long strips) in compression using separation of variables without any pre-assumed deformation profile. These solutions can satisfy the exact forms of the equilibrium equations and all essential boundary conditions as well as the weak form of the natural boundary conditions. Therefore the predicted stress, displacement, and effective modulus have found excellent agreement with finite element modeling (FEM) results over a wide range of Poisson's ratio and aspect ratio. The analytical and FEM results of the stress, displacement, and effective modulus are highly sensitive to Poisson's ratio, especially near 0.5. Therefore we also propose a viable means to simultaneously measure the intrinsic Young's modulus and Poisson's ratio of elastically compressible layers without camera settings. When Poisson's ratio approaches 0.5, our solutions can degenerate to classical solutions for incompressible elastic layers.

Section: Numerical Resultsmentioning

confidence: 92%

Analytical solutions for bonded elastically compressible layers

Qiao

Lu²

2015

“…They presented approximate expressions to E a for blocks of circular and long rectangular cross-section, which were derived not only with the reasonable assumption that plane cross-sections of the block normal to the axis of the block remain plane but also with the free lateral surfaces assumed to have parabolic deformed shapes. On the other hand, the analyses of Horton et al (2002Horton et al ( , 2003 were completed without the necessity of making this second assumption, and in fact they confirmed the invalidity of assuming a parabolic lateral profile especially for blocks whose shape factor is small. Subsequently, Gent and Meinecke (1970) suggested that the apparent Young's modulus, E GM a , for a block of elliptical cross-section, with semi-major and minor axes a and b, and of axial height h, could be determined from…”

Section: Introductionmentioning

confidence: 90%

“…The analytical techniques used are generalizations of those developed by Horton et al (2002Horton et al ( , 2003 in studying blocks of circular and annular cross-sections. Gent and Lindley (1959) and Gent (1994) developed widely used approximate relations for the apparent Young's modulus, E a , for bonded blocks of incompressible rubber subjected to compression.…”

Section: Introductionmentioning

confidence: 99%

Axial loading of elliptical-section bonded rubber blocks

Horton¹,

Tupholme

2007

NoClosed-form expressions for the small axial deflection and stress distribution of axially loaded rubber blocks of elliptical cross-section, whose ends are bonded to rigid plates, are derived using a superposition approach. The governing equations and conditions are satisfied exactly, based upon the classical theory of elasticity. Easily calculable expressions are derived for the corresponding apparent Young¿s modulus and the modified apparent Young¿s modulus in forms analogous to those previously given for blocks of circular cross-section

“…As reviewed in Pinarbasi et al (2006) in detail, in the last century, many researchers (e.g., Lindley, 1979;Gent, 1994;Horton et al, 2002) have studied the behavior of rigidly-bonded elastic layers. Most of these studies have been conducted to determine their compression stiffness.…”

Section: Introductionmentioning

confidence: 99%

Elastic layers bonded to flexible reinforcements

Pinarbaşi

Mengi

2008

Elastic layers bonded to reinforcing sheets are widely used in many engineering applications. While in most of the earlier applications, these layers are reinforced using steel plates, recent studies propose to replace ''rigid'' steel reinforcement with ''flexible'' fiber reinforcement to reduce both the cost and weight of the units/systems. In this study, a new formulation is presented for the analysis of elastic layers bonded to flexible reinforcements under (i) uniform compression, (ii) pure bending and (iii) pure warping. This new formulation has some distinct advantages over the others in literature. Since the displacement boundary conditions are included in the formulation, there is no need to start the formulation with some assumptions (other than those imposed by the order of the theory) on stress and/or displacement distributions in the layer or with some limitations on geometrical and material properties. Thus, the solutions derived from this formulation are valid not only for ''thin'' layers of strictly or nearly incompressible materials but also for ''thick'' layers and/or compressible materials. After presenting the formulation in its most general form, with regard to the order of the theory and shape of the layer, its applications are demonstrated by solving the governing equations for bonded layers of infinite-strip shape using zeroth and/or first order theory. For each deformation mode, closed-form expressions are obtained for displacement/stress distributions and effective layer modulus. The effects of three key parameters: (i) shape factor of the layer, (ii) Poisson's ratio of the layer material and (iii) extensibility of the reinforcing sheets, on the layer behavior are also studied.