Large Deformation and Adhesive Contact Studies of Axisymmetric Membranes

Abstract

A model membrane contact system consisting of an acrylic copolymer membrane and polydimethyl-siloxane substrate was utilized to evaluate a recently developed nonlinear large-deformation adhesive contact analysis. Direct measurements of the local membrane apex strain during non-contact inflation indicated that the neo-Hookean model provides an accurate measure of membrane strain and supports its use as the strain energy function for the analysis. A time dependent modulus emerges from the analysis, with principal tensions obtained from a comparison of predicted and experimental membrane profiles. A displacement controlled geometry was more easily modeled than the pressure controlled geometry, the applicability of the analysis was limited by wrinkling instabilities. The substantial viscoelastic behavior of these membranes made it difficult to describe the entire membrane with a single modulus, given the nonuniform deformation history of the membranes. Given the difficulty in determining membrane tension from the measured pressure and profile fits using the model, the peel energy was used as a simpler measure of adhesion. Using an analytical balance in the displacement controlled geometry, the membrane tension at the contact line was directly measured. Coupled with contact angle imaging, the peel energy was determined. For the model membranes studied, this peel energy described the membrane/substrate adhesive interactions quite well, giving well-defined peel energies that were independent of the detailed strain state of the membrane.

Large deformation contact mechanics of a pressurized long rectangular membrane. II. Adhesive contact

“…As a result, the contact length remains unchanged during this period. Such contact pinning or crack trapping has been observed in experiments [5,11,16]. It is indicated by the horizontal dashed line in figure 3.…”

“…In this work, we carried out detailed analysis for two limiting cases: frictionless and no-slip adhesive contact. Wrinkling or buckling of the membrane near the contact line is often observed in axis-symmetric geometry during stage 3 [11]. Wrinkling is caused by the membrane tension in the hoop direction becoming compressive.…”

Large deformation contact mechanics of long rectangular membranes. I. Adhesionless contact

“…For a clamped film under uniform pressure, this assumption is justified when the maximum deflection d is greater than the film thickness h 0 (see Timoshenko & WoinowskyKrieger [21]), a condition that is easily satisfied in practically all contact experiments. For example, in the experiments of Laprade et al [22], the film thickness is approximately 1 µm, whereas the maximum deflection is approximately 1-3 mm.…”

Nonlinear viscoelastic contact mechanics of long rectangular membranes

“…Many of these works address situations where membrane deflections are small, so that small strain theory can be applied to simplify the analysis. However, in many experiments, membrane strains can be sufficiently large [13,14] so that large deformation theory based membrane contact models [15][16][17][18][19] need to be used to provide an accurate description of the phenomenon. Many polymer and biological membranes exhibit viscoelastic behaviour that cannot be adequately described by elasticity models.…”

“…Many polymer and biological membranes exhibit viscoelastic behaviour that cannot be adequately described by elasticity models. Viscoelasticity can significantly affect the deflection and adhesion strength of membranes, as shown by recent experimental works [13,14,20]. The coupling of viscoelastic dissipation, interfacial adhesion and large deformation makes the interpretation of test results extremely difficult.…”