Constitutive models for confined elastomeric layers: Effects of nonlinearity and compressibility

Elastomers tend to undergo large deformations accompanied by small volumetric changes. For elastomeric layers sandwiched between rigid plates, large deformations can be significantly limited by the constraints imposed by the plates. Further, those constraints can be enhanced by material’s inability to undergo large volumetric changes. From this perspective, it is appropriate to examine the validity of constitutive models, in which an elastomer is treated as incompressible, for analysis of the confined layers. Here, this issue is addressed by considering the mechanical response of sandwiched elastomeric layers using three constitutive models. The first one, referred to as compressible neo-Hookean, is regarded as exact. The other two models are regarded as approximations. Of those two, the first one neglects nonlinearity and the second one neglects compressibility. Accordingly, the modeling errors associated with the former are treated as measures of importance of nonlinearity, and the modeling errors associated with the latter are treated as measures of importance of compressibility. The modeling errors are evaluated using the force–displacement curve and the mean stress at the layer center as the quantities of interest. Numerical results are presented for rubber and polydimethylsiloxane (PDMS), characterized by Poisson’s ratios ν=0.4999 and ν=0.49, respectively. It is shown that, even when the forces applied to the plates are large, considering nonlinearity is important for thick but not for thin layers. In contrast, considering compressibility is important for thin layers. The need for considering compressibility is further assessed by introducing a competition parameter, which reinforces the notion that compressibility is important for modeling PDMS layers and thin rubber layers.