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The measured force during a puncture test is found to increase when the needle tip is near to the vial walls. An experimental method for quantifying this increase in stiffness is developed.

 

The most widely-used representation of the compressible, isotropic, neo-Hookean hyperelastic model is considered in this paper. The version under investigation is that which is implemented in the commercial finite element software ABAQUS, ANSYS and COMSOL. Transverse stretch solutions are obtained for the following homogeneous deformations: uniaxial loading, equibiaxial loading in plane stress, and uniaxial loading in plane strain. The ground-state Poisson’s ratio is used to parameterize the constitutive model, and stress solutions are computed numerically for the physically permitted range of its values. Despite its broad application to a number of engineering problems, the physical limitations of the model, particularly in the small to moderate stretch regimes, are not explored. In this work, we describe and analyze results and make some critical observations, underlining the model’s advantages and limitations. For example, a snap-back feature of the transverse stretch is identified in uniaxial compression, a physically undesirable behavior unless validated by experimental data. The domain of this non-unique solution is determined in terms of the ground-state Poisson’s ratio and the state of stretch and stress. The analyses we perform are essential to enable the understanding of the characteristics of the standard, compressible, isotropic, neo-Hookean model used in ABAQUS, ANSYS and COMSOL. In addition, our results provide a framework for the parameter-fitting procedure needed to characterize this standard, compressible, isotropic neo-Hookean model in terms of experimental data.

 

Abstract Experimental evidence suggests that suction may play a role in the attachment strength of mushroom-tipped adhesive structures, but the system parameters which control this effect are not well established. A fracture mechanics-based model is introduced to determine the critical stress for defect propagation at the interface in the presence of trapped air. These results are compared with an experimental investigation of millimeter-scale elastomeric structures. These structures are found to exhibit a greater increase in strength due to suction than is typical in the literature, as they have a large tip diameter relative to the stalk. The model additionally provides insight into differences in expected behavior across the design space of mushroom-shaped structures. For example, the model reveals that the suction contribution is length-scale dependent. It is enhanced for larger structures due to increased volume change, and thus the attainment of lower pressures, inside of the defect. This scaling effect is shown to be less pronounced if the tip is made wider relative to the stalk. An asymptotic result is also provided in the limit that the defect is far outside of the stalk, showing that the critical stress is lower by a factor of 1/2 than the result often used in the literature to estimate the effect of suction. This discrepancy arises as the latter considers only the balance of remote stress and pressure inside the defect and neglects the influence of compressive tractions outside of the defect.