A novel inhomogeneous deformation field model for cylindrical specimens for unconfined compression testing

Compression methods when testing polymer materials from quasi-static to dynamic loading rates require the use of cylindrical specimens due symmetry. For soft materials, which have more complex non-linear response such as hyperelastic or viscoelastic compared to traditional engineering materials, additional challenges arise when obtaining their material parameters. Previous studies have been found scarce in investigating and developing mathematical models to predict this complex deformation field whenever friction is considered during unconfined compression testing. We present an analytical approach to model this "barreling effect" that is derived from inhomogeneous deformation field that accumulates mass in the center region of the specimen. This reduces the contact surface area that directly affects the computation of material constants e.g. stress. Our novel method successfully describes this effect quantitatively, providing an analytical solution that models the deformation field for a wide range of finite strains and variety materials. This approach has been experimentally proved to dramatically increase the accuracy by up to 17% compared to existing methodologies that are based only on the homogeneous deformation approach, which to date, is the most common model to characterize the general material's mechanical response.