Wave propagation and instabilities in monolithic and periodically structured elastomeric materials undergoing large deformations

Wave propagation in elastomeric materials undergoing large deformations is relevant in numerous application areas, including nondestructive testing of materials and ultrasound techniques, where finite deformations and corresponding stress states can influence wave propagation and hence interpretation of data. In the case of periodically structured hyperelastic solids, the effect of deformation on the propagation of acoustic waves can be even more dramatic. In fact, transformations in the periodic patterns have been observed upon application of load due to microstructural elastic instabilities, providing opportunities for transformative phononic crystals which can switch band-gap structure in a sudden, but controlled manner. Here both analytical and numerical techniques are presented for assessing the influence of finite deformations on the propagation of elastic waves in both monolithic as well as periodically structured elastomeric materials. Both elastic instabilities and propagation of acoustic waves are strongly influenced by geometric pattern, material properties and loading conditions, giving different opportunities for tuning and manipulating the location and presence of instabilities and phononic band gaps.