Elastic-Plastic Wave Propagation in Phononic Crystals

Abstract

We investigate the propagation of plastic waves in a periodic, one-dimensional acoustic material (i.e., phononic crystal). The fundamentals of elastic and plastic wave propagation in constant cross-section, one-dimensional rods are first developed using the method of characteristics. We then utilize a semi-analytical (SA) procedure, based on the method of characteristics, to predict the propagation of plastic waves in periodic, variable cross-section rods. The SA procedure is validated using time-domain finite element simulations for both elastic and elastic-plastic waves. Subsequently, we pose a phononic crystal with a dogbone-like unit cell geometry, analyze its elastic band structure, and then predict its performance at elastic and plastic amplitudes using the developed semi-analytical procedure. We pay particular attention to bandgap effects, a well-known characteristic of phononic crystals, and study the effect elastic bandgaps have on plastic wave propagation and associated residual strains. The study lays the groundwork for investigation of pulse shaping in plastic phononic crystals, a subject of interest for applications related to split Hopkinson bar testing.