Granular materials

Our group’s work on granular materials involves developing predictive continuum models for dense granular flow. Granular materials are mixtures of discrete, macroscopic particles and are ubiquitous in nature as well as in everyday life – in forms such as sand, gravel, pharmaceutical pills, food grains, and industrial powders. However, certain mechanical behaviors of these materials remain challenging to predictively model, including dense flow and size-segregation phenomena. Predictive models are crucial to robust engineering design involving granular media, and the benefits of improved modeling capabilities are numerous.

One aim of our group’s research has been to elucidate the rheology of steady flows of a dense collection of dry, hard particles that are roughly all the same size (monodisperse). The challenge is that local constitutive equations that relate the local stress state to the local state of strain rate at a point cannot capture the phenomenology of dense granular flows, since the deformation of a granular media displays a strong dependence on the size of the constituent grains, and to this end, we pursue nonlocal continuum modeling.

Another aim of our group’s work on dense granular materials relates to modeling size-segregation in dense, bidisperse granular systems, made up of particles of two sizes. Dense granular systems, consisting of particles of disparate sizes, segregate based on size during flow, resulting in complex, coupled segregation and flow patterns. We utilize discrete-element method (DEM) simulations of flow of dense, bidisperse granular systems to inform continuum constitutive equations for the relative flux of large and small particles.

Constitutive modeling of elastomeric foams (in collaboration with the Franck Lab)

Viscoelastic elastomeric foams are widely used in equipment for impact protection and exhibit mechanical behavior marked by high compressibility and strong coupling between the volumetric and distortional responses. Developing predictive constitutive models for these materials remains challenging despite their ubiquity. Our group’s work seeks to (1) develop and validate constitutive models for elastomeric foam materials, including viscoelastic, poroelastic, and temperature-dependent behavior, and (2) utilize these models to design improved protective equipment, such as helmets.

Modeling of inertial microcavitation in soft materials (in collaboration with the Franck Lab)

Another research interest in our group relates to inertial microcavitation in soft materials, focusing on the dynamics of small bubbles formed in soft solids that are as compliant as a few kilopascals using either laser- or ultrasound-based methods. The motivation for this work is twofold: (1) inertial microcavitation is a novel route for mechanical characterization of soft materials at high strain-rates (greater than 1000 1/s) – a task which is beyond existing experimental techniques – and (2) inertial microcavitation in brain tissue is a potential mechanism of traumatic brain injury.

Modeling of dielectric elastomer composites

Another research thrust pertains to the mechanics of dielectric elastomers (DEs). DEs are electrically-insulating elastomeric materials, which are capable of large deformation and electrical polarization, and are used as smart transducers for converting between mechanical and electrical energy. We have developed a finite-element-based numerical simulation capability for DE composites. One potential application of this work is that of tunable phononic crystals, which are periodic materials that display phononic band gaps – frequency ranges in which elastic waves are prohibited – that may be tuned through the application of an electric field. Phononic crystals made from soft materials are capable of undergoing significant, reversible deformations so that the acoustic response of the material may be actively tuned in response to a changing environment. As a novel route to tunability, phononic crystals may be made from DEs so that their acoustic response may be tuned through electrical stimuli. Our simulation capability may be used to design electrically-tunable, soft phononic crystals, addressing both electroelastic wave propagation through a pre-deformed state and the onset of electromechanical instabilities in DE composites.