 |
Center for Nonlinear Studies |
Granular solids are ubiquitous and impact diverse areas of engineering and science ranging from material development to biomaterials to geophysics. These materials span the spectrum from highly consolidated dense solids formed of particulate precursors to soft membranes formed of cell aggregations to confined packings of non-cohesive particles. In all their forms, they represent material systems that have posed intractable challenges to the description of their behavior. Their macro-scale behavior (or collective behavior of grains) are linked directly to their granular-structure and grain-pair interfacial mechanisms. Thus, mathematical description of their mechanical response must begin from the conception of grain-interactions. From this point of departure, either discrete or continuum descriptions can be elaborated. The question remains though how these materials with complex micro-structures and grain-interactions be analyzed efficiently? Even more importantly, how their granular structure and grain-scale mechanics be predefined to produce predictable material behavior?With the aid of examples drawn from discrete simulations and continuum models, and novel grain-scale experimental measurements, this presentation will show why/where traditional approaches are not successful and challenge us to seek innovations. The presentation will emphasize simplicity over complexity and primarily follow energy and variational methods to deduce tractable and plausible models and explanations. More than 2 decade old measured kinematics (displacements and rotations) in disk assemblies [1] and new experiments with controlled grain interactions [2], will be utilized as basis to motivate the granular micromechanics approach (GMA). This approach provides a paradigm that bridges the discrete models to appropriate continuum model, and obviates the need for extensive mechano-morphological parameters required for discrete models. Through GMA, micromorphic continuum model connected to the grain-scale can be deduced [3-5], which show on one hand the type of information lost, and on the other, the advantages gained when adopting this type of continuum model. The obtained model provides interesting predictions for granular media. These include wave dispersions and frequency band gaps [6-7], macro-scale anisotropy traced to grain-scale tension-compression asymmetry [8-9], chirality and negative Poisson’s ratio [2]. This presentation will also discuss examples applications of GMA continuum model to those of interest to rate-dependent and rate-independent damage, plasticity and failure [9-11], such as in geomechanics
Host: Duan Zhong Zhang