Session: Rising Stars of Mechanical Engineering Celebration & Showcase

Paper Number: 148654

148654 - Squishy Granular Mechanics 

Soft granular assemblies are encountered in many natural systems and are important motifs in many engineered applications, from powder compaction to pharmaceuticals and biosystems.
Understanding the mechanical behaviors of such granular systems is essential for their translational applications.  

In soft granular assemblies, the macroscopic force-displacement (F-d) response is expected to be different from the classical Hertzian relation. For instance, compression experiments on spherical hydrogel granular assemblies in cubic lattice arrangements show F ~ d^n with n ~ 2.2, much larger than the Hertzian exponent of 1.5. The high deformability of individual particles has also been found to influence clogging with potential particle fracturing during their flow through silos. More recent works on two-dimensional soft granular systems with compressible neo-Hookean particles show that with increasing compressibility the packing fraction evolves more slowly and becomes increasingly nonlinear with applied strain while the macroscopic stress-strain behavior becomes more compliant.

Often, the role of loading rate and its interaction with the material time-scales in deformable granular packings are of interest. It is understood that the mechanics of these systems is fundamentally rooted in the inter-particle interactions  associated with viscoelastic contact mechanics. Yet, full-scale discrete element method (DEM) simulations become important as complex multi-particle interactions can occur in such assemblies.     

We study the rate-dependent mechanics of viscoelastic granular packings using finite element DEM. Using a two-dimensional, square lattice of particles as a motif mimicking nominally mono-disperse deformable granular packings, we perform a suite of finite element simulations under rate-dependent uniaxial compaction followed by unloading. The focus is on understanding the macroscopic force-displacement relations and the porosity evolution as a function of the viscoelastic relaxation parameters.

For the constituent parameters considered here, the force-displacement relations show a two-stage power-law behavior, which is associated with the relative contributions of viscous dissipation and elastic effects at a particular loading rate. If the loading time-scale is much longer than the shear and bulk relaxation time-scales, both (dissipation-governed and elasticity-governed) regimes exist. For much shorter loading time-scales only the elasticity governed regime prevails. In both scenarios, the relaxation modulus ratio has a negligible effect. By contrast, it plays a role when the loading and relaxation time-scales are comparable. For a given shear to bulk relaxation time-scale ratio, there is a critical shear relaxation modulus above which both regimes may exist.

For a given loading rate, the nonlinearity of the porosity evolution depends on the constituent relaxation parameters and is found to be captured well by a simple analytical model. The heterogeneity of stresses during the compaction and recovery phases provide insights into the emergent complex micromechanics in simple granular motifs. Upon unloading, particles may experience transient tensile pressures, which could have implications on their failure. 

Presenting Author: Shailendra Joshi University of Houston

Presenting Author Biography: Shailendra Joshi is Kalsi Associate Professor in the Department of Mechanical Engineering at University of Houston (UH). Prior to joining UH, he was an associate professor (2015-2018) and an assistant professor (2008-2014) at the National University of Singapore. During 2005-2008, he was a post-doctoral fellow in the Department of Mechanical Engineering at Johns Hopkins University. He earned his PhD in Civil Engineering from Indian Institute of Technology Bombay in 2002. After a short stint as a visiting scientist at the University of Stuttgart (2002), he worked as a research engineer at GE-India Technology Centre (2003-2005). His research interest is in understanding, modeling and controlling material responses through the mechanics of defects and failure processes at multiple length-scales and time-scales. He is an NSF CAREER recipient. He is an Associate Editor of Mechanics of Materials.

Authors:

Srinivas Selvaraju University of Houston
Nikhil Karanjgaokar Worcester Polytechnic Institute
Shailendra Joshi University of Houston