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Higher order continuum model based upon granular micromechanics

For continuum modeling of materials with granular microstructure, the relevant representative unit can be described as collection of grains using the concept of coarse graining by combining atoms and molecules into larger grains. The granular micromechanics approach provides a successful paradigm for developing continuum models of these material systems. In this approach, the inter-granular interactions are conceived in a statistical sense to describe the essential grain-scale and sub-granular scale mechanisms. The resultant models offer the versatility of investigating the influence of both the macro-scale parameters and the grain-scale parameters on the overall stress-strain response by incorporating the effect of meso-scale grain interactions through the inter-granular force-displacement relationship, orientation vectors and average tensorial fabric measures. The advantages are clear since (1) the computational needs are far smaller and particle assembly generation are not required, (2) the models naturally exhibit macro-scale effects, and (3) can readily represent micro-scale effects of particle interactions. The granular micromechanics approach traces its genesis to the continuum models of grain packings developed in the second-half of the last century; however, this approach has antecedents in the early development of continuum mechanics. In recent years, these models have undergone further refinement and have been successfully applied to model a number of phenomena exhibited by granular materials [1]. In the proposed presentation, we will further develop granular micromechanics framework and focus on some recent results that consider both mean field grain movements as well as fluctuations from mean fields. As a result we find a non-classical continuum model that includes additional strain measures as well as their gradients. The derived model is applied to study the wave dispersion relationships and show interesting band gap phenomena.
[1] Misra, A. and Singh, V, (2014) “Thermomechanics based nonlinear rate-dependent coupled damage-plasticity granular micromechanics model,” Continuum Mechanics and Thermodynamics, (doi: 10.1007/s00161-014-0360-y)

Author(s):

Anil Misra    
University of Kansas
United States

Payam Poorsolhjouy    
University of Kansas
United States