Particle mechanics and micromorphic media. Part II: Kinematic measures and energetic evaluation

Abstract

The second part of this bipartite series on the micromorphic contribution of particle-based microstructures to continuum-mechanical theories is mainly concerned with the relation between particle and continuum kinematics. Extending the governing relations and the stress homogenisation of Part I by the introduction of a tensor-valued micromorphic angular momentum balance and a micromorphic balance of mechanical work yields new insights in the impact of dyadic stress moments in micromorphicity. Furthermore, it contributes to identify work-conjugated pairs of standard and extended micromorphic continuum contributions based on an investigation of ensembles of deformable particles taken as a Representative Elementary Volume (REV) both at the mesoscopic and the macroscopic scale. By use of geometrically linear kinematics, it is furthermore shown how micromorphic deformations subdivide in micropolar and microstrain contributions. Deriving the specific volume-averaging formalism for deformation measures of REV with a finite number of particles additionally allows for a direct evaluation of the individual contributions based on Discrete-Element (DE) simulations, thus yielding an excellent possibility to include particle mechanics in continuum-mechanical approaches with complex microstructures.