From particle mechanics to micromorphic continua

Abstract

Classical material tests observe the macroscopic behaviour of structures and materials. However, the material response to an external loading always results from the composition and the interaction of the material at different time and length scales. Kinematically extended microcontinuum theories offer one way of incorporating some microstructural effects into a continuum-based modelling strategy. Thereby, the macroscopic motion at a material point is extended by a micromotion that should consider all relevant microscopic deformation mechanisms. The focus of this monograph is on the relation between the mechanics of granular media and one type of microcontinuum theories, the so-called micromorphic approach. Therefore, a homogenisation method that links particle-based information from the microscale with macroscopic quantities of micromorphic character is presented. To verify the established homogenisation methodology, particle-based simulations of material failure in granular materials are used, supplying the necessary microstructural information, which are then processed towards the scale of Representative Elementary Volumes (REV). The idealised model allows for the transition of the continuously formulated averaging formalisms towards discrete forms in which only a finite number of particles are evaluated for the computation of the stress and strain quantities on the level of an REV.