Abstract
The constitutive description of the mechanical behavior of granular systems is of great interest to the fields of geotechnics and various other related applications. By taking into account the discrete nature of the microstructure of a granular assembly, numerous different discrete models have been developed, Most of them are based on a finite number of discrete, semi-rigid spherical or polygon-shaped particles interacting by means of contact forces. The specification of an appropriate contact law is probably the most significant part of the discrete model. For example, the contact behavior can be formulated in a linear or nonlinear elastic fashion according to the classical Hertz model or include frictional effects along the line of Coulomb's friction law. In order to compare the results of the discrete element simulation with macroscopic measurements, different averaging techniques can be applied to derive homogenized quantities characterizing the overall behavior of the assembly. Thus, the definition of the macroscopic stress tensor has been studied intensively in the beginning of the 80s and can now be considered as well-established
While discrete models take into account the individual behavior of each single particle, continuum-based approaches can only describe the material behavior in an average sense. Although, in most cases, the choice of the specific constitutive formulation is motivated by microstructural considerations, the material response is characterized exclusively in terms of stresses or strains and a set of internal variables, which represent microstructural effects in a phenomenological fashion. The microplane plasticity model is a classical representative of this class of continuum-based constitutive models. It is based on the early ideas of Mohr, who suggested to characterize the response of a material point by describing its behavior in various representative directions in space. Similar to the particle models, the choice of the constitutive assumption relating the corresponding stress and strain vector of each direction can be considered as the most important feature of the model. The overall response of the material point is obtained by integrating the resulting stress vectors over the entire solid angle.
Although derived from two completely different fields, both models show significant similarities from a theoretical point of view. This contribution aims at highlighting the equivalences of the two different material formulations. Therefore, the basic ideas of the microplane model are summarized as well as a basic introduction to discrete particle modelling. Particular interest is dedicated to the fact, that the initially continuous microplane model has to be discretized for computational reasons while the initially discrete particle model must be 'continuumized' in order to relate its material parameters to macroscopic quantities. Finally, the two different approaches are compared and advantages and disadvantages of both formulations are discussed.
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