Local stress analysis in granular materials at a mesoscale

Abstract

SUMMARYThe purpose of this paper is to contribute to the change of scale techniques developed for granular materials. The proposed approach consists in considering an intermediate scale between the macroscales and microscales, called the mesoscale, using the classical homogenization scheme. In this approach, the mesoscale for 2D granular materials was defined at the level of local volumes, called mesodomains, which are local closed structures composed of particles in contact. In this paper, we focused on defining a local stress field at this scale. Two different methods are proposed, both based on the equivalent continuum mean stress but using different approximations of the mean stress tensor for each mesodomain. The two proposed methods were then compared to each other. Analyses performed on the stress field at the mesoscale show that this local field is heterogeneous and, in particular, that its heterogeneity is significantly structured at this scale. The distribution of the local mean stress (first invariant of the local stress tensor) is uniform in any mesodomain, whereas the distribution of the stress deviator (second invariant of the deviatoric part of the local stress tensor) is significantly dependent on the elongation direction and on the elongation degree of the mesodomains. The local stress ratio (ratio of the stress deviator to the mean stress) is higher within the mesodomains that are elongated in the global compression direction than that within the ones elongated in the global extension direction.

Experimental testing of pre-stressed granular assemblies as a surrogate material for the dynamic analysis of launcher cryogenic tanks

“…Filling of granular grains is an important issue because of its heterogeneous and discrete nature. Many studies in literature show that the mechanical behavior of granular materials depends on internal organization of contacts in granular system [11,12,23,26,27]. More importantly, the filling process should be done carefully and slowly in order to avoid the localized distribution of grains in the system.…”

On the relevance of the meso-scale in an upscaling approach for granular materials

“…We propose to define an intermediate scale at which both the local strain and stress fields can be consistently defined and the local texture can be consistently described [3,5,6].…”

“…The definition of the strain tensor increment of a mesodomain m, δε m , is based on the definition of the incremental gradient tensor for a triangular element e proposed by [9,10] and used in [3][4][5][6]11]:…”

Randomly-fluctuating heterogeneous continuum model of a ballasted railway track

“…An alternative approach consists in modeling the ballast as a continuous medium, using the stress tensor as the static variable and the displacement field as the kinematical variable. The stress and strain tensors can be derived, respectively, from the contact forces network [111,91,14,67,92,69] and the displacements of the grains [106,51,18,13,89,29] in discrete simulations, but the relation between the parameters of the continuum and granular models is not obvious. Such continuum models have been developed along various directions [77,7]:…”