A strain–displacement–fabric relationship for granular materials

In this micromechanical study of the behaviour of granular materials, relationships are investigated between deformation at the continuum macro-scale and at the micro-scale of interparticle contacts. Special attention is paid to the role of the microstructure, or fabric, as it is well known to have a strong influence on the behaviour of granular materials. Two-dimensional Discrete Element Method simulations of isobaric tests have been used to formulate truncated Fourier series representations for suitably-averaged relative displacement increment vectors at interparticle contacts and of parameters that describe the fabric. Based on a micromechanical expression for the average strain tensor that is valid in the two-dimensional case considered here and on these Fourier series representations, a Strain–Displacement–Fabric relationship has been derived that links the macro-scale dilatancy rate to the micro-scale relative displacements and fabric. Results of the Discrete Element Method simulations, using samples with different densities, have been employed to verify the accuracy of the proposed relationship for the dilatancy rate.