Micromechanical Insights Into the Effective Stresses

The changes of free energy in deforming systems of spherical grains in partial saturation are analyzed with the help of numerical simulations. In such system and in the elastic regime we obtain the effective stress as the work conjugate of the macroscopic deformation. It is found that the Love-Weber stress - which is frequently supposed to play the role of effective stress in multiphase systems - is equal to the effective stress only in regular packings. In random packings on the other hand, it does not compare consistently with the numerical results. Further, the results show that some changes of the elastic free energy associated to the micro-scale deformation occur independently of the macroscopic deformation, in contrast with a classical assumption of energy separation.