2ND-GRADIENT CONSTITUTIVE THEORY FOR GRANULAR MATERIAL WITH RANDOM PACKING STRUCTURE

A second-gradient constitutive law for granular media is derived, in which stress is a function of the second order of strain gradient. The constitutive coefficients for granular materials with an isotropic packing structure are derived in explicit terms of inter-particle stiffness and particle size. In the present constitutive theory, the total number of elastic constants for the isotropic granular material is four: two of them are the usual Lame constants; the other two are associated with the second gradient of strain. The derived constitutive relationships illustrate the important role of micro-scale properties in the macro-scale behavior. The influence of inter-particle stiffness and particle size on the response of material due to the second gradient of strain is discussed. This paper also discusses the connection between the second-gradient theory and non-local theory. The second-gradient theory can be regarded as the first-order approximation of non-local theory.