In the spirit of Germain the most general objective stored elastic energy for a second gradient material is deduced using a literature result of Fortuné & Vallée. Linear isotropic constitutive relations for stress and hyperstress in terms of strain and strain-gradient are then obtained proving that these materials are characterized by seven elastic moduli and generalizing previous studies by Toupin, Mindlin and Sokolowski. Using a suitable decomposition of the strain-gradient, it is found a necessary and sufficient condition, to be verified by the elastic moduli, assuring positive definiteness of the stored elastic energy. The problem of warping in linear torsion of a prismatic second gradient cylinder is formulated, thus obtaining a possible measurement procedure for one of the second gradient elastic moduli.

Natural soils are usually heterogeneous and characterized with complex microstructures. Sand–clay mixtures are often used as simplified soils to investigate the mechanical properties of soils with various compositions (from clayey to sandy soils) in the laboratory. Performing laboratory tests on a sand–clay mixture with definite clay fraction can provide information to understand the simplified soils’ mechanical behavior and better predict natural soils’ behavior at the engineering scale. This paper reviews previous investigations on sand–clay mixture and soil–structure interface direct shear test. It finds that even though there are many investigations on sand–clay mixtures and soil–structure interfaces that consider pure sand or pure clay, limited data on the mechanical behavior of the interface between sand–clay mixture and structure materials are available. Knowledge is missing on how the clay content influences the mechanical behavior of interface and how the soil particles’ arrangement changes as the clay content increases. Further study should be performed to investigate the interface in terms of a reconstituted sand–clay mixture and structure by interface direct shear test, to highlight the influence of clay fraction on the interface response, under various loading conditions.