Abstract:

We discuss the methods usually employed for continuous mechanical modeling of geotechnical materials, of which roughly speaking there are two. The first -- called hydrodynamic because it was originally used for deriving the Navier-Stokes equations -- is mainly adopted by physicists, who applied it to systems such as solids, superfluid, liquid crystals, polymer solutions and granular matter. To set up and close the set of differential equations, it starts from generally valid principles including thermodynamics (especially its second law, or the positivity of entropy production), conservation laws (for mass, energy and momentum), and the concept of spontaneously broken-symmetry (for variables such as elastic strain or quantum phase). The second approach to continuous mechanics is constitutive modeling, usually employed by engineers for the study of systems such as plastic solids, non-Newtonian fluids, geotechnical materials. It aims to directly construct functional relations among stress, strain, their rates, velocity, density and temperature, and use these to close momentum conservation (i.e. the force balance). Since both hydrodynamic and constitutive modeling for geotechnical materials are reported in the literature recently, it is worthwhile -- as we do, concisely, in the present paper – to clarify their respective ideology and range of validity, and discuss their similarities and differences. We point out especially what the complete set of state variables in either theory is, and how the treatment of the yield surface and plastic dissipation differ.

Key words: constitutive relations, hydrodynamics, thermodynamics, granular physics.