GENERALIZATION OF THE STRESS TENSOR TO NONUNIFORM FLUIDS AND SOLIDS AND ITS RELATION TO SAINT-VENANT STRAIN COMPATIBILITY CONDITIONS

Combining some results from the classical theory of elasticity with the modern functional derivative approach to nonuniform systems, we obtain a well-defined stress tensor for nonuniform equilibrium fluids and solids. This stress tensor is symmetric and satisfies the force-balance equation, so it provides an unambiguous route to quantities such as the surface free energy. The ambiguities associated with earlier stress-tensor definitions are traced back to their failure to take account of Saint-Venants strain compatibility conditions. © 1990 The American Physical Society.