ABSTRACT
This chapter establishes conditions for the existence of hydrostatic pressures in a class of hyperelastic incompressible materials subjected to finite deformations. It considers the deformation of an incompressible hyperelastic body relative to a fixed reference configuration. Equilibrium problems for such bodies are often approached as problems of finding minima of the total potential energy. The chapter reviews briefly the ideas underlying the proof of the existence of minimizers. It introduces some assumptions concerning the regularity of minimizers which are sufficient to prove the existence of a hydrostatic pressure.
