On the conditions of potentiality in finite elasticity and hypo-elasticity

Thermodynamic approaches to ®nite elasticity are almost generally accepted. Nevertheless, there is still a lack of proof for the necessity of potential strain-stress relations in generally de®ned elasticity and hypo-elasticity. This situation has resulted in ambiguous applications of the general concept of elasticity to the description of irreversible phenomena in viscoelastic solids and liquids. This paper makes a brief review of the general concepts of elasticity and hypo-elasticity, with most of the attention paid to the Eulerian description, employed in viscoelastic theories. Then it is demonstrated that all hypothetical materials with non-potential ®nite elastic or hypo-elastic constitutive relations can create an energy from nothing, i.e. work as perpetual motion machines. This gives a `physicalʹ proof of necessity of potential conditions in general ®nite elasticity and hypo-elasticity and their extensions to ®nite viscoelasticity.