On the existence of an elastic potential for a simple material without memory

Summary It is shown that a compressible elastic body — not necessarily homogeneous or isotropic — is hyperelastic provided the work done by all external forces acting on an arbitrary part of the body vanishes for every sufficiently smooth cyclic motion in which each material point returns to its initial position with a velocity equal to its initial velocity.Dedicated to Clifford Truesdell on his 60^th Birthday