Strain energy functions for a poisson power law function in simple tensionof compressible hyperelastic materials

The most general strain energy function that yields a power law relationshi p between the principal stretches in the simple tension of nonlinear, elast ic, homogeneous, compressible, isotropic materials is obtained. The approac h taken generalises that used by Blatz and Ko. The strain energy function o btained depends on the choice of two stretch invariants. The forms of the s train energy function for a number of such choices are obtained. Finally, s ome consequences of the choice of strain energy function on the stress-stra in relationship for uniaxial tension are investigated.