ON THE EXISTENCE OF A STRETCH FOR A PRESCRIBED STRESS IN ISOTROPIC, INCOMPRESSIBLE ELASTIC-MATERIALS

The authors show that an isotropic, incompressible elastic material ca n support any system of homogeneous tractions if it satisfies a streng thened form of Truesdell's inequalities. Specifically, if this strengt hened condition is satisfied, the Cauchy and first Piola-Kirchhoff str ess tensors can assume all values. The strengthened condition is satis fied by certain Mooney-Rivlin and neo-Hookean materials, and implies b oth the Baker-Ericksen inequalities and a restriction proposed by Carr oll and McCarthy. Finally, it also implies two growth conditions, eith er one of which is sufficient to guarantee the existence result for th e Cauchy stress tensor.