The authors show that an isotropic, incompressible elastic material can support any system of homogeneous tractions if it satisfies a strengthened form of Truesdell's inequalities. Specifically, if this strengthened condition is satisfied, the Cauchy and first Piola-Kirchhoff stress tensors can assume all values. The strengthened condition is satisfied by certain Mooney-Rivlin and neo-Hookean materials, and implies both the Baker-Ericksen inequalities and a restriction proposed by Carroll and McCarthy. Finally, it also implies two growth conditions, either one of which is sufficient to guarantee the existence result for the Cauchy stress tensor.
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