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Mathematics and Mechanics of Solids
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On the Existence of a Stretch for a Prescribed Stress in Isotropic, Incompressible Elastic Materials

Thomas R. Nordenholz

Oliver M. O'Reilly

Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740

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.

Mathematics and Mechanics of Solids, Vol. 3, No. 2, 169-181 (1998)
DOI: 10.1177/108128659800300203
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