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Two new universal relations in nonlinear elasticity and some related matters. (English) Zbl 0827.73008
Summary: Two inequalities which for certain deformation classes may be viewed as universal relations are shown to hold for two distinct subclasses of unconstrained rubberlike solids. The inequalities express the fact that the mean stress corresponding to any purely distortional deformation originating from a given ground state is dominated by (and, respectively, dominates) the mean stress in that ground state. Also discussed is a case in which the deformations involved are necessarily homogeneous.

MSC:
74B20 Nonlinear elasticity
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