Injectivity of the Cauchy-stress tensor along rank-one connected lines under strict rank-one convexity condition

Abstract

In this note, we show that the Cauchy stress tensor $\sigma$ in nonlinear elasticity is injective along rank-one connected lines provided that the constitutive law is strictly rank-one convex. This means that $\sigma (F+\xi \otimes \eta )=\sigma (F)$ implies $\xi \otimes \eta =0$ under strict rank-one convexity.

References in corpus (1)

• Hyperelastic bodies under homogeneous Cauchy stress induced by non-homogeneous finite deformations

Cited by in corpus (6)

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• Hyperelastic bodies under homogeneous Cauchy stress induced by three-dimensional non-homogeneous deformations