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

Patrizio Neff; L. Angela Mihai

doi:10.1007/s10659-016-9609-y

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arXiv · 1608.05247

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

Patrizio Neff·L. Angela Mihai

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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.

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BibTeX RIS

Patrizio Neff, L. Angela Mihai. 2016-08-18. Injectivity of the Cauchy-stress tensor along rank-one connected lines under strict rank-one convexity condition. https://doi.org/10.1007/s10659-016-9609-y

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