Injectivity of the Cauchy-stress tensor along rank-one connected lines   under strict rank-one convexity condition
  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. 
Patrizio Neff, L. Angela Mihai
math.CA