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A stress that only rotates

The block carries a constant uniaxial Cauchy stress along its own axis and is spun as a rigid body. Laboratory components σ₁₁, σ₂₂, σ₁₂ change because the basis is fixed. The Jaumann rate ∇σ = σ̇ − Wσ + σW is identically zero: no constitutive response has occurred.