In-plane rotations of vectorial and tensorial properties

II.1.11.3 In-plane rotations of vectorial and tensorial properties

The material scalar properties are left unmodified by in-plane rotations. The same is true for the out-of-plane quantities $q_{3}$ and $λ_{33}^{T}$ . The transformation of components for ${q}$ and $[λ^{T}]$ is noted with the transformation matrices defined in expressions (II.1.10) to (II.1.10):

{[λ^{T}]}_{12} = {[S_{-}]}_{(θ)} \cdot {[λ^{T}]}_{x y} \cdot {[S_{+}]}_{(θ)},

{[λ^{T}]}_{x y} = {[S_{+}]}_{(θ)} \cdot {[λ^{T}]}_{12} \cdot {[S_{-}]}_{(θ)},

{q}_{x y} = {[S_{+}]}_{(θ)} \cdot {q}_{12},

{q}_{12} = {[S_{-}]}_{(θ)} \cdot {q}_{x y} .

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