= Deviatoric strain
{title2=$\operatorname{dev}\varepsilon=\varepsilon-\frac1d(\operatorname{tr}\varepsilon)I$}
The <deviatoric strain> is the trace-free part of the <infinitesimal strain tensor>. It removes the isotropic volume change. The decomposition is <orthogonal> for the <Frobenius inner product>, because a trace-free <matrix> has zero <Frobenius inner product> with $I$. Consequently
$$
|\varepsilon|_F^2=|\operatorname{dev}\varepsilon|_F^2+\frac1d(\operatorname{tr}\varepsilon)^2.
$$
For $\varepsilon=\tfrac12(\nabla v+(\nabla v)^{\mathsf T})$, its <trace> is $\operatorname{div}v$.
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