Correction to ‘On a new class of electroelastic bodies. I’

Proc. R. Soc. A 469, 20120521. (Published online November 14, 2012) (doi:10.1098/rspa.2012.0521)

In §3c of [1] (Case 2), the linearized strain tensor ε is given as (see eqn (3.21) therein) $\mathit{\epsilon }=\hat{\mathfrak{f}}(\mathit{\tau },\mathbf{E},\mathbf{a})$, where τ is the total stress tensor, $\mathbf{E}$ is the electric field and $\mathbf{a}$ is a direction field such that $\parallel \mathbf{a}\parallel =1$ (the direction where the body is transversely isotropic). There are two missing terms in eqn (3.22) of that paper for the explicit representation for ε (see [2]). The corrected expression for ε is

where ${\hat{\alpha }}_r$, r=0,1,…,9 are scalar functions that depend on the invariants formulated in terms of τ, $\mathbf{E}$ and $\mathbf{a}$, which for brevity are not shown here.

In eqn (3.33) of [1] (Case 4 in §3c), there are also two missing terms for the representation for $\mathit{\tau }=\mathfrak{f}(\mathbf{b},\mathbf{E},\mathbf{D})$, where $\mathbf{b}$ is the left Cauchy–Green tensor and $\mathbf{D}$ is the electric displacement. The corrected expression for $\mathit{\tau }=\mathfrak{f}(\mathbf{b},\mathbf{E},\mathbf{D})$ is

where γ_r, r=0,1,…,9 are scalar functions that depend on the invariants formulated in terms of $\mathbf{b}$, $\mathbf{E}$ and $\mathbf{D}$, which for brevity are not shown here.

The additional terms added in (3.22) and (3.33) do not have any influence in the rest of the results presented in that paper [1].