denoted $\b{X}$ and $\b{x}$, respectively. The associated linear deformation map, i.e. the (volume) deformation gradient, is denoted by $\b{F}:=\p \b{x} / \p \b{X} =  {\b{g}}_i \dyad {\b{G}}{}^i$, and maps material line elements $\d\b{X} \in T \c{B}_0$ (tangent to $\c{B}_0$) to spatial line elements $\d{\b{x}}\in T \c{B}_t$ via the relation $\d{\b{x}} = {\b{F}} \cdot \d{\b{X}}$. The co- and contravariant basis vectors in the material and spatial configurations are denoted $\b{G}_i$ and $\b{g}^i$, respectively. The displacement of a material point is denoted $\b{u} = \b{\varphi}(\b{X},t) - \b{X}$. The volume deformation gradient $\b{F}$ is rank-sufficient with inverse $\b{f}:=\p \b{X} / \p \b{x}= {\b{G}}_i \dyad {\b{g}}{}^i$. The determinant of the deformation gradient and its inverse are given by $J = \det \b{F} > 0$ and $j = \det \b{f} = 1 / J > 0$, respectively.

Let $\c{S}_0$ and $\c{S}_t$ denote the surface of the continuum body in the material and spatial configurations, respectively. The outward unit normals to $\c{S}_0$ and $\c{S}_t$ are denoted $\b{N}$ and $\b{n}$, respectively. Material particles on the surface are denoted $\h{\b{X}}$ in the material configuration and are *attached* to the volume, i.e. $\h{\b{X}}=\b{X}|_{\p{\c{B}_0}}$. Consequently, $\c{S}_0 = \p\c{B}_0$. Furthermore, we assume that the surface is material in the sense that 