Compared to the general Green–Lagrange strain, some terms are neglected due to the zero value as a result of Eqs. (1) and (2). Notice that the Green–Lagrange strain results into nonzero transverse normal strain and shear strain in the face sheets. However, when an Euler–Bernoulli beam is considered, we usually consider only the axial normal strain *ϵ*_{xx} regardless of the analysis being linear or nonlinear. In the literature, some researchers include these two strain components *ϵ*_{zz} and *γ*_{xz} with zero linear part and nonzero nonlinear part in the face sheets, e.g., in Ref. [15]. The effects of these two additional strain components would be discussed later. For convenience, the strain components of the face sheets are written as
Display Formula

(6a)$\u03f5xxt,b(x,z)=\u2202ut,b(x,z)\u2202x+\alpha 12[\u2202ut,b(x,z)\u2202x]2+\alpha 22[\u2202wt,b(x,z)\u2202x]2\u2009$

Display Formula(6b)$\u03f5zzt,b(x,z)=\alpha 32[\u2202ut,b(x,z)\u2202z]2\u2009$

Display Formula(6c)$\gamma xzt,b(x,z)=\alpha 4\u2202ut,b(x,z)\u2202x\u2202ut,b(x,z)\u2202z\u2009$