## Appendix A Surface Strain FRFs for a Bending Plate  
The components of the _full-field generalised strain_\(FRFs\)\(\mathbf{H}_{\varepsilon_{g}}(x,y,\omega)\in\mathbb{C}\) are calculated--by the differentiations20 along \(j=(x,y,z)\) and \(k=(x,y,z)\) directions, applied on the 3D _rectome map_\(\mathbf{H}_{d}(x,y,\omega)\in\mathbb{C}\)--at every map location and frequency:  
Footnote 20: Computed by means of a robust differential operator as in [17; 99; 100], but with more details in particular shown in the Appendix of [6].  
\[H_{\varepsilon_{g}}(x,y,\omega)_{jk}=\frac{1}{2}\Bigg{(}\frac{\partial\mathbf{H}_ {d}(x,y,\omega)_{j}}{\partial q_{k}}+\frac{\partial\mathbf{H}_{d}(x,y,\omega)_{k }}{\partial q_{j}}\Bigg{)}\in\mathbb{C}. \tag{1}\]  
The _out-of-plane_\((z)\) bending-related displacements, in a plate of thickness \(s\), give their contributions to the following _bending-related strain FRF tensor_\(\mathbf{H}_{\varepsilon_{b}}(x,y,\omega)\in\mathbb{C}\) components, as:  
\[\begin{split}& H_{\varepsilon_{b}}(x,y,\omega)_{xx}=-\frac{s}{2} \frac{\partial^{2}\mathbf{H}_{d}(x,y,\omega)_{z}}{\partial x^{2}}\in\mathbb{C},\, H_{\varepsilon_{b}}(x,y,\omega)_{yy}=-\frac{s}{2}\frac{\partial^{2}\mathbf{H}_{d}(x,y, \omega)_{z}}{\partial y^{2}}\in\mathbb{C},\\ & H_{\gamma_{b}}(x,y,\omega)_{xy}=H_{\gamma_{b}}(x,y,\omega)_{yx }=-s\frac{\partial^{2}\mathbf{H}_{d}(x,y,\omega)_{z}}{\partial x\partial y}\in \mathbb{C}.\end{split} \tag{2}\]  
The superficial _total strain FRF tensor_\(\mathbf{H}_{\varepsilon}(x,y,\omega)\in\mathbb{C}\) is the sum of the above-mentioned contributions:  
\[\mathbf{H}_{\varepsilon}(x,y,\omega)=\mathbf{H}_{\varepsilon_{g}}(x,y,\omega)+\mathbf{H} _{\varepsilon_{b}}(x,y,\omega)\in\mathbb{C}. \tag{3}\]  
Note that in the TEFFMA testing only the _out-of-plane_ displacements were measurable: Equation (1) gives, therefore, a minor contribution, while the major contribution comes from Equation (2), taking into account also the different derivative order.  
The functional relation \(\mathcal{D}_{\varepsilon}()\), incorporating the steps of Equations (1)-(3), working on the _rectome map_\(\mathbf{H}_{d}(x,y,\omega)\in\mathbb{C}\), releases the _total strain FRF tensor_\(\mathbf{H}_{\varepsilon}(x,y,\omega)\in\mathbb{C}\):  
\[\mathbf{H}_{\varepsilon}(x,y,\omega)=\mathcal{D}_{\varepsilon}(\mathbf{H}_{d}(x,y, \omega))\in\mathbb{C} \tag{4}\]In the TEFFMA project's testing only _out-of-plane_ measurements were above the sensitivity threshold, resulting in \(\mathbf{H_{d}}(x,y,\omega)_{x}=\mathbf{H_{d}}(x,y,\omega)_{y}=\mathbf{0}\), while \(\mathbf{H_{d}}(x,y,\omega)_{z}\) was constant in \(z\); limited to this work, it happens that \(H_{\varepsilon_{g}}(x,y,\omega)_{xx}=H_{\varepsilon_{g}}(x,y,\omega)_{yy}=H_{ \varepsilon_{g}}(x,y,\omega)_{xy}=H_{\varepsilon_{g}}(x,y,\omega)_{yx}=H_{ \varepsilon_{g}}(x,y,\omega)_{zz}=0\), therefore \(H_{\varepsilon_{g}}(x,y,\omega)_{xz}=H_{\varepsilon_{g}}(x,y,\omega)_{xx}\) and \(H_{\varepsilon_{g}}(x,y,\omega)_{yz}=H_{\varepsilon_{g}}(x,y,\omega)_{zy}\) are the only computable contributions. Following these evidences, the _total strain FRF tensor_ can be newly arranged in the following matrix as \(\mathbf{\hat{H}_{\varepsilon}}(x,y,\omega)\), where one can notice a marked _in-plane_\((x,y)\) magnitude-related relevance of the components:  
\[\mathbf{\hat{H}_{\varepsilon}}(x,y,\omega)=\begin{bmatrix}H_{\varepsilon_{b}}(x,y, \omega)_{xx}&H_{\tau_{b}}(x,y,\omega)_{xy}&H_{\varepsilon_{g}}(x,y,\omega)_{ x}\\ H_{\tau_{b}}(x,y,\omega)_{yx}&H_{\varepsilon_{b}}(x,y,\omega)_{yy}&H_{ \varepsilon_{g}}(x,y,\omega)_{yx}\\ H_{\varepsilon_{g}}(x,y,\omega)_{xx}&H_{\varepsilon_{g}}(x,y,\omega)_{zy}&0 \end{bmatrix}\in\mathbb{C}. \tag{10}\]