## 3 Experiments
### [PERSON]'s Modulus Measurement of a Homogeneous Phantom
Considering the frictions on the top and bottom surface of the phantom, the boundary conditions were as follows:  
\[\left\{ \begin{array}{c}u|_{z=z_{\mathrm{b}},z=z_{\mathrm{t}}}=0\\ v|_{z=z_{\mathrm{b}},z=z_{\mathrm{t}}}=0\\ w|_{z=z_{\mathrm{b}}}=0\\ T|_{z=z_{\mathrm{t}}}=T_{0}\end{array} \right. \tag{20}\]  
where \(T_{0}\) was the applied pressure, i.e., \(T_{0}=-0.046\) N/(4.24 \(\times\) 10\({}^{-3}\) m \(\times\) 4.24 \(\times\) 10\({}^{-3}\) m) = \(-\)2558.7 Pa; \(z_{\mathrm{t}}\) and \(z_{\mathrm{b}}\) were the locations of the top and bottom surfaces of the phantom where the in-plane displacements were zeros. \(z_{\mathrm{t}}\) = 908.8 \(\upmu\)m was calculated according to the location of the white line in Figure 3c. \(z_{\mathrm{b}}\) = \(-\)10,691.2 \(\upmu\)m calculated by subtracting \(l_{z}\) from \(z_{\mathrm{t}}\). According to the boundary conditions, the virtual displacement fields were chosen as follows:  
\[\mathbf{u}^{*(1)}=\left( \begin{array}{c}0\\ 0\\ z-z_{\mathrm{b}}\end{array} \right) \tag{21}\]  
\[\mathbf{u}^{*(2)}=\left( \begin{array}{c}x(z-z_{\mathrm{b}})(z-z_{\mathrm{t} })\\ 0\\ 0\end{array} \right) \tag{22}\]  
Hence, the virtual strain fields were  
\[\varepsilon^{*(1)}=\left( \begin{array}{cccc}0&0&1&0&0&0\end{array} \right)^{ \mathrm{T}} \tag{23}\]  
\[\varepsilon^{*(2)}=\left( \begin{array}{c}(z-z_{\mathrm{b}})(z-z_{\mathrm{t} })\\ 0\\ 0\\ x(z-z_{\mathrm{b}}+z-z_{\mathrm{t}})\\ 0\end{array} \right) \tag{24}\]  
The coefficient matrix \(\mathbf{A}\) in Equation (11) were written as  
\[A_{11}=\sum_{k=1}^{M}\varepsilon_{3,k}v_{k}\;, \tag{25}\] \[A_{12}=\sum_{k=1}^{M}\left[\varepsilon_{1,k}(z_{k}-z_{\mathrm{b} })(z_{k}-z_{\mathrm{t}})+\varepsilon_{3,k}x_{k}(2z_{k}-z_{\mathrm{b}}-z_{ \mathrm{t}})\right]v_{k}\;,\] \[A_{22}=\sum_{k=1}^{M}\left[(\varepsilon_{2,k}+\varepsilon_{3,k}) (z_{k}-z_{\mathrm{b}})(z_{k}-z_{\mathrm{t}})-\frac{1}{2}\varepsilon_{5,k}x_{k }(2z_{k}-z_{\mathrm{b}}-z_{\mathrm{t}})\right]v_{k}\;,\]  
where \(M\) is the number of the matched points in DVC and \(M\) = 405; \(v_{k}\) is the volume of the \(k\)th mesh (point) and \(v_{k}\) = \(LxLyLz/M\). According to Equation (13) and static equilibrium, the virtual work vector \(\mathbf{B}\) is  
\[B_{1}=TLxLy(Lz-z_{\mathrm{b}})-TLxLy(0-z_{\mathrm{b}}), \tag{26}\]  
\[B_{2}=0.\]  
Then, coefficient matrix \(\mathbf{A}\) and the virtual work vector \(\mathbf{B}\) were input to Equation (14) to solve the elastic constants. \(Q_{11}\) and \(Q_{12}\) were calculated to be 2.2046 \(\times\) 10\({}^{6}\) Pa and 1.1070 \(\times\) 10\({}^{6}\) Pa. [PERSON]'s modulus and [PERSON]'s ratio were then calculated to be 1464.5 kPa and 0.334 respectively, by inputting\(\mathbf{Q}\) to Equation (15). The [PERSON]'s modulus of the phantom was also measured by a uniaxial tensile test, which resulted in 1471.0 kPa. The relative discrepancy between the results obtained by the two methods is \(\sim\)1%. The Poisson's ratio, calculated by dividing the average \(\varepsilon_{z}\) from the lateral strain obtained by DVC, was 0.306, where the the quadratic mean of \(\varepsilon_{x}\) and \(\varepsilon_{y}\) was taken as the lateral strain. The [PERSON]'s ratio calculated by VFM was 0.334, which is 8% different to 0.306.