## 3 Numerical Model Definition  
### Material Definition  
The numerical modelling was performed in the finite element software ABAQUS/Explicit [32]. Non-linear material behaviour is applied by means of different prescribed material models in the program. The tensile and compressive behaviour of the TRC faces was implemented by combining the elastic and concrete damaged plasticity (CDP) material model. The compressive behaviour of the TRC faces was implemented in the elastic material model. Hence, the linear elastic behaviour was described by the compressive E-modulus of 26 GPa and the Poisson ratio of 0.21 [33] of the cement. For the CDP model, the requested input parameters were the dilation angle (\(\psi=36\)), the potential flow eccentricity (\(\varepsilon=0.1\)), the proportion of the ultimate compressive stress in a biaxial test to the uniaxial compressive stress (\(f_{b0}/f_{c}=1.0\)), the shape of the deviatoric cross section (\(K_{c}=0.667\)) and the numerical viscosity parameter (\(\mu=10^{-7}\)). The values of these parameters were based on the ones described in [34]. Besides previously mentioned parameters, the non-linear tensile behaviour and ultimate compressive strength of the TRC were implemented in the uniaxial tensile stress-strain input of the CDP model. The compressive strength was limited to 58 MPa, while the complete tensile behaviour of the TRC faces, including the linear elastic part, was inserted. The used characteristic values are shown in Table 2.  
The initial linear elastic behaviour of the XPS foam was implemented by the elastic material model, and defined by the E-modulus and the Poisson ratio. The E-modulus, inputted into the numerical model, was based on the previously determined shear characteristics. Linear elastic analytical bending models for sandwich panels, described in [35; 36], show that the deflection due to shear (80%) was significantly larger than the deflection due to bending (20%). Therefore, the applied E-modulus was calculated from the shear modulus (see Section 2.2) and the Poisson ratio (0.5) [19] of the XPS core.  
The non-linear behaviour of the foam was modelled by the crushable foam-volumetric foam hardening material model. This model took into account the increased deformation of the foam in compression due to buckling of the cell walls, but required an isotropic material [32]. The crushable foam model requires the following parameters: the ratio between the initial yield stress in uniaxial compression and the initial yield stress in hydrostatic compression \(\sigma_{c}{}^{0}/p^{0}{}_{c}\) (compression yield stress ratio), as well as the ratio between the hydrostatic tension and the initial yield stress in hydrostatic compression \(p_{t}/p^{0}{}_{c}\) (hydrostatic yield stress ratio). The hydrostatic tension and initial yield stress in hydrostatic compression were set to 0.15 MPa and 0.14 MPa, respectively, as described in [19]. The initial yield stress in uniaxial compression was determined experimentally and set to 0.21 MPa (see Figure 3c). These values led to a compression yield stress ratio of 1.5 and a hydrostatic yield stress ratio of 1.07. The nonlinear behaviour of the foam was implemented through the yield stress and uniaxial plastic strain obtained from the average stress-strain curve of the thickness direction (Figure 3c). This non-linear material model implies the use of a dynamic explicit analysis, which is implemented with a time period of 10 and a mass scaling factor of 0.000001, in order to improve the speed of the analysis.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Matrix** & **Matrix** & **End of Multiple** & **End of Multiple** & **Ultimate** & **Ultimate** \\
**Cracking** & **Cracking Stress** & **Cracking Strain** & **Cracking Strain** & **Failure Stress** & **Failure Strain** \\ \hline
2.28 MPa & 0.00022 & 3.38 MPa & 0.0033 & 7.43 MPa & 0.0087 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Characteristic values for the average tensile TRC curve.