## 2 Materials
### Foam Cores
#### 2.2.1 Uniaxial Compression Tests  
The material behaviour of the XPS foams under uniaxial compression was investigated by testing cubes measuring 50 mm \(\times\) 50 mm \(\times\) 50 mm in an Instron 5985 universal testing machine (Instron, Norwood, MA, USA). The compressive response was revealed through two test series. In series 1, the anisotropy of the foams was investigated by loading cubes in the thickness (normal) direction (ND), the longitudinal direction (LD) and the transverse direction (TD) of the extruded plates. The crosshead velocity of the test machine was set to 3.0 mm/min in these tests, corresponding to an initial strain rate of \(1\times 10^{-3}\) s\({}^{-1}\). In series 2, the strain-rate sensitivity of the foams was examined by running tests on specimens in ND with an elevated crosshead velocity of 30 mm/min and 300 mm/min, respectively, corresponding to initial strain rates of \(1\times 10^{-2}\) s\({}^{-1}\) and \(1\times 10^{-1}\) s\({}^{-1}\). The complete test matrix and nominal material parameters are given in [7]. Before testing, each sample was given an identification number before being carefully measured and weighed. These measurements were used to determine the densities of the samples, see Table 2. The imaged surface of the sample was painted with a speckle pattern to enable use of 2D-DIC to measure compressive strains. The samples were compressed between two hardened steel plates during testing. A 100 kN calibrated load cell registered the load, while a digital camera was used to take pictures of one side of the samples at a frequency of 1 Hz. The in-house DIC-software eCorr was used to extract displacement and strain fields from the acquired pictures. All samples exhibited typical closed-cell foam behaviour, consisting of a linear elastic region followed by a plateau region spanning over a wide strain range, ending in a densification region where the stresses increase rapidly over a narrow strain range [6]. A slight anisotropic behaviour of the foams was observed, where the response in the LD and TD was similar, while slightly higher plateau stresses and lower densification strains were seen for tests in the ND. For most engineering purposes, the three XPS foams may be considered isotropic. Table 2 displays the mean density \(\rho\), standard deviation SD, elastic modulus E, yield stress \(\sigma_{\rm y}\), plateau stress \(\sigma_{\rm p}\) and densification strain \(\varepsilon_{\rm D}\) based on the compression tests in ND at a strain rate of \(1\times 10^{-3}\) s\({}^{-1}\)[6]. These results show that the elastic modulus, the yield stress and the plateau stress display a distinct increase with foam density, consistent with the expected behaviour for closed-cell foams [2]. In addition, the densification strain was comparable for the different densities. All three foam densities displayed a similar level of strain hardening. Figure 2a shows true stress-strain curves for the three densities in ND at different strain rates. As the scatter was low, only a representative test for each density and strain rate is shown for legibility. An apparent increase in yield and plateau stress was found with increasing strain rate, while the densification strain was mostly unaffected by strain rate. The results from the representative tests will later be used to calibrate a rate-dependent modification of the Deshpande-Fleck constitutive model for crushable foams (see Section 4.2). Based on DIC analyses, [PERSON] and [PERSON] [6] showed that the XPS foams used in this study have a distinct strain localisation during compression. As the samples were compressed, strains first localised in a band in the middle of the XPS-250 and XPS-400 samples before the band propagated towards the top and bottom surfaces. The strain localisation in XPS-700 was similar but occurred in two bands