<figure><img src="image_25.png" /><figcaption>**Figure 24.** Temperature profiles prediction as a function of time (straight lines; average numerical temperature in orange dashed line) for an E-glass/vinyl ester/balsa sandwich composite, with a 20% water content in relation to the porosity volume fraction of the balsa core, at a heat flux of 50 kW/m².</figcaption></figure>

Post-combustion mechanical properties for the moisturized sample were predicted in a similar way to the ones for the dry sandwich composite material. As shown previously, water content alters the thermal answer during heat flux exposition (fire) and therefore directly influences the post-combustion mechanical properties. Figure 25 shows the combustion advancing front prediction defined for a degradation rate of 50%, for a moisturized E-glass/vinyl ester/balsa sandwich composite material having a 20% water content in relation to the porosity volume fraction of the balsa core. For comparison, Figure 25 also includes the combustion advancing front prediction for the same dry material (0% water content). It could be highlighted that degradation is considerably affected by water content, due to the coupling between the evaporation process and all the others thermal phenomena. It is interesting to observe that the balsa core is degraded with very different behavior. Indeed, for the dry material, it could be highlighted a change in slope around 1500 s of exposure time to the heat flux, in correspondence with a gradual rise in temperature to about 300 °C in the middle of the core. For this degradation time, the material has already lost a large part of its mass, and the temperature is now sufficient to largely degrade the hemicellulose and cellulose, and to induce the degradation of the lignin contained in the balsa [47]. From a chemical point of view, the balsa core then enters into the phase of passive pyrolysis in which the lignin decomposes very slowly. As for the hydrated material, it decomposes much more slowly and in a progressive and constant manner. Of course this is also related to the predicted temperature variation in the core. After 1500 s of exposure, we observe a gap of 25% of the position of the combustion advancing front, which is maintained around 3500 s. For a very long time (>5000 s), the internal temperature of balsa in its different thicknesses are almost identical for both samples (dry and hydrated), and the two curves tend to overlap, inducing a similar amount of residues (char). It is interesting to note that the kinetics of decomposition of the balsa core, on the upper half of the core (heat flux side), of the wet material is about 0.005 mm·s⁻¹, and about 0.01 mm·s⁻¹ for the dry one.

Having predicted the variation of the combustion advancing front in the wet material, it is possible to calculate the equivalent flexural modulus (Figure 26) at a heat flux of 50 kW/m² and for a degradation level of 50%. We observe the same tendency for both sample (dry and wet), with slightly longer ruins in the case of the hydrated material. Remember here that the skins for the two samples are considered without water diffusion. The observed difference in Figure 26 is then not due to the residual water content in the front skin but induced by the water vapor flow produced during water evaporation contained inside the balsa, which might slightly cool the front interface and so the front skin. The
<figure><img src="image_26.png" /><figcaption>**Figure 24.** Temperature profiles prediction as a function of time (straight lines; average numerical temperature in orange dashed line) for an E-glass/vinyl ester/balsa sandwich composite, with a 20% water content in relation to the porosity volume fraction of the balsa core, at a heat flux of 50 kW/m².</figcaption></figure>

Post-combustion mechanical properties for the moisturized sample were predicted in a similar way to the ones for the dry sandwich composite material. As shown previously, water content alters the thermal answer during heat flux exposition (fire) and therefore directly influences the post-combustion mechanical properties. Figure 25 shows the combustion advancing front prediction defined for a degradation rate of 50%, for a moisturized E-glass/vinyl ester/balsa sandwich composite material having a 20% water content in relation to the porosity volume fraction of the balsa core. For comparison, Figure 25 also includes the combustion advancing front prediction for the same dry material (0% water content). It could be highlighted that degradation is considerably affected by water content, due to the coupling between the evaporation process and all the others thermal phenomena. It is interesting to observe that the balsa core is degraded with very different behavior. Indeed, for the dry material, it could be highlighted a change in slope around 1500 s of exposure time to the heat flux, in correspondence with a gradual rise in temperature to about 300 °C in the middle of the core. For this degradation time, the material has already lost a large part of its mass, and the temperature is now sufficient to largely degrade the hemicellulose and cellulose, and to induce the degradation of the lignin contained in the balsa [47]. From a chemical point of view, the balsa core then enters into the phase of passive pyrolysis in which the lignin decomposes very slowly. As for the hydrated material, it decomposes much more slowly and in a progressive and constant manner. Of course this is also related to the predicted temperature variation in the core. After 1500 s of exposure, we observe a gap of 25% of the position of the combustion advancing front, which is maintained around 3500 s. For a very long time (>5000 s), the internal temperature of balsa in its different thicknesses are almost identical for both samples (dry and hydrated), and the two curves tend to overlap, inducing a similar amount of residues (char). It is interesting to note that the kinetics of decomposition of the balsa core, on the upper half of the core (heat flux side), of the wet material is about 0.005 mm·s⁻¹, and about 0.01 mm·s⁻¹ for the dry one.

Having predicted the variation of the combustion advancing front in the wet material, it is possible to calculate the equivalent flexural modulus (Figure 26) at a heat flux of 50 kW/m² and for a degradation level of 50%. We observe the same tendency for both sample (dry and wet), with slightly longer ruins in the case of the hydrated material. Remember here that the skins for the two samples are considered without water diffusion. The observed difference in Figure 26 is then not due to the residual water content in the front skin but induced by the water vapor flow produced during water evaporation contained inside the balsa, which might slightly cool the front interface and so the front skin. The
combustion advancing front in the front skin is, therefore, slightly slower in the case of the wet specimen (Figure 25). The complete loss of flexural strength occurs with an additional delay of 200 s in favor of the hydrated material. The developed advanced hygro-thermo-mechanical model correctly takes into account the evolution of water content inside each constituent of the sandwich material.

<figure><img src="image_26.png" /><figcaption>**Figure 25.** Prediction of the combustion advancing front for a moisturized E-glass/vinyl ester/balsa sandwich composite material (wet, red curve) at a heat flux of 50 kW/m², with a 20% water content in relation to the porosity volume fraction of the balsa core using the hygro-thermal model. Prediction comparison of the combustion advancing front for the same dry material (green curve).</figcaption></figure>

<figure><img src="image_27.png" /><figcaption>**Figure 26.** Post-combustion time dependence of the normalized flexural modulus. Comparison of numerical predictions as a function of combustion time between pure thermal (dry sample, green curve) and hygro-thermal (wet sample, red curve; 20% water content in relation to the porosity volume fraction of the balsa core) models for an E-glass/vinyl ester/balsa sandwich composite at a heat flux of 50 kW/m² and for a degradation level of 50%.</figcaption></figure>

**5. Conclusions**

Does water content alter the thermo-mechanical behavior and properties of sandwich composite material during a fire scenario?
combustion advancing front in the front skin is, therefore, slightly slower in the case of the wet specimen (Figure 25). The complete loss of flexural strength occurs with an additional delay of 200 s in favor of the hydrated material. The developed advanced hygro-thermo-mechanical model correctly takes into account the evolution of water content inside each constituent of the sandwich material.

<figure><img src="image_27.png" /><figcaption>**Figure 25.** Prediction of the combustion advancing front for a moisturized E-glass/vinyl ester/balsa sandwich composite material (wet, red curve) at a heat flux of 50 kW/m², with a 20% water content in relation to the porosity volume fraction of the balsa core using the hygro-thermal model. Prediction comparison of the combustion advancing front for the same dry material (green curve).</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>**Figure 26.** Post-combustion time dependence of the normalized flexural modulus. Comparison of numerical predictions as a function of combustion time between pure thermal (dry sample, green curve) and hygro-thermal (wet sample, red curve; 20% water content in relation to the porosity volume fraction of the balsa core) models for an E-glass/vinyl ester/balsa sandwich composite at a heat flux of 50 kW/m² and for a degradation level of 50%.</figcaption></figure>

**5. Conclusions**

Does water content alter the thermo-mechanical behavior and properties of sandwich composite material during a fire scenario?
The thermal decomposition of sandwich composite materials can be adequately predicted thanks to numerical models, such as the presented one-dimensional hygro-thermal model of Legrand et al. The present numerical model also allows to accurately predict the post-combustion mechanical properties for sandwich composites having polymer laminated skins and combustible core. The results well underline the effects related to the presence of water content field within the sandwich composite material, sometimes inducing a large change in the evolution of key parameters, such as the mass loss and the combustion advancing front. Of course, the greater the heat flux at the surface of the material, and with a large amount of water diffused into the skins and the core, the more the behavior of the material and its properties are modified, for each component (skins and core) as a function of time and also of the thickness. Thus, the use of the proposed model makes it possible to successfully predict these thermal behaviors at both the components and material scales, in a large variety of scenarios (value of the heat flux, ambient conditions of temperature and pressure, etc.) and sandwich materials (geometry, nature of the resin and the core, type of reinforcing fibers, nature of the resin infused into the core, hydration rate, porosity rate, etc.).

An extension to a 2D or 3D model could be formulated in order to take into account for spatial different properties and mechanisms, such as conductivity and expansion, depending on the composite material direction. Post-combustion mechanical properties are estimated by a combination of a bi-layer model (char and virgin) for each constituent of the sandwich material. Therefore, they depend directly on the thermal response. Even if a good agreement between experimental and numerical data has been found here, it is envisaged to improve the model in order to consider the complexity of sandwich materials mechanical phenomena, such as damage and failure. These phenomena could be especially important for thinner composites skins and for interfaces between skins and the core, which are not modeled in the presented model interfaces modeling would enable to more accurately predict post-combustion mechanical performances during first steps of mechanical degradation, even before any considerable thermal decomposition. That requires to propose new mechanical models to know the material stress-strain state, including explicit temperature dependences on material behavior and mechanical properties. Thus, a change to the ply scale modeling is recommended. This approach will allow to analyze not only post-combustion performances but also more accurate thermo-mechanical response during the material exposition to the heat source. Despite that, and as indicated, the presented model is in very acceptable agreement since thermal decomposition starts, which represent a critical phenomenon for naval and aeronautics materials.

The highlight of the presented model is the ability to play on the amount of water present in the constituents of the material in order to accurately predict the thermal response for wet or humid materials in a fire scenario. Indeed, left in normal conditions of pressure and temperature, the balsa already picks up between 8% and 15% by weight of water. If this sample is then used in the manufacture of sandwich plate, the finalized material is hydrated and its thermo-mechanical behavior has changed. Later, depending on its use and the environment, the water content of this sandwich material can still evolve. Further research should ongoing to better describe the influence of moisture on the thermal properties, such as heat capacity, conductivity, permeability, or thermal expansion coefficients, and mechanical properties, such as ply and interfaces stiffness and strengths. Thus, future works must focus on the analysis about how the water content affects not only the thermal response but also the mechanical one, which seems necessary to better understand different failures modes and durability of composites materials in extreme conditions. Particularly in the marine or aeronautical industries, materials are subject to large variations of water content and temperature. In addition, because of the flexibility of the model, this study is part of the investigation of the thermal and hygroscopic durability of materials.

**Author Contributions:** Conceptualization, J.P.M.C. and V.L.; Formal analysis, J.P.M.C. and V.L.; Funding acquisition, F.J.; Investigation, J.P.M.C. and V.L.; Methodology, V.L.; Software, J.P.M.C., V.L. and S.F.; Supervision, V.L. and S.F.; Validation, V.L.; Visualization, J.P.M.C. and V.L.; Writing—original draft, J.P.M.C. and V.L.; Writing—review & editing, J.P.M.C., V.L., S.F., and F.J. All authors have read and agreed to the published version of the manuscript.
The thermal decomposition of sandwich composite materials can be adequately predicted thanks to numerical models, such as the presented one-dimensional hygro-thermal model of Legrand et al. The present numerical model also allows to accurately predict the post-combustion mechanical properties for sandwich composites having polymer laminated skins and combustible core. The results well underline the effects related to the presence of water content field within the sandwich composite material, sometimes inducing a large change in the evolution of key parameters, such as the mass loss and the combustion advancing front. Of course, the greater the heat flux at the surface of the material, and with a large amount of water diffused into the skins and the core, the more the behavior of the material and its properties are modified, for each component (skins and core) as a function of time and also of the thickness. Thus, the use of the proposed model makes it possible to successfully predict these thermal behaviors at both the components and material scales, in a large variety of scenarios (value of the heat flux, ambient conditions of temperature and pressure, etc.) and sandwich materials (geometry, nature of the resin and the core, type of reinforcing fibers, nature of the resin infused into the core, hydration rate, porosity rate, etc.).

An extension to a 2D or 3D model could be formulated in order to take into account for spatial different properties and mechanisms, such as conductivity and expansion, depending on the composite material direction. Post-combustion mechanical properties are estimated by a combination of a bi-layer model (char and virgin) for each constituent of the sandwich material. Therefore, they depend directly on the thermal response. Even if a good agreement between experimental and numerical data has been found here, it is envisaged to improve the model in order to consider the complexity of sandwich materials mechanical phenomena, such as damage and failure. These phenomena could be especially important for thinner composites skins and for interfaces between skins and the core, which are not modeled in the presented model interfaces modeling would enable to more accurately predict post-combustion mechanical performances during first steps of mechanical degradation, even before any considerable thermal decomposition. That requires to propose new mechanical models to know the material stress-strain state, including explicit temperature dependences on material behavior and mechanical properties. Thus, a change to the ply scale modeling is recommended. This approach will allow to analyze not only post-combustion performances but also more accurate thermo-mechanical response during the material exposition to the heat source. Despite that, and as indicated, the presented model is in very acceptable agreement since thermal decomposition starts, which represent a critical phenomenon for naval and aeronautics materials.

The highlight of the presented model is the ability to play on the amount of water present in the constituents of the material in order to accurately predict the thermal response for wet or humid materials in a fire scenario. Indeed, left in normal conditions of pressure and temperature, the balsa already picks up between 8% and 15% by weight of water. If this sample is then used in the manufacture of sandwich plate, the finalized material is hydrated and its thermo-mechanical behavior has changed. Later, depending on its use and the environment, the water content of this sandwich material can still evolve. Further research should ongoing to better describe the influence of moisture on the thermal properties, such as heat capacity, conductivity, permeability, or thermal expansion coefficients, and mechanical properties, such as ply and interfaces stiffness and strengths. Thus, future works must focus on the analysis about how the water content affects not only the thermal response but also the mechanical one, which seems necessary to better understand different failures modes and durability of composites materials in extreme conditions. Particularly in the marine or aeronautical industries, materials are subject to large variations of water content and temperature. In addition, because of the flexibility of the model, this study is part of the investigation of the thermal and hygroscopic durability of materials.

**Author Contributions:** Conceptualization, J.P.M.C. and V.L.; Formal analysis, J.P.M.C. and V.L.; Funding acquisition, F.J.; Investigation, J.P.M.C. and V.L.; Methodology, V.L.; Software, J.P.M.C., V.L. and S.F.; Supervision, V.L. and S.F.; Validation, V.L.; Visualization, J.P.M.C. and V.L.; Writing—original draft, J.P.M.C. and V.L.; Writing—review & editing, J.P.M.C., V.L., S.F., and F.J. All authors have read and agreed to the published version of the manuscript.
**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

**Nomenclature**

<table><tr><td>A</td><td>Pre-exponential factor of Arrhenius law (s<sup>-1</sup>)</td></tr><tr><td>c<sub>i</sub></td><td>Specific heat of state i (J·kg<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>c<sub>p</sub></td><td>Specific heat of the material (J·kg<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>c<sub>pg</sub></td><td>Specific heat of gas (J·kg<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>c<sub>pvH<sub>2</sub>O</sub></td><td>Specific heat of water vapor (J·kg<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>d</td><td>Total thickness (m)</td></tr><tr><td>d<sub>c</sub></td><td>Carbonized layer thickness (m)</td></tr><tr><td>d<sub>n</sub></td><td>Balance bending forces' thickness (m)</td></tr><tr><td>E<sub>a</sub></td><td>Activation energy (J·mol<sup>-1</sup>)</td></tr><tr><td>E</td><td>Young modulus (MPa)</td></tr><tr><td>&lt;EI&gt;</td><td>Flexural modulus (MN·m<sup>2</sup>)</td></tr><tr><td>f<sub>c</sub></td><td>Correction factor (-)</td></tr><tr><td>h<sub>g</sub></td><td>Enthalpy of pyrolysis gases (J·kg<sup>-1</sup>)</td></tr><tr><td>h<sub>s</sub></td><td>Enthalpy of the solid material (J·kg<sup>-1</sup>)</td></tr><tr><td>h<sub>conv</sub></td><td>Convective heat transfer coefficient (W·m<sup>-2</sup>·K<sup>-1</sup>)</td></tr><tr><td>I</td><td>Quadratic moment (m<sup>4</sup>)</td></tr><tr><td>k<sub>g</sub></td><td>Thermal conductivity of volatile gases (W·m<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>k<sub>i</sub></td><td>Thermal conductivity of state i (W·m<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>k<sub>x</sub></td><td>Thermal conductivity of solid material (W·m<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>L</td><td>Thickness of material (m)</td></tr><tr><td>m<sub>g</sub></td><td>Volatile gases mass (kg)</td></tr><tr><td>ṁ<sub>g</sub></td><td>Mass flow rate per unit area of pyrolysis gases through the reaction zone (kg·s<sup>-1</sup>·m<sup>-2</sup>)</td></tr><tr><td>m<sub>m</sub></td><td>Mass of matrix (kg)</td></tr><tr><td>m<sub>s</sub></td><td>Solid mass of material (kg)</td></tr><tr><td>m<sub>H<sub>2</sub>O</sub></td><td>Water mass (kg)</td></tr><tr><td>M</td><td>Average molecular weight of gases (kg·mol<sup>-1</sup>)</td></tr><tr><td>n</td><td>Order of decomposition reaction</td></tr><tr><td>P</td><td>Internal pressure of gases (atm)</td></tr><tr><td>q''<sub>radiation</sub></td><td>Heat flux (W·m<sup>-2</sup>)</td></tr><tr><td>Q<sub>p</sub></td><td>Heat of decomposition (J·kg<sup>-1</sup>)</td></tr><tr><td>R</td><td>Gas constant (8.314 J·mol<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>t</td><td>Time (s)</td></tr><tr><td>T</td><td>Temperature (K)</td></tr><tr><td>T<sub>∞</sub></td><td>Ambient temperature (K)</td></tr><tr><td>V<sub>f</sub></td><td>Volume fraction of fibers (%)</td></tr><tr><td>V<sub>m</sub></td><td>Volume fraction of the matrix (%)</td></tr><tr><td>x</td><td>Through-thickness coordinate (m)</td></tr><tr><td>X</td><td>Mass fraction (-)</td></tr><tr><td>α</td><td>Remaining fraction of virgin material (-)</td></tr><tr><td>α<sub>i</sub></td><td>Linear thermal expansion coefficient of state i (K<sup>-1</sup>)</td></tr><tr><td>γ</td><td>Permeability of material (m<sup>2</sup>)</td></tr><tr><td>Δh<sub>fg</sub></td><td>Latent heat of water (J·kg<sup>-1</sup>)</td></tr><tr><td>Δh<sub>l</sub></td><td>Evaporation heat of free liquid water (J·kg<sup>-1</sup>)</td></tr><tr><td>Δh<sub>desorp</sub></td><td>Evaporation heat of bound water (J·kg<sup>-1</sup>)</td></tr><tr><td>ψ<sub>i</sub></td><td>Permeability coefficient of state i (K<sup>-1</sup>)</td></tr><tr><td>ε<sub>m</sub></td><td>Material surface emissivity (-)</td></tr></table>
**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

**Nomenclature**

<table><tr><td>A</td><td>Pre-exponential factor of Arrhenius law (s<sup>-1</sup>)</td></tr><tr><td>c<sub>i</sub></td><td>Specific heat of state i (J·kg<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>c<sub>p</sub></td><td>Specific heat of the material (J·kg<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>c<sub>pg</sub></td><td>Specific heat of gas (J·kg<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>c<sub>pvH<sub>2</sub>O</sub></td><td>Specific heat of water vapor (J·kg<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>d</td><td>Total thickness (m)</td></tr><tr><td>d<sub>c</sub></td><td>Carbonized layer thickness (m)</td></tr><tr><td>d<sub>n</sub></td><td>Balance bending forces' thickness (m)</td></tr><tr><td>E<sub>a</sub></td><td>Activation energy (J·mol<sup>-1</sup>)</td></tr><tr><td>E</td><td>Young modulus (MPa)</td></tr><tr><td>&lt;EI&gt;</td><td>Flexural modulus (MN·m<sup>2</sup>)</td></tr><tr><td>f<sub>c</sub></td><td>Correction factor (-)</td></tr><tr><td>h<sub>g</sub></td><td>Enthalpy of pyrolysis gases (J·kg<sup>-1</sup>)</td></tr><tr><td>h<sub>s</sub></td><td>Enthalpy of the solid material (J·kg<sup>-1</sup>)</td></tr><tr><td>h<sub>conv</sub></td><td>Convective heat transfer coefficient (W·m<sup>-2</sup>·K<sup>-1</sup>)</td></tr><tr><td>I</td><td>Quadratic moment (m<sup>4</sup>)</td></tr><tr><td>k<sub>g</sub></td><td>Thermal conductivity of volatile gases (W·m<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>k<sub>i</sub></td><td>Thermal conductivity of state i (W·m<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>k<sub>x</sub></td><td>Thermal conductivity of solid material (W·m<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>L</td><td>Thickness of material (m)</td></tr><tr><td>m<sub>g</sub></td><td>Volatile gases mass (kg)</td></tr><tr><td>ṁ<sub>g</sub></td><td>Mass flow rate per unit area of pyrolysis gases through the reaction zone (kg·s<sup>-1</sup>·m<sup>-2</sup>)</td></tr><tr><td>m<sub>m</sub></td><td>Mass of matrix (kg)</td></tr><tr><td>m<sub>s</sub></td><td>Solid mass of material (kg)</td></tr><tr><td>m<sub>H<sub>2</sub>O</sub></td><td>Water mass (kg)</td></tr><tr><td>M</td><td>Average molecular weight of gases (kg·mol<sup>-1</sup>)</td></tr><tr><td>n</td><td>Order of decomposition reaction</td></tr><tr><td>P</td><td>Internal pressure of gases (atm)</td></tr><tr><td>q''<sub>radiation</sub></td><td>Heat flux (W·m<sup>-2</sup>)</td></tr><tr><td>Q<sub>p</sub></td><td>Heat of decomposition (J·kg<sup>-1</sup>)</td></tr><tr><td>R</td><td>Gas constant (8.314 J·mol<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>t</td><td>Time (s)</td></tr><tr><td>T</td><td>Temperature (K)</td></tr><tr><td>T<sub>∞</sub></td><td>Ambient temperature (K)</td></tr><tr><td>V<sub>f</sub></td><td>Volume fraction of fibers (%)</td></tr><tr><td>V<sub>m</sub></td><td>Volume fraction of the matrix (%)</td></tr><tr><td>x</td><td>Through-thickness coordinate (m)</td></tr><tr><td>X</td><td>Mass fraction (-)</td></tr><tr><td>α</td><td>Remaining fraction of virgin material (-)</td></tr><tr><td>α<sub>i</sub></td><td>Linear thermal expansion coefficient of state i (K<sup>-1</sup>)</td></tr><tr><td>γ</td><td>Permeability of material (m<sup>2</sup>)</td></tr><tr><td>Δh<sub>fg</sub></td><td>Latent heat of water (J·kg<sup>-1</sup>)</td></tr><tr><td>Δh<sub>l</sub></td><td>Evaporation heat of free liquid water (J·kg<sup>-1</sup>)</td></tr><tr><td>Δh<sub>desorp</sub></td><td>Evaporation heat of bound water (J·kg<sup>-1</sup>)</td></tr><tr><td>ψ<sub>i</sub></td><td>Permeability coefficient of state i (K<sup>-1</sup>)</td></tr><tr><td>ε<sub>m</sub></td><td>Material surface emissivity (-)</td></tr></table>
$\epsilon_s$ Source emissivity (-)

$\zeta$ Dimensionless expansion factor (-)

$\eta$ Dimensionless permeability factor (-)

$\mu$ Gases viscosity (Pa·s)

$\rho$ Material density (kg·m⁻³)

$\sigma$ Stefan-Boltzmann constant (5.67 × 10⁸ W·m⁻²·K⁻⁴)

$\Phi$ Porosity of material (-)

Subscripts

a Activation

c Carbonized state

composite Composite

conv Convection

0 Initial state

f Final state

fiber Fiber

fsp Fiber saturation point

g Gas

$H_2O$ Water

inf Inferior

m Matrix

p Pyrolysis

s Solid, Source

sat Saturation

sup Superior

v Virgin state

$vH_2O$ Water vapor

References

1. Legrand, V.; Merdrignac-Conanec, O.; Paulus, W.; Hansen, T.C. Study of the Thermal Nitridation of Nanocrystalline Ti(OH)₄ by X-ray and in Situ Neutron Powder Diffraction. *J. Phys. Chem. A* **2012**, *116*, 9561–9567. [CrossRef] [PubMed]

2. Legrand, V.; Pillet, S.; Weber, H.-P.; Souhassou, M.; Letard, J.-F.; Guionneau, P.; LeComte, C. On the precision and accuracy of structural analysis of light-induced metastable states. *J. Appl. Cryst.* **2007**, *40*, 1076–1088. [CrossRef]

3. Legrand, V.; Pillet, S.; Carbonera, C.; Souhassou, M.; Létard, J.-F.; Guionneau, P.; LeComte, C. Optical, Magnetic and Structural Properties of the Spin-Crossover Complex [Fe(btr)₂(NCS)₂]·H₂O in the Light-Induced and Thermally Quenched Metastable States. *Eur. J. Inorg. Chem.* **2007**, *2007*, 5693–5706. [CrossRef]

4. Legrand, V.; Carbonera, C.; Pillet, S.; Souhassou, M.; Létard, J.F.; Guionneau, P.; LeComte, C. Photo-crystallography: From the structure towards the electron density of metastable states. *J. Phys. Conf. Ser.* **2005**, *21*, 73–80. [CrossRef]

5. Gloaguen, D.; Oum, G.; Legrand, V.; Fajoui, J.; Moya, M.-J.; Pirling, T.; Kockelmann, W. Intergranular Strain Evolution in Titanium During Tensile Loading: Neutron Diffraction and Polycrystalline Model. *Met. Mater. Trans.* **A** **2015**, *46*, 5038–5046. [CrossRef]

6. Hounkpati, V.; Fréour, S.; Gloaguen, D.; Legrand, V.; Kelleher, J.; Kockelmann, W.; Kabra, S. In situ neutron measurements and modelling of the intergranular strains in the near-β titanium alloy Ti-β21S. *Acta Mater.* **2016**, *109*, 341–352. [CrossRef]

7. Legrand, V.; Kockelmann, W.; Frost, C.D.; Hauser, R.; Kaczorowski, D. Neutron diffraction study of the non-Fermi liquid compound CeNiGa2: Magnetic behaviour as a function of pressure and temperature. *J. Phys. Condens. Matter* **2013**, *25*, 206001. [CrossRef]

8. Legrand, V.; Le Gac, F.; Guionneau, P.; Létard, J. Neutron powder diffraction studies of two spin transition Fe(II)-complexes under pressure. *J. Appl. Crystallogr.* **2008**, *41*, 637–640. [CrossRef]
$ε_s$ Source emissivity (-)

$ζ$ Dimensionless expansion factor (-)

$η$ Dimensionless permeability factor (-)

$μ$ Gases viscosity (Pa·s)

$ρ$ Material density (kg·m⁻³)

$σ$ Stefan-Boltzmann constant (5.67 × 10⁸ W·m⁻²·K⁻⁴)

$Φ$ Porosity of material (-)

Subscripts

a Activation

c Carbonized state

composite Composite

conv Convection

0 Initial state

f Final state

fiber Fiber

fsp Fiber saturation point

g Gas

$H_2O$ Water

inf Inferior

m Matrix

p Pyrolysis

s Solid, Source

sat Saturation

sup Superior

v Virgin state

$vH_2O$ Water vapor

References

1. Legrand, V.; Merdrignac-Conanec, O.; Paulus, W.; Hansen, T.C. Study of the Thermal Nitridation of Nanocrystalline Ti(OH)₄ by X-ray and in Situ Neutron Powder Diffraction. *J. Phys. Chem. A* **2012**, *116*, 9561–9567. [CrossRef] [PubMed]

2. Legrand, V.; Pillet, S.; Weber, H.-P.; Souhassou, M.; Letard, J.-F.; Guionneau, P.; LeComte, C. On the precision and accuracy of structural analysis of light-induced metastable states. *J. Appl. Cryst.* **2007**, *40*, 1076–1088. [CrossRef]

3. Legrand, V.; Pillet, S.; Carbonera, C.; Souhassou, M.; Létard, J.-F.; Guionneau, P.; LeComte, C. Optical, Magnetic and Structural Properties of the Spin-Crossover Complex [Fe(btr)₂(NCS)₂]·H₂O in the Light-Induced and Thermally Quenched Metastable States. *Eur. J. Inorg. Chem.* **2007**, *2007*, 5693–5706. [CrossRef]

4. Legrand, V.; Carbonera, C.; Pillet, S.; Souhassou, M.; Létard, J.F.; Guionneau, P.; LeComte, C. Photo-crystallography: From the structure towards the electron density of metastable states. *J. Phys. Conf. Ser.* **2005**, *21*, 73–80. [CrossRef]

5. Gloaguen, D.; Oum, G.; Legrand, V.; Fajoui, J.; Moya, M.-J.; Pirling, T.; Kockelmann, W. Intergranular Strain Evolution in Titanium During Tensile Loading: Neutron Diffraction and Polycrystalline Model. *Met. Mater. Trans.* **A** **2015**, *46*, 5038–5046. [CrossRef]

6. Hounkpati, V.; Fréour, S.; Gloaguen, D.; Legrand, V.; Kelleher, J.; Kockelmann, W.; Kabra, S. In situ neutron measurements and modelling of the intergranular strains in the near-β titanium alloy Ti-β21S. *Acta Mater.* **2016**, *109*, 341–352. [CrossRef]

7. Legrand, V.; Kockelmann, W.; Frost, C.D.; Hauser, R.; Kaczorowski, D. Neutron diffraction study of the non-Fermi liquid compound CeNiGa2: Magnetic behaviour as a function of pressure and temperature. *J. Phys. Condens. Matter* **2013**, *25*, 206001. [CrossRef]

8. Legrand, V.; Le Gac, F.; Guionneau, P.; Létard, J. Neutron powder diffraction studies of two spin transition Fe(II)-complexes under pressure. *J. Appl. Crystallogr.* **2008**, *41*, 637–640. [CrossRef]
9. Legrand, V.; Pechev, S.; Létard, J.-F.; Guionneau, P. Synergy between polymorphism, pressure, spin-crossover and temperature in [Fe(PM-BiA)₂(NCS)₂]: A neutron powder diffraction investigation. *Phys. Chem. Chem. Phys.* **2013**, *15*, 13872–13880. [CrossRef]

10. Legrand, V.; Pillet, S.; Souhassou, M.; Lugan, N.; LeComte, C. Extension of the Experimental Electron Density Analysis to Metastable States: A Case Example of the Spin Crossover Complex Fe(btr)₂(NCS)₂·H₂O. *J. Am. Chem. Soc.* **2006**, *128*, 13921–13931. [CrossRef]

11. Rizk, G.; Legrand, V.; Khalil, K.; Casari, P.; Jacquemin, F. Durability of sandwich composites under extreme conditions: Towards the prediction of fire resistance properties based on thermo-mechanical measurements. *Compos. Struct.* **2018**, *186*, 233–245. [CrossRef]

12. Rizk, G.; Nahas, R.; Khalil, K.; Challita, G.; Legrand, V.; Casari, P.; Jacquemin, F. Durability of composite assemblies under extreme conditions: Thermomechanical damage prediction of a double-lap bonded composite assembly subject to impact and high temperature. *Compos. Struct.* **2019**, *213*, 58–70. [CrossRef]

13. Pering, G.A.; Farrell, P.V.; Springer, G.S. Degradation of tensile and shear properties of composites exposed to fire or high temperature. *J. Compos. Mater.* **1980**, *14*, 54–66.

14. Henderson, J.B.; Wiebelt, J.A.; Tant, M.R. A Model for the Thermal Response of Polymer Composite Materials with Experimental Verification. *J. Compos. Mater.* **1985**, *19*, 579–595. [CrossRef]

15. Gibson, A.; Wu, Y.S.; Chandler, H.W.; Wilcox, J.A.D.; Bettess, P. A Model for the Thermal Performance of Thick Composite Laminates in Hydrocarbon Fires. *Rev. De L'institut Français Du Pétrole* **1995**, *50*, 69–74. [CrossRef]

16. Mouritz, A.P.; Gibson, A.G. Fire properties of polymer composite materials. In *Solid Mechanics and its Applications*; Springer: Berlin/Heidelberg, Germany, 2006.

17. Lattimer, B.Y.; Ouellette, J.; Trelles, J. Thermal Response of Composite Materials to Elevated Temperatures. *Fire Technol.* **2011**, *47*, 823–850. [CrossRef]

18. Henderson, J.B.; Wiecek, T.E. A Mathematical Model to Predict the Thermal Response of Decomposing, Expanding Polymer Composites. *J. Compos. Mater.* **1987**, *21*, 373–393. [CrossRef]

19. Ramnath, B.V.; Alagarraja, K.; Elanchezhian, C. Review on Sandwich Composite and their Applications. *Mater. Today Proc.* **2019**, *16*, 859–864. [CrossRef]

20. Mouritz, A.; Feih, S.; Kandare, E.; Mathys, Z.; Gibson, A.; Jardin, P.D.; Case, S.W.; Lattimer, B. Review of fire structural modelling of polymer composites. *Compos. Part A Appl. Sci. Manuf.* **2009**, *40*, 1800–1814. [CrossRef]

21. Costa, J.P.M.; Legrand, V.; Fréour, S. Durability of Composite Materials under Severe Temperature Conditions: Influence of Moisture Content and Prediction of Thermo-Mechanical Properties During a Fire. *J. Compos. Sci.* **2019**, *3*, 55. [CrossRef]

22. McCracken, A.; Sadeghian, P. Partial-composite behavior of sandwich beams composed of fiberglass face sheets and woven fabric core. *Thin-Walled Struct.* **2018**, *131*, 805–815. [CrossRef]

23. Sabah, S.A.; Kueh, A.; Al-Fasih, M. Comparative low-velocity impact behavior of bio-inspired and conventional sandwich composite beams. *Compos. Sci. Technol.* **2017**, *149*, 64–74. [CrossRef]

24. Abir, M.; Tay, T.; Ridha, M.; Lee, H. Modelling damage growth in composites subjected to impact and compression after impact. *Compos. Struct.* **2017**, *168*, 13–25. [CrossRef]

25. He, W.; Lu, S.; Yi, K.; Wang, S.; Sun, G.; Hu, Z. Residual flexural properties of GFRP sandwich structures with aluminum honeycomb cores after low-velocity impact. *Int. J. Mech. Sci.* **2019**, *161*, 105026. [CrossRef]

26. He, W.; Yao, L.; Meng, X.; Sun, G.; Xie, D.; Liu, J. Effect of structural parameters on low-velocity impact behaviour of aluminium honeycomb sandwich structures with GFRP face sheets. *Thin-Walled Struct.* **2019**, *137*, 411–432. [CrossRef]

27. Crupi, V.; Epasto, G.; Guglielmino, E. Collapse modes in aluminum honeycomb sandwich panels under bending and impact loading. *Int. J. Impact Eng.* **2012**, *43*, 6–15. [CrossRef]

28. Sun, X.; Wisnom, M.R.; Hallett, S.R. Interaction of inter- and intralaminar damage in scaled quasi-static indentation tests: Part 2—Numerical simulation. *Compos. Struct.* **2016**, *136*, 727–742. [CrossRef]

29. Legrand, V.; Tranvan, L.; Casari, P.; Jacquemin, F. Structure-properties relationships of moisturized sandwich composite materials under extreme temperature conditions (fire resistance). *Compos. Struct.* **2020**, *235*, 111774. [CrossRef]
9. Legrand, V.; Pechev, S.; Létard, J.-F.; Guionneau, P. Synergy between polymorphism, pressure, spin-crossover and temperature in [Fe(PM-BiA)₂(NCS)₂]: A neutron powder diffraction investigation. *Phys. Chem. Chem. Phys.* **2013**, *15*, 13872–13880. [CrossRef]

10. Legrand, V.; Pillet, S.; Souhassou, M.; Lugan, N.; LeComte, C. Extension of the Experimental Electron Density Analysis to Metastable States: A Case Example of the Spin Crossover Complex Fe(btr)₂(NCS)₂·H₂O. *J. Am. Chem. Soc.* **2006**, *128*, 13921–13931. [CrossRef]

11. Rizk, G.; Legrand, V.; Khalil, K.; Casari, P.; Jacquemin, F. Durability of sandwich composites under extreme conditions: Towards the prediction of fire resistance properties based on thermo-mechanical measurements. *Compos. Struct.* **2018**, *186*, 233–245. [CrossRef]

12. Rizk, G.; Nahas, R.; Khalil, K.; Challita, G.; Legrand, V.; Casari, P.; Jacquemin, F. Durability of composite assemblies under extreme conditions: Thermomechanical damage prediction of a double-lap bonded composite assembly subject to impact and high temperature. *Compos. Struct.* **2019**, *213*, 58–70. [CrossRef]

13. Pering, G.A.; Farrell, P.V.; Springer, G.S. Degradation of tensile and shear properties of composites exposed to fire or high temperature. *J. Compos. Mater.* **1980**, *14*, 54–66.

14. Henderson, J.B.; Wiebelt, J.A.; Tant, M.R. A Model for the Thermal Response of Polymer Composite Materials with Experimental Verification. *J. Compos. Mater.* **1985**, *19*, 579–595. [CrossRef]

15. Gibson, A.; Wu, Y.S.; Chandler, H.W.; Wilcox, J.A.D.; Bettess, P. A Model for the Thermal Performance of Thick Composite Laminates in Hydrocarbon Fires. *Rev. De L'institut Français Du Pétrole* **1995**, *50*, 69–74. [CrossRef]

16. Mouritz, A.P.; Gibson, A.G. Fire properties of polymer composite materials. In *Solid Mechanics and its Applications*; Springer: Berlin/Heidelberg, Germany, 2006.

17. Lattimer, B.Y.; Ouellette, J.; Trelles, J. Thermal Response of Composite Materials to Elevated Temperatures. *Fire Technol.* **2011**, *47*, 823–850. [CrossRef]

18. Henderson, J.B.; Wiecek, T.E. A Mathematical Model to Predict the Thermal Response of Decomposing, Expanding Polymer Composites. *J. Compos. Mater.* **1987**, *21*, 373–393. [CrossRef]

19. Ramnath, B.V.; Alagarraja, K.; Elanchezhian, C. Review on Sandwich Composite and their Applications. *Mater. Today Proc.* **2019**, *16*, 859–864. [CrossRef]

20. Mouritz, A.; Feih, S.; Kandare, E.; Mathys, Z.; Gibson, A.; Jardin, P.D.; Case, S.W.; Lattimer, B. Review of fire structural modelling of polymer composites. *Compos. Part A Appl. Sci. Manuf.* **2009**, *40*, 1800–1814. [CrossRef]

21. Costa, J.P.M.; Legrand, V.; Fréour, S. Durability of Composite Materials under Severe Temperature Conditions: Influence of Moisture Content and Prediction of Thermo-Mechanical Properties During a Fire. *J. Compos. Sci.* **2019**, *3*, 55. [CrossRef]

22. McCracken, A.; Sadeghian, P. Partial-composite behavior of sandwich beams composed of fiberglass face sheets and woven fabric core. *Thin-Walled Struct.* **2018**, *131*, 805–815. [CrossRef]

23. Sabah, S.A.; Kueh, A.; Al-Fasih, M. Comparative low-velocity impact behavior of bio-inspired and conventional sandwich composite beams. *Compos. Sci. Technol.* **2017**, *149*, 64–74. [CrossRef]

24. Abir, M.; Tay, T.; Ridha, M.; Lee, H. Modelling damage growth in composites subjected to impact and compression after impact. *Compos. Struct.* **2017**, *168*, 13–25. [CrossRef]

25. He, W.; Lu, S.; Yi, K.; Wang, S.; Sun, G.; Hu, Z. Residual flexural properties of GFRP sandwich structures with aluminum honeycomb cores after low-velocity impact. *Int. J. Mech. Sci.* **2019**, *161*, 105026. [CrossRef]

26. He, W.; Yao, L.; Meng, X.; Sun, G.; Xie, D.; Liu, J. Effect of structural parameters on low-velocity impact behaviour of aluminium honeycomb sandwich structures with GFRP face sheets. *Thin-Walled Struct.* **2019**, *137*, 411–432. [CrossRef]

27. Crupi, V.; Epasto, G.; Guglielmino, E. Collapse modes in aluminum honeycomb sandwich panels under bending and impact loading. *Int. J. Impact Eng.* **2012**, *43*, 6–15. [CrossRef]

28. Sun, X.; Wisnom, M.R.; Hallett, S.R. Interaction of inter- and intralaminar damage in scaled quasi-static indentation tests: Part 2—Numerical simulation. *Compos. Struct.* **2016**, *136*, 727–742. [CrossRef]

29. Legrand, V.; Tranvan, L.; Casari, P.; Jacquemin, F. Structure-properties relationships of moisturized sandwich composite materials under extreme temperature conditions (fire resistance). *Compos. Struct.* **2020**, *235*, 111774. [CrossRef]
30. Ding, A.; Wang, J.; Ni, A.; Li, S. Assessment on the ageing of sandwich composites with vinylester-based composite faces and PVC foam core in various harsh environments. *Compos. Struct.* **2019**, *213*, 71–81.
[CrossRef]

31. Anjang, A.; Chevali, V.; Lattimer, B.; Case, S.; Feih, S.; Mouritz, A. Post-fire mechanical properties of sandwich composite structures. *Compos. Struct.* **2015**, *132*, 1019–1028. [CrossRef]

32. Florio, J.; Henderson, J.B.; Test, F.L.; Hariharan, R. A study of the effects of the assumption of local thermal equilibrium on the overall thermally-induced response of a decomposition, glass-filled polymer composite. *Int. J. Heat Mass Transf.* **1991**, *34*, 135–147. [CrossRef]

33. Anjang, A.; Chevali, V.; Feih, S.; Mouritz, A.; Anjang, A. Deterioration of the fire structural resistance of sandwich composite under tension due to water absorption. *Compos. Part A Appl. Sci. Manuf.* **2016**, *87*, 263–270. [CrossRef]

34. Feih, S.; Mathys, Z.; Gibson, A.G.; Mouritz, A.P. Modeling Compressive Skin Failure of Sandwich Composites in Fire. *J. Sandw. Struct. Mater.* **2008**, *10*, 217–245. [CrossRef]

35. Goodrich, T.; Nawaz, N.; Feih, S.; Lattimer, B.Y.; Mouritz, A.P. High-temperature mechanical properties and thermal recovery of balsa wood. *J. Wood Sci.* **2010**, *56*, 437–443. [CrossRef]

36. Buch, J.D. Thermal Expansion Behavior of a Thermally Degrading Organic Matrix Composite. In *Thermomechanical Behavior of High-Temperature Composites*; ASME Publication AD-04; ASME: New York, NY, USA, 1982.

37. Lattimer, B.Y.; Ouellette, J. Properties of composite materials for thermal analysis involving fires. *Compos. Part A Appl. Sci. Manuf.* **2006**, *37*, 1068–1081. [CrossRef]

38. Wolfram, S. An Elementary Introduction to the Wolfram Language. The Numerical Method of Lines. Available online: https://reference.wolfram.com/language/tutorial/NDSolveMethodOfLines.html (accessed on 15 September 2017).

39. Mouritz, A.; Mathys, Z. Post-fire mechanical properties of marine polymer composites. *Compos. Struct.* **1999**, *47*, 643–653. [CrossRef]

40. Mouritz, A.; Mathys, Z. Post-fire mechanical properties of glass-reinforced polyester composites. *Compos. Sci. Technol.* **2001**, *61*, 475–490. [CrossRef]

41. Theulen, J.; Peijs, T. Optimization of the bending stiffness and strength of composite sandwich panels. *Compos. Struct.* **1991**, *17*, 87–92. [CrossRef]

42. Lautenberger, C.; Fernandez-Pello, C. A model for the oxidative pyrolysis of wood. *Combust. Flame* **2009**, *156*, 1503–1513. [CrossRef]

43. Zhuge, J.; Gou, J.; Chen, R.-H.; Kapat, J. Finite element modeling of post-fire flexural modulus of fiber reinforced polymer composites under constant heat flux. *Compos. Part A Appl. Sci. Manuf.* **2012**, *43*, 665–674. [CrossRef]

44. Bai, Y.; Keller, T.; Vallé, T. Modeling of thermo-physical properties and thermal responses for FRP composites in fire. In Proceedings of the Asia Pacific Conference on FRP in Structures, Hong Kong, China, 12–14 December 2007.

45. Polyester Resins. Available online: http://www.exelcomposites.com/fi-fi/english/composites/rawmaterials/resins.aspx (accessed on 15 September 2017).

46. Goodrich, T.W. Thermophysical Properties and Microstructural Changes of Composite Materials at Elevated Temperature. Ph.D. Thesis, Faculty of the Virginia Polytechnic Institute and State University, Blacksburg, VA, USA, 2009.

47. Tranvan, L.; Legrand, V.; Jacquemin, F. Thermal decomposition kinetics of balsa wood: Kinetics and degradation mechanisms comparison between dry and moisturized materials. *Polym. Degrad. Stab.* **2014**, *110*, 208–215. [CrossRef]

48. Yu, B.; Post, N.L.; Lesko, J.J.; Keller, T. Experimental investigations on temperature-dependent thermo-physical and mechanical properties of pultruded GFRP composites. *Acta* **2008**, *469*, 28–35. [CrossRef]

49. Humeau, C.; Davies, P.; Jacquemin, F. An experimental study of water diffusion in carbon/epoxy composites under static tensile stress. *Compos. Part A Appl. Sci. Manuf.* **2018**, *107*, 94–104. [CrossRef]

50. de Parscau, B.; Jacquemin, F.; le Corre, S.; Lefébure, P. Characterization and modeling of the polymerization-dependent moisture absorption behavior of an epoxy carbon fibre reinforced composite material. *J. Compos. Mater.* **2016**, *50*, 2495–2505. [CrossRef]
30. Ding, A.; Wang, J.; Ni, A.; Li, S. Assessment on the ageing of sandwich composites with vinylester-based composite faces and PVC foam core in various harsh environments. *Compos. Struct.* **2019**, *213*, 71–81.
[CrossRef]

31. Anjang, A.; Chevali, V.; Lattimer, B.; Case, S.; Feih, S.; Mouritz, A. Post-fire mechanical properties of sandwich composite structures. *Compos. Struct.* **2015**, *132*, 1019–1028. [CrossRef]

32. Florio, J.; Henderson, J.B.; Test, F.L.; Hariharan, R. A study of the effects of the assumption of local thermal equilibrium on the overall thermally-induced response of a decomposition, glass-filled polymer composite. *Int. J. Heat Mass Transf.* **1991**, *34*, 135–147. [CrossRef]

33. Anjang, A.; Chevali, V.; Feih, S.; Mouritz, A.; Anjang, A. Deterioration of the fire structural resistance of sandwich composite under tension due to water absorption. *Compos. Part A Appl. Sci. Manuf.* **2016**, *87*, 263–270. [CrossRef]

34. Feih, S.; Mathys, Z.; Gibson, A.G.; Mouritz, A.P. Modeling Compressive Skin Failure of Sandwich Composites in Fire. *J. Sandw. Struct. Mater.* **2008**, *10*, 217–245. [CrossRef]

35. Goodrich, T.; Nawaz, N.; Feih, S.; Lattimer, B.Y.; Mouritz, A.P. High-temperature mechanical properties and thermal recovery of balsa wood. *J. Wood Sci.* **2010**, *56*, 437–443. [CrossRef]

36. Buch, J.D. Thermal Expansion Behavior of a Thermally Degrading Organic Matrix Composite. In *Thermomechanical Behavior of High-Temperature Composites*; ASME Publication AD-04; ASME: New York, NY, USA, 1982.

37. Lattimer, B.Y.; Ouellette, J. Properties of composite materials for thermal analysis involving fires. *Compos. Part A Appl. Sci. Manuf.* **2006**, *37*, 1068–1081. [CrossRef]

38. Wolfram, S. An Elementary Introduction to the Wolfram Language. The Numerical Method of Lines. Available online: https://reference.wolfram.com/language/tutorial/NDSolveMethodOfLines.html (accessed on 15 September 2017).

39. Mouritz, A.; Mathys, Z. Post-fire mechanical properties of marine polymer composites. *Compos. Struct.* **1999**, *47*, 643–653. [CrossRef]

40. Mouritz, A.; Mathys, Z. Post-fire mechanical properties of glass-reinforced polyester composites. *Compos. Sci. Technol.* **2001**, *61*, 475–490. [CrossRef]

41. Theulen, J.; Peijs, T. Optimization of the bending stiffness and strength of composite sandwich panels. *Compos. Struct.* **1991**, *17*, 87–92. [CrossRef]

42. Lautenberger, C.; Fernandez-Pello, C. A model for the oxidative pyrolysis of wood. *Combust. Flame* **2009**, *156*, 1503–1513. [CrossRef]

43. Zhuge, J.; Gou, J.; Chen, R.-H.; Kapat, J. Finite element modeling of post-fire flexural modulus of fiber reinforced polymer composites under constant heat flux. *Compos. Part A Appl. Sci. Manuf.* **2012**, *43*, 665–674. [CrossRef]

44. Bai, Y.; Keller, T.; Vallé, T. Modeling of thermo-physical properties and thermal responses for FRP composites in fire. In Proceedings of the Asia Pacific Conference on FRP in Structures, Hong Kong, China, 12–14 December 2007.

45. Polyester Resins. Available online: http://www.exelcomposites.com/fi-fi/english/composites/rawmaterials/resins.aspx (accessed on 15 September 2017).

46. Goodrich, T.W. Thermophysical Properties and Microstructural Changes of Composite Materials at Elevated Temperature. Ph.D. Thesis, Faculty of the Virginia Polytechnic Institute and State University, Blacksburg, VA, USA, 2009.

47. Tranvan, L.; Legrand, V.; Jacquemin, F. Thermal decomposition kinetics of balsa wood: Kinetics and degradation mechanisms comparison between dry and moisturized materials. *Polym. Degrad. Stab.* **2014**, *110*, 208–215. [CrossRef]

48. Yu, B.; Post, N.L.; Lesko, J.J.; Keller, T. Experimental investigations on temperature-dependent thermo-physical and mechanical properties of pultruded GFRP composites. *Acta* **2008**, *469*, 28–35. [CrossRef]

49. Humeau, C.; Davies, P.; Jacquemin, F. An experimental study of water diffusion in carbon/epoxy composites under static tensile stress. *Compos. Part A Appl. Sci. Manuf.* **2018**, *107*, 94–104. [CrossRef]

50. de Parscau, B.; Jacquemin, F.; le Corre, S.; Lefébure, P. Characterization and modeling of the polymerization-dependent moisture absorption behavior of an epoxy carbon fibre reinforced composite material. *J. Compos. Mater.* **2016**, *50*, 2495–2505. [CrossRef]
51. Youssef, G.; Fréour, S.; Jacquemin, F. Stress-dependent Moisture Diffusion in Composite Materials. *J. Compos. Mater.* **2009**, *43*, 1621–1637. [CrossRef]

52. Legrand, V.; Tranvan, L.; Jacquemin, F.; Casari, P. Moisture-uptake induced internal stresses in balsa core sandwich composite plate: Modeling and experimental. *Compos. Struct.* **2015**, *119*, 355–364. [CrossRef]

53. Sand, U.; Sandberg, J.; Larfeldt, J.; Fdhila, R.B. Numerical prediction of the transport and pyrolysis in the interior and surrounding of dry and wet wood log. *Appl. Energy* **2008**, *85*, 1208–1224. [CrossRef]

54. Grönli, M. A Theoretical and Experimental Study of the Thermal Degradation of Biomass. Ph.D. Thesis, NTNU Norges Teknisk-Naturvitenskaplige Universitet, Trondheim, Norway, 1996.

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

<figure><img src="image_28.png" /></figure>

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
51. Youssef, G.; Fréour, S.; Jacquemin, F. Stress-dependent Moisture Diffusion in Composite Materials. *J. Compos. Mater.* **2009**, *43*, 1621–1637. [CrossRef]

52. Legrand, V.; Tranvan, L.; Jacquemin, F.; Casari, P. Moisture-uptake induced internal stresses in balsa core sandwich composite plate: Modeling and experimental. *Compos. Struct.* **2015**, *119*, 355–364. [CrossRef]

53. Sand, U.; Sandberg, J.; Larfeldt, J.; Fdhila, R.B. Numerical prediction of the transport and pyrolysis in the interior and surrounding of dry and wet wood log. *Appl. Energy* **2008**, *85*, 1208–1224. [CrossRef]

54. Grönli, M. A Theoretical and Experimental Study of the Thermal Degradation of Biomass. Ph.D. Thesis, NTNU Norges Teknisk-Naturvitenskaplige Universitet, Trondheim, Norway, 1996.

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

<figure><img src="image_29.png" /></figure>

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).