Comparative study of three cellular materials under
blast and sustained shock wave

David Drouet, Jean-Luc Hanus, Damien Laporte, Gaëtan Prod'homme,
Ludovic Blanc, Steven Kerampran, Julien Le-Clanche, Michel Arrigoni

► To cite this version:

David Drouet, Jean-Luc Hanus, Damien Laporte, Gaëtan Prod'homme, Ludovic Blanc, et al. Comparative study of three cellular materials under blast and sustained shock wave. International Journal of Impact Engineering, 2025, 207, pp.105509. 10.1016/j.ijimpeng.2025.105509. hal-05304525

HAL Id: hal-05304525

https://hal.science/hal-05304525v1

Submitted on 21 Oct 2025

**HAL** is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

# Comparative study of three cellular materials under blast and sustained shock wave

David Drouet<sup>a,b,*</sup> <sup>IDI</sup>, Jean-Luc Hanus<sup>b</sup> <sup>IDI</sup>, Damien Laporte<sup>c</sup>, Gaëtan Prod'homme<sup>d</sup>, Ludovic Blanc<sup>f</sup> <sup>IDI</sup>, Steven Kerampran<sup>e</sup>, Julien Le-Chanche<sup>e</sup>, Michel Arrigoni<sup>e</sup>

## ARTICLE INFO

### Key words:

Cellular material

Shock tube

Blast

Insulation

Attenuation

Protection

## ABSTRACT

This study investigates the mechanical response of three cellular materials—polyisocyanurate (PIR), autoclaved aerated concrete (AAC), and Aluminum Lightweight Foam (ALF, Nufoam® 140)—under blast and shock loading conditions. The research aims to provide experimental data for optimizing building protection against explosion hazards. Laboratory-scale tests were conducted using a shock tube to generate blast and sustained shock waves. The materials' responses were analyzed using high-speed imaging and digital image correlation.

Results indicate that PIR exhibits significant deformation under sustained shocks but shows recovery under blast loading. AAC demonstrates erosion-based energy dissipation, with material loss concentrated at the extremities. ALF, serving as a reference, shows excellent mechanical energy dissipation. The study highlights the potential of these materials for applications requiring both thermal insulation and blast resistance, contributing to the development of predictive tools and larger-scale experiment designs.

## 1. Introduction

In the field of industrial safety, the protection of existing and future buildings and their occupants from explosion hazards and specifically from blast wave loading has been a significant issue since the advent of the industrial era. Initially those concerns emerge with first dust or gas explosions in mines and then with significant accidents at SEVESO sites. Major disasters, such as the Tianjin explosion [1] and the destructive explosion in Beirut [2], have underscored the importance of blast protection.

With increasing urban management of industrial risks and the growing need for citizen and building protection against malicious explosions, many construction projects are being undertaken. These projects require guidelines and recommendations to optimize protection while minimizing financial and environmental impacts.

Current structural and architectural recommendations focus on protecting people and minimizing damage from accidental explosions [3]. However, these guidelines primarily apply to new buildings. For

existing structures, various renovation techniques have been proposed, including reinforcing load-bearing elements with composite materials [4], using perimeter walls [5], and employing composite sandwich panels [6] or wood panel filled-up with sand [7]. In addition to those solutions, the dispersion of aqueous foams has been suggested as a non-permanent solution to improve mitigation of secondary blast [8,9].

Often derived from military practices, these techniques call on cutting-edge technologies and present a high cost/effectiveness ratio. To optimize these protection costs, it is appropriate to take advantage of state programs to enhance the energetic renovation of existing buildings and evaluate technical solutions that meet both requirements, energetic performance and blast resistance of existing buildings in exposed areas. Many building energy efficiency codes set requirements for insulation of the building envelope [10–12]. Building insulation relies on the use of aerated materials, which also have the property of being able to absorb a significant proportion of the blast energy by compaction.

Such technical cladding can be seen as sacrificial coatings and is the most widely studied technological solution. These single- or double-skin

<footnote><sup>a</sup> Univ. Bretagne Sud, IRDL, UMR CNRS 6027, 56100 Lorient, France</footnote>

<footnote><sup>b</sup> LaMé - INSA CVL, Univ. Orléans, Univ. Tours, 88 boulevard Lahitolle, 18022 Bourges Cedex, France</footnote>

<footnote><sup>c</sup> NUVIA, 85 Avenue Archimède, 13857 Aix-en-Provence, Cedex 03 - France</footnote>

<footnote><sup>d</sup> Ineris, 88 Bvd Lahitolle, 18020, Bourges Cedex, France</footnote>

<footnote><sup>e</sup> ENSTA, IRDL UMR 6027 CNRS, 2, rue François Verny, 29806 Brest Cedex 9, France</footnote>

<footnote><sup>f</sup> ISL, 5 Rue du Général Cassagnou, 68300 Saint-Louis, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: david.drouet@st-cyr.terre-net.defense.gouv.fr (D. Drouet).</footnote>
claddings comprise a compactable core sandwiched between one or two metal plates. The plates distribute stress and increase bending stiffness, while the core, usually made of cellular material, absorbs energy by deformation, buckling, or compaction [13–16]. An economical solution for combining protection and energy efficiency could be to use cellular materials such as those used for thermal insulation.

Building insulation traditionally depends on a limited set of materials, which have seen property improvements over time. Emerging solutions now offer comparable or superior performance in overall environmental balance, considering the entire life cycle. However, their adoption in Europe remains limited [17].

Mineral wools dominate the building renovation market due to their superior fire resistance. However, materials like polyisocyanurate (PIR) show superior thermal properties and fire resistance. These properties drive strong growth and replace older polymers like polystyrene and polyurethane [17]. PIR also starts to serve as core material in sandwich panels [18]. In parallel, Autoclaved Aerated Concrete (AAC) is gaining popularity in the new building industry, offering both structural and insulation functions. AAC's incombustible nature and ability to absorb blast and fragment impacts have led to recommendations for its use in ammunition depots [19]. This measure helps prevent sympathetic detonation. For renovation applications, where the existing building provides the primary structure, lighter, non-structural, and better insulating AAC versions are preferred [20]. Although the quasi-static properties of these recent ultra-light materials are well understood, their dynamic properties and energy-absorbing performances need further investigation.

This study addresses this gap by creating an experimental dataset. This dataset describes the mechanical response of commercially available high-performance insulating materials to explosive-type stresses, in both near-field and far-field contexts. The resulting mechanical responses will aid in selecting materials for blast mitigation. This study includes Aluminum Foam (ALF) to establish a baseline for mechanical performance. Although ALF is not an insulator, its behavior as a metallic foam is well-documented for shock absorption. This behavior provides a reference [21–23].

As part of a collaboration between LaMé INSA CVL, Bourges, France with IRDL ENSTA, Brest, France for near-field experiments and ISL, Saint Louis, France with INERIS, Bourges, France for far-field experiments, this paper focuses on laboratory-scale tests at LaMé INSA CVL, and IRDL ENSTA, for the material's near-field response. The first part describes the materials selected and the evaluation of their mechanical properties. Then, in the second part, the shock tube configuration for blast or sustained shock is explained. The third part details the material's response to the blast and sustained shock experiments. It examines the experimental data, compares the interaction of the material with the shock waves and highlights some of the limitations of this experiment.

## 2. Materials

This section details the three selected materials: Aluminum Lightweight Foam (ALF), polyisocyanurate (PIR), and autoclaved aerated concrete (AAC). It focuses on their main physical properties, with particular attention to evaluating their mechanical properties.

### 2.1. Aluminum lightweight foam (ALF)

ALF (Nufoam® 140) is a lightweight aluminum foam designed for mechanical energy dissipation. With a density of 144.8 ± 3.3 kg/m³, it exhibits a mechanical behavior similar to that described by Barthélémy et al. [24] and Hanssen et al. [25]. Due to its excellent shock absorption capabilities, ALF serves as the reference material in this study. However, with a thermal conductivity of 0.8–1 W/mK, it is not intended for insulation applications. The material's 15 mm average cell size plays a crucial role in its mechanical behavior, affecting strain localization and energy dissipation.

### 2.2. Polyisocyanurate (PIR)

Polyisocyanurate (PIR) is a lightweight, closed-cell polymer foam known for its excellent thermal insulation and energy absorption properties. Manufactured by Recticel (Bourges, France) under the Fitorall® brand, it is available as foam panels with 0.2 mm aluminum outer foils. From a morphological point of view, it is a rigid, closed-cell polymer foam with a cell size of around a tenth of a millimeter. With a low density of 29.55 ± 0.97 kg/m³ and very low thermal conductivity (0.022 W/mK), PIR is one of the most efficient and cost-effective insulators used in construction.

### 2.3. Autoclaved aerated concrete (AAC)

Autoclaved Aerated Concrete (AAC) is a lightweight, porous cementitious material engineered for thermal insulation and energy dissipation. It consists of sand, limestone cement, and water, with aluminum powder added to generate hydrogen bubbles. These bubbles create a porous structure, which becomes stable after autoclave curing.

Due to its ability to dissipate energy when crushed, AAC is a promising candidate for blast protection. Mespoulet, on denser AAC (550 kg/m³) demonstrated an increased compressive strength under dynamic loading [26]. Liu et al. [27] highlighted its Dynamic Increase Factor (DIF) of 1.2 to 1.8 at strain rates exceeding 10 s⁻¹, attributing this to micro-inertia effects and gas flow between cells, forming a gas cushion that dampens impact forces. Recognizing its protective capabilities, the British Ministry of Defense has integrated AAC into ammunition storage facilities [28,19], and researchers have explored its use in sacrificial cladding [29,30].

For this study, we selected Multipor® AAC, manufactured by Xella Thermopierre (Stulln, Germany). With a high porosity, it achieves a low thermal conductivity of 0.045 W/mK and a density of 108.7 ± 2.3 kg/m³. The mortar's volumetric mass of 1859 kg/m³ results in a relative density of 6 %, classifying it as a cellular material [31]. The average cell size is 1.58 mm, and as a ceramic material, it offers excellent fire resistance.

### 2.4. Mechanical properties in compression

The compressive stress-strain curves for foams, irrespective of the skeleton material, exhibit three distinct regimes: (i) a linear elastic region characterized by reversible deformations, (ii) a non-linear behavior with a plateau region where the material undergoes crushing, and (iii) a densification region where the material's compaction capacity is exceeded, leading to significant stiffening [31]. Several parameters are used to characterize the mechanical response in these three stages. The Young's modulus (E) is evaluated at the transition from reversible to compaction behavior. At this transition, the elastic limit, yield stress (σy), and corresponding yield strain (εy) are also evaluated. The plateau stress (σp) represents the average stress experienced during the plateau regime, while the densification strain (εD) marks the point beyond which the cellular foam material continues to absorb energy, albeit with a very rapid increase in stress.

To determine the densification strain and plateau stress in an objective manner, we employed the energetic efficiency approach [32]. During the foam compression, the energy absorbed per unit volume is the area under the stress-strain curve. The energy absorption efficiency parameter, η(ε), is defined as the energy absorbed per unit volume divided by the corresponding stress value.

$$ \eta(\epsilon) = \frac{1}{\sigma(\epsilon)} \int_{\epsilon_y}^{\epsilon} \sigma(\xi) \, d\xi \quad (1) $$

The onset strain of densification (εD) is defined as which this efficiency has a global maximum. We then evaluated the plateau stress σp
between the specified values.

$$ \sigma_p = \frac{\int_{\varepsilon_y}^{\varepsilon_D} \sigma(\xi) d\xi}{\varepsilon_D - \varepsilon_y} \qquad (2) $$

PIR characterization is partially built on previous work by El Yamani [33], while additional experimental data on AAC [28] and ALF were obtained in this study.

We performed displacement-controlled compression tests using a MTS electromechanical machine equipped with a 5 kN load cell. We conducted at least three replications for each material. We deduced the mean compressive strain from the relative displacement of the two loading platens. To minimize friction effects, we applied a Teflon dry lubricant at the interfaces between platens and specimen.

During compression tests, we recorded a sequence of high-resolution images of the front surface. These images captured the front surface spray-painted with a black and white speckle pattern. We post-processed these images using Digital Image Correlation (DIC) with CorreliSTC [34]. DIC enables access to full-field displacements and strains at the specimen surfaces. It also helps localize strain concentration zones during the compression plateau phase.

In the early stages of deformation, we used the DIC strain field to cross-validate strain measurements. These measurements were obtained via press displacement sensors (Eng. Strain). We also assessed strain homogeneity to evaluate the material's elastic properties.

Before each compression test, we measured and weighed the samples to determine their density in kg/m³. For AAC, we followed the EN 1352 standard [35] to measure the Young's modulus (E) independently of pseudo-elasticity. We also noted the elastic limit and corresponding yield strain.

Table 1 and Fig. 1 summarize the key mechanical properties of the three foams. Although these materials exhibit similar strength levels, they offer insights into three distinct compaction mechanisms and shock wave interactions.

Based on loading and unloading curves, the Young's modulus of ALF was measured at 57.7 MPa, while the yield strength reached 0.26 ± 17 % MPa. Below the yield strain (2 ± 0.4 %), ALF exhibits pseudo-elastic behavior, meaning it can undergo a moderate amount of irreversible deformation before entering the plasticity.

PIR exhibits transverse isotropy, characterized by a Young's modulus of 10.9 MPa in the out-of-plane direction (foam growth) and 4.2 MPa in the orthogonal direction. Under compression, the material follows a weakly strain-rate-dependent behavior, with a quasi-static stress plateau of 0.24 MPa. Due to its very low thermal conductivity (0.022 W/mK), PIR is one of the most efficient and cost-effective insulators used in construction.

The mechanical properties of AAC change with varying humidity levels [36,37]. This study focuses on dry AAC. Following NF-EN-1352 standards [35], the quasi-static Young's modulus was measured at 82.9 ± 3.9 % MPa. The tangent modulus, estimated from the reloading phase of the stress-strain curve, reached 131.6 ± 3.1 % MPa, indicating viscoelastic behavior. Yield stress was measured at 0.217 ± 4.8 % MPa, with pseudo-elasticity observed for strains below 1 ± 0.3 %. Samples were unconfined (L/D = 2), showing localized fracture initiation at the upper end, later forming an hourglass shape as Eng. strain exceeded 80 % densification strain.

<caption>Table1</caption>

Summary of materials mean parameters: heat conductivity coefficient (K), density (ρ), Young modulus (E), yield strain (ε<sub>y</sub>), yield stress (σ<sub>y</sub>), densification strain (ε<sub>D</sub>) and plateau stress (σ<sub>p</sub>).

<table><thead><tr><th></th><th>K (W/mK)</th><th>ρ<br>(kg/m3)</th><th>E<br>(MPa)</th><th>ε<sub>y</sub><br>(%)</th><th>σ<sub>y</sub><br>(MPa)</th><th>ε<sub>D</sub><br>(%)</th><th>σ<sub>p</sub><br>(MPa)</th></tr></thead><tbody><tr><td>ALF</td><td>0.8–1</td><td>145</td><td>57.7</td><td>2</td><td>0.26</td><td>52</td><td>0.26</td></tr><tr><td>PIR</td><td>0.022</td><td>29.5</td><td>10.9</td><td>3</td><td>0.20</td><td>63</td><td>0.24</td></tr><tr><td>AAC</td><td>0.045</td><td>109</td><td>82.9</td><td>1</td><td>0.22</td><td>74</td><td>0.095</td></tr></tbody></table>

### 3. Experimental setup

This study employs a shock tube with an 80 × 80 mm² square cross-section to generate two types of shock waves:

1. Blast waves, using a 40 mm long driver section.

2. Sustained shock waves, created with a 920 mm long driver section.

A Mylar film of varying thickness separates the high-pressure driver section from the low-pressure driven section, controlling the pressure differential required for the tests.

#### 3.1. Pressure measurement

Pressure measurements were recorded using PCB® 113B21 piezoelectric sensors [38] placed at the end of the driven section (Fig. 2). These sensors feature a 400 kHz bandwidth and a 2.5 µs rise time, ensuring high-frequency response.

The signals were processed through a PCB® 482C05 conditioner, then sampled using a National Instruments® PXIe-1073 system, equipped with a PXIe-5105 digitizer [39]. This acquisition system operates at 12-bit resolution with a sampling rate of 10 M Sample/s and is triggered by the rising edge of sensor C1 (Fig. 2).

#### 3.2. Data acquisition

A Photron® Nova S-9 high-speed camera [40] captured the shock-specimen interaction at 50,000 frames per second (fps) with a 384 × 352-pixel resolution.

To ensure full visibility of the front and back faces of the sample, 75 mm-long wood spacers were positioned at the tube's end. A transparent protective layer was placed between the specimen and the tube wall to prevent window abrasion from AAC and ALF particles. However, this slightly reduced the effective cross-section of AAC and ALF samples from 80 × 80 mm² to 71 × 71 mm².

The interface between the shock tube walls and the samples allows for sufficient space for air, introducing a non-axial load that is visible in some PIR samples. Due to some sample collapse connected to this three-dimensional loading, some tests, considered as unrepresentative of sustained shock conditions, were eliminated.

We post-processed the sequence of images of the speckled lateral surface of the specimen using PyDic software [41]. This DIC post-processing enabled us to evaluate displacement and strain fields at different stages of specimen deformation. Fig. 3 shows an example of the grid used. We measured the relative displacements of the sample's front and rear interfaces over time. By eliminating rigid body motion from sample rebound against the tube's rear face, we obtained mean Eng. strain measurements. These measurements are shown in Fig. 3.

We can take advantage of these measurements from DIC get an estimation of the stress transmitted by the foam, in the absence of a force sensor on the rear face. Thanks to the previously identified mechanical response in compression (Fig.1), the mean Eng. strain can be used to evaluate a mean stress applied during the foam compaction. The measured transient axial displacement fields developed in the specimens during dynamic compaction can be used to calculate the transient axial acceleration field throughout the specimen. Employing a non-parametric approach [42], previously utilized in impact shock tube experiments with polymer foams by Koohbor et al. [43], the pressure on the back face can be reconstructed. This is achieved by knowing the loading on the front face estimated with sensor C5 and reconstructing the inertia stress within the specimen from full-field displacement data, as follows:

$$ P_{BF}(t) = P_{FF}(t) + \int_{x=0}^{x=L} \rho(x, t) \frac{\partial^2 u_x(x, t)}{\partial t^2} dx \qquad (3) $$
<figure><img src="image_3.png" /><figcaption>Fig. 1. Engineering stress response in quasi-static regime along the Engineering strain for ALF (145 kg/m³) in red, PIR (29.5 kg/m³) in green, and AAC (109 kg/m³) in blue. These curves reflect the ability of the three materials to dissipate energy post-failure.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 2. Schematic view of the position of the sensors in the test section of the shock tube. For the dimensions of the shock tube, the high-pressure chamber used for the blast is 40 mm long, and the test section is 3720 mm long.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Image capture for digital image correlation. The PyDic grid is highlighted in purple and the yellow sub grids are used to compute a mean Eng. strain.</figcaption></figure>

Here, $P_{BF}(t)$ represents the pressure at the back face at time $t$, $P_{FF}(t)$ represents the pressure at the front face at time $t$, $\rho(x, t)$ is the density at time $t$, and $u_x(x, t)$ is the longitudinal displacement along the tube axis at time $t$. Assuming a uniaxial longitudinal strain state, the current density distribution is deduced as $(x, t) = \rho_0/(1+\epsilon(x, t))$.

To illustrate this method, we submitted a PIR sample to a blast wave. This material exhibits a low mechanical wave speed of approximately 600 m/s, resulting in a delayed dynamic equilibrium. Using the method

outlined by Koohbor [43] with the pressure reading from sensor C5, we reconstructed the stress at the sample's interface, as shown in Fig. 4. The evaluated pressure at the back surface shows a sharp rise 0.17 ms after the shock at front face. This initial delay is fully consistent with the transit time through a 100 mm sample with a uniaxial wave speed of 608 m/s deduced from the PIR density and Young's modulus. The blue curve then indicates that the Koohbor method reconstructs the stress on the back face as an oscillation of the stress recorded by C5. These oscillations
<figure><img src="image_6.png" /><figcaption>Fig. 4. Input and output pressure for a PIR sample (08/17/2022 04) under blast wave loading.</figcaption></figure>

are consistent with several rounds of reflections in specimen for stress wave to “ring up” to a state of stress equilibrium. Some spikes can be attributed to the use of second order derivatives of noisy displacements with a high framing rate and without initial smoothing [43].

### 3.3. Signal analysis

The shock tube generates two distinct pressure profiles, as illustrated in Fig. 5:

1. Blast waves are characterized by a sharp pressure rise followed by exponential decay, leading to a negative pressure differential. As the blast wave impacts the sample, a reflected pressure wave forms, generating a secondary pressure rise for the five sensors (Fig. 5-a). Due to exponential decay, sensors closer to the sample record a greater cumulative pressure rise. The signal parameters—including overpressure, arrival time, and positive phase duration—were identified using a Friedlander waveform [44].

2. Sustained shock waves begin with a sharp rise (Fig. 5-b), followed by a near-constant pressure plateau termed the Hugoniot state, reflecting the equilibrium of the incident supersonic flow. The initial pressure peak occurs as the shock wave reaches the sensor, and the second peak arises from the reflected wave at the sample's interface.

<figure><img src="image_7.png" /><figcaption>Fig. 5. Pressure records from C1 to C5. (a) shows the blast wave configuration applied to a PIR sample (08/17/2022 04). (b) shows a sustained shock wave configuration applied to an ALF sample (01/26/2023 04).</figcaption></figure>

Both incident and reflected pressure levels were recorded for each sample. This loading type carries more energy than a blast wave, it effectively simulates industrial gas explosions and offers valuable insights into energy dissipation mechanisms in materials.

During the loading phase, with an incoming airflow velocity of approximately 300 m/s, the C5 sensor does not fully capture the dynamic pressure contribution. However, as the reflected airflow velocity is governed by interface displacement, it gradually decreases and eventually drops to zero when the material becomes fully compacted. At this point, the static pressure measured by C5 (violet curve in Fig. 5) provides a reliable approximation of the actual pressure applied to the sample interface at the end of the loading phase.

Fig. 5(b) shows sensor pressure readings for an ALF sample with tube protection. The first pressure increase occurs when the incoming shock wave reaches the sensor, followed by a second increase caused by the first reflected shock wave returning from the sample's interface. Unexpectedly, a more gradual pressure increase or a second reflected compressive wave is also visible.

<figure><img src="image_8.png" /><figcaption>Fig. 6. The foam sample subjected to the sustained shock undergoes rapid compression, culminating in deceleration while reaching the compaction limit. This deceleration, from 85 m/s to 0 in 300 µs can create a second reflected compressive wave that propagates towards sensors C5, C2 and C1.</figcaption></figure>

<figure><img src="image_9.png" /></figure>
Fig. 6 provides an explanation for this second reflection, illustrating the time-position graph of the sample’s interface interacting with the sustained shock.

When sensor C5 detects the first reflection as a shock wave, the second reflection may appear as a compressive wave, signaling the end of the compression phase and indicating that the material has reached its compacted state. This phenomenon resembles a hydrodynamic ‘ram’ effect, similar to when water flow is abruptly halted.

A third pressure increase may sometimes occur, but since it happens after full sample compression, it is not considered in this study.

For each sensor recording in the blast signal, the pressure evolution follows a Friedlander waveform [44]. The time-dependent pressure profile is given by Eq. (3), where:

* $P_0$ is the atmospheric pressure,

* $t_d$ is the positive phase duration,

* $t_a$ is the time marking the start of pressure rise,

* $P_s$ is the peak pressure,

* $\lambda$ is the time constant.

$$P(t) = P_0 + \left(1 - \frac{t - t_a}{t_d}\right) P_s e^{-\frac{t - t_a}{t_d}}, \quad t_a < t < t_a + t_d \quad (4)$$

The positive impulse $I^+$ is then given by Eq. (4):

$$I^+ = t_d \frac{P_s}{\lambda} \left(1 + \frac{e^{-\lambda} - 1}{\lambda}\right) [N.s/m^2] \quad (5)$$

Fig. 7 compares the peak overpressure and positive impulse of 1 kg of TNT with those identified from the Friedlander signal from sensor C1 during each test of our blast wave campaign. It reveals that the current configuration does not allow both the peak pressure and the positive impulse to be equally representative of a scaled distance for the TNT equivalent. Since the peak pressure equivalent shows a monotonous evolution, it will be preferred over the impulse equivalence.

Based on the peak pressure ($P_s$) and positive impulse ($I^+$), Fig. 8 provides an overview of the blast tests conducted with ALF, PIR, and AAC. The tests fit a linear relationship that depends on the geometry of the shock tube and the gas within it. A more detailed overview, including sustained shocks, is presented in the annexes.

## 4. Results

The results are divided into two categories:

1. Blast Loading: The blast pressure signal provides peak pressure and positive impulse values related to the scaled distance of 1 kg eq. TNT.

2. Sustained Shock Loading: Sustained shocks induce higher deformations, making them useful for material behavior modeling.

For all three materials, PyDic software [41] was used to extract displacement data from the whole surface of the specimen and especially from the front and rear edges of the samples for an evaluation of mean Eng. strain. Since no direct force measurement was available, analysis mainly focused on pressure sensor readings and sample compaction responses. This section presents the results for ALF (Aluminum Lightweight Foam – Nufoam® 140), AAC (Autoclaved Aerated Concrete – Multipor®) and Polyisocyanurate Foam (PIR – Fitforall®).

### 4.1. Aluminum lightweight foam (ALF)

ALF is an aluminum lightweight foam (144.8 ± 3.3 % kg/m³) with high energy dissipation capacity but low thermal insulation properties. It serves as the reference dissipative material for comparison with the two thermal insulators.

#### 4.1.1. Blast response

Fig. 9 illustrates the strain response of ALF under blast loads of comparable intensities. Using DIC for strain and strain rate measurements, it reveals three distinct phases: initial strain growth driven by the blast front, occurring at an unsteady strain rate of 10 to 50 s⁻¹; a plateau phase where deformation stabilizes in some tests; and an elastic recovery phase, where the sample partially returns to its initial length before reaching its final slightly compacted state.

Notably, none of the tests produced a reflected pressure of 0.26 MPa, the threshold needed to reach ALF’s yield stress, which equates to a scaled distance of 2.8 m for 1 kg TNT [3]. Despite similar pressure profiles, variability in response is likely due to pore size effects. The pores are polydispersed, with diameters up to 15 mm, relative to a 71 × 71 mm² sample size. The pseudo-elastic behavior of the foam matrix also affects the response, as local plastic deformations adapt to the support surface while the rest of the sample remains elastic. Consequently, ALF demonstrates pseudo-elastic behavior, but the occurrence of the compaction response may vary due to polydispersed pores and localized plasticity effects.

<figure><img src="image_10.png" /><figcaption>Fig. 7. Peak pressure and positive impulse of the blast tests conducted in the shock tube to the UFC (2008) data for 1 kg eq. TNT.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig. 8. For the three material, this plot summarizes the overpressure ($P_s$) and positive impulsion ($I^+$) identified on blast tests.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 9. Pressure recorded by sensor five near the ALF interface, synchronized with the corresponding Eng. strain recorded by the camera for three blasts on ALF. For comparison with the pressure signals, the material’s yield stress is added as a black horizontal line. The three tests shown correspond to IDs: 01/25/2023 06 for Strain 1, sample 01/25/2023 07 for Strain 2, and 01/26/2023 01 for Strain 3 from Table 2.</figcaption></figure>

As previously emphasized, an estimation of the transmitted pressure can be obtained from the mean Eng. Strain or evaluated from the front loading taking into inertia stresses within the specimen using the full-field displacement and deformation response (Eqn. (3)) (Fig. 10).

The reconstructed stress at the sample's interface, is shown in Fig. 9.

<figure><img src="image_13.png" /><figcaption>Fig. 10. Input and output pressures for a ALF sample under blast wave loading.</figcaption></figure>

The evaluated pressure at the back surface shows a sharp rise 0.1 ms after the shock at front face. This initial delay remains consistent with the transit time through a 75 mm sample with a uniaxial wave speed of 630 m/s deduced from the ALF density and Young's modulus. Some oscillations are observed and again explained by the need of several round-trips in specimen before stress equilibrium. The test shown correspond to ID 01/25/2023 06 from Table 2.

### 4.1.2. Sustained shock response

Fig. 11 compares the strain evolution of ALF in two sustained shock tests. The reflected shock pressure exceeds the material's yield strength (0.26 MPa), leading to permanent deformation, where the material deforms by approximately 25 %. DIC analysis reveals that both tests exhibit similar strain evolution, with maximum strain rates of 420 s⁻¹ for Shot 1 and 407 s⁻¹ for Shot 2. Finally, in the pressure signal, the end of compaction is marked by a gradual increase of overpressure between 3.5 and 4.5 ms.

During the manufacturing process of ALF, aluminum accumulates at the front and rear ends of the sample, forming a denser skin. This skin layer initially distributes the load over the foam cells, making the material's optimal usage direction orthogonal to these skins.

Fig. 12(a) highlights the position of these skins in the sample (el-lipse). Moving toward the center, cell walls become thinner, leading to localized deformation initiation at the core. Deformation then remains confined to a plane orthogonal to the loading axis (Fig. 12(b-c-d)).
<caption>**Table 2**</caption>

Summary of the experimental test matrix. The table lists all shock tube tests conducted, categorized by material (ALF, PIR, AAC) and loading type (blast or sustained shock). Key parameters such as test date, sample ID, overpressure, and shock speed are provided for each test. A total of 8 tests were performed on ALF (6 blast, 2 sustained), 20 on PIR (14 blast, 6 sustained), and 21 on AAC (20 blast, 1 sustained).

<table><thead><tr><th>ID</th><th>ΔP (bar)</th><th>Speed (m/s)</th><th>Type</th><th>Material</th><th>Figure</th></tr></thead><tbody><tr><td>01/26/2023 01</td><td>0.89</td><td>464</td><td>Blast</td><td>ALF</td><td>9(3), 24</td></tr><tr><td>01/26/2023 02</td><td>0.90</td><td>465</td><td>Blast</td><td>ALF</td><td>10</td></tr><tr><td>01/26/2023 03</td><td>0.90</td><td>464</td><td>Blast</td><td>ALF</td><td></td></tr><tr><td>01/25/2023 05</td><td>1.01</td><td>480</td><td>Blast</td><td>ALF</td><td></td></tr><tr><td>01/25/2023 06</td><td>0.99</td><td>477</td><td>Blast</td><td>ALF</td><td>9(1), 10, 25</td></tr><tr><td>01/25/2023 07</td><td>0.98</td><td>473</td><td>Blast</td><td>ALF</td><td>9(2)</td></tr><tr><td>01/26/2023 04</td><td>1.81</td><td>564</td><td>Sustained shock</td><td>ALF</td><td>5(b), 11, 13, 14, 27</td></tr><tr><td>01/26/2023 05</td><td>1.60</td><td>544</td><td>Sustained shock</td><td>ALF</td><td>11, 12, 14</td></tr><tr><td>08/18/2022 09</td><td>0.457</td><td>409</td><td>Blast</td><td>PIR</td><td></td></tr><tr><td>08/18/2022 10</td><td>0.446</td><td>408</td><td>Blast</td><td>PIR</td><td></td></tr><tr><td>08/18/2022 11</td><td>0.462</td><td>409</td><td>Blast</td><td>PIR</td><td></td></tr><tr><td>08/17/2022 04</td><td>1.116</td><td>484</td><td>Blast</td><td>PIR</td><td>4, 5(a), 15(2), 25</td></tr><tr><td>08/18/2022 05</td><td>1.163</td><td>493</td><td>Blast</td><td>PIR</td><td></td></tr><tr><td>08/18/2022 06</td><td>1.103</td><td>485</td><td>Blast</td><td>PIR</td><td></td></tr><tr><td>08/18/2022 07</td><td>0.842</td><td>456</td><td>Blast</td><td>PIR</td><td>15(3), 24</td></tr><tr><td>08/18/2022 08</td><td>0.681</td><td>438</td><td>Blast</td><td>PIR</td><td>16</td></tr><tr><td>08/18/2022 09</td><td>0.753</td><td>446</td><td>Blast</td><td>PIR</td><td></td></tr><tr><td>08/18/2022 10</td><td>0.723</td><td>444</td><td>Blast</td><td>PIR</td><td></td></tr><tr><td>08/18/2022 11</td><td>0.838</td><td>457</td><td>Blast</td><td>PIR</td><td></td></tr><tr><td>08/18/2022 12</td><td>1.000</td><td>468</td><td>Blast</td><td>PIR</td><td></td></tr><tr><td>08/18/2022 01</td><td>1.161</td><td>491</td><td>Blast</td><td>PIR</td><td>15(1)</td></tr><tr><td>01/24/2023 01</td><td>1.050</td><td>477</td><td>Blast</td><td>PIR</td><td></td></tr><tr><td>08/16/2022 01</td><td>1.05</td><td>499</td><td>Sustained shock</td><td>PIR</td><td></td></tr><tr><td>08/16/2022 02</td><td>1.02</td><td>494</td><td>Sustained shock</td><td>PIR</td><td>17(3), 20(3)</td></tr><tr><td>08/16/2022 03</td><td>1.03</td><td>464</td><td>Sustained shock</td><td>PIR</td><td>17(2), 20(2)</td></tr><tr><td>08/16/2022 04</td><td>1.03</td><td>513</td><td>Sustained shock</td><td>PIR</td><td></td></tr><tr><td>08/16/2022 05</td><td>1.02</td><td>522</td><td>Sustained shock</td><td>PIR</td><td>17(1), 18, 20(1), 27</td></tr><tr><td>08/16/2022 06</td><td>1.02</td><td>523</td><td>Sustained shock</td><td>PIR</td><td>19</td></tr><tr><td>08/18/2022 02</td><td>0.45</td><td>407</td><td>Blast</td><td>AAC</td><td></td></tr><tr><td>08/18/2022 03</td><td>0.52</td><td>416</td><td>Blast</td><td>AAC</td><td></td></tr><tr><td>08/18/2022 04</td><td>0.63</td><td>429</td><td>Blast</td><td>AAC</td><td></td></tr><tr><td>08/18/2022 05</td><td>0.78</td><td>448</td><td>Blast</td><td>AAC</td><td></td></tr><tr><td>08/18/2022 06</td><td>0.82</td><td>452</td><td>Blast</td><td>AAC</td><td></td></tr><tr><td>08/18/2022 07</td><td>0.82</td><td>452</td><td>Blast</td><td>AAC</td><td></td></tr><tr><td>08/18/2022 08</td><td>1.08</td><td>480</td><td>Blast</td><td>AAC</td><td></td></tr><tr><td>08/18/2022 09</td><td>0.85</td><td>455</td><td>Blast</td><td>AAC</td><td></td></tr><tr><td>08/18/2022 10</td><td>0.77</td><td>438</td><td>Blast</td><td>AAC</td><td></td></tr><tr><td>08/18/2022 11</td><td>0.85</td><td>455</td><td>Blast</td><td>AAC</td><td></td></tr><tr><td>08/18/2022 12</td><td>1.13</td><td>487</td><td>Blast</td><td>AAC</td><td></td></tr><tr><td>08/18/2022 13</td><td>1.24</td><td>500</td><td>Blast</td><td>AAC</td><td>22(2), 25</td></tr><tr><td>08/18/2022 14</td><td>1.29</td><td>506</td><td>Blast</td><td>AAC</td><td>22(3)</td></tr><tr><td>08/18/2022 15</td><td>1.29</td><td>505</td><td>Blast</td><td>AAC</td><td>22(1)</td></tr><tr><td>01/25/2023 01</td><td>1.01</td><td>476</td><td>Blast</td><td>AAC</td><td></td></tr><tr><td>01/25/2023 02</td><td>1.03</td><td>479</td><td>Blast</td><td>AAC</td><td></td></tr><tr><td>01/25/2023 03</td><td>1.08</td><td>485</td><td>Blast</td><td>AAC</td><td></td></tr><tr><td>01/25/2023 04</td><td>1.03</td><td>480</td><td>Blast</td><td>AAC</td><td></td></tr><tr><td>01/26/2023 01</td><td>0.90</td><td>465</td><td>Blast</td><td>AAC</td><td>24</td></tr><tr><td>01/26/2023 02</td><td>0.87</td><td>463</td><td>Blast</td><td>AAC</td><td></td></tr><tr><td>19/07/2022 03</td><td>1.01</td><td>567</td><td>Sustained shock</td><td>AAC</td><td></td></tr></tbody></table>

Under sustained shocks, ALF exhibits reduced response variability, with larger deformations highly localized in the sample center.

In these experiments, an estimation of the transmitted pressure cannot be obtained from the front loading taking into inertia stresses as previously done for blast experiments. As soon as the strain highly localized, the value of the displacements and in turn the value of the local accelerations are not correctly evaluated (Fig. 13).

In this situation, an estimation of a mean transmitted pressure can be obtained from the mean Eng. strain shown in Fig. 11 taking into account the material behavior (Fig. 1). The result is shown in Fig. 14. As expected, since the mean Eng. strain remains lower than the strain at the onset of densification - approximately half of its value - the ALF foam mitigates the incident shock. This result must be used with caution because the validity of this analysis is limited in time. It does not take into account the time need for stress equilibrium and, as can be observed in Fig. 12.d, after 1.4 ms the sample loosened around their lateral surface generating very complex pressure wave interactions.

## 4.2. Polyisocyanurate (PIR)

Polyisocyanurate (PIR) is a closed-cell polymer foam with high thermal insulation and moderate mechanical dissipation properties. Compared to ALF and AAC, PIR exhibits higher deformation levels under sustained shocks but shows partial recovery under blast loading.

PIR may display undesirable behavior when exposed to shock waves. Recorded images reveal that air occasionally seeped around the sample edges, introducing multi-axial loading. The shock wave's flow pressure exerts force on the orthogonal faces, disrupting the unidirectional stress state. This results in local material overloading and causes the sample to bend. To maintain consistent analysis, samples showing this behavior were excluded from the dataset. The subsequent analysis concentrates on PIR samples with insignificant multi-axial loading effects.

### 4.2.1. Blast response

Fig. 15 illustrates the strain response of PIR under varying blast pressures. As reflected overpressure rises, deformation increases, as
<figure><img src="image_14.png" /><figcaption>Fig. 11. Pressure recorded by the C5 sensor near the sample interface and the Eng. strain recorded by the camera for two sustained shock tests on ALF as a function of time. The yield strength is plotted for comparison. The tests shown correspond to IDs: 01/26/2023 04 for Strain 1, sample 01/26/2023 05 for Strain 2 from Table 2.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 12. Sample of ALF interacting with a sustained shock. We used PyDic [41] to track material points and Herhez++ [45] to calculate the Hencky strain, highlighting strain localization on a scale from -0.2 (black) to -2 (white). The sequence is as follows: (a) t = 0 ms, before the shock; (b) t = 0.5 ms, showing the onset of localization indicated by the ellipse; (c) t = 0.7 ms, depicting the intensification of localization in the weakened zone, also marked by the ellipse; and (d) t = 1.4 ms, representing the end of loading.</figcaption></figure>

depicted by three representative strain curves. When the reflected overpressure remains below the yield stress of 0.24 MPa, deformation stays minimal (≤ 2% strain). However, when the reflected overpressure reaches 0.24 MPa, deformation becomes substantial (> 4%). This corresponds to the expected overpressure for a 1 kg TNT equivalent charge at a scaled distance of 2.85 m/kg¹/³ [3]. Remarkably, upon unloading, all blast tests demonstrated full recovery, occasionally exceeding the recording time. Furthermore, during the loading phase, the strain rate

varied between 50 and 100 s⁻¹.

As previously shown in Fig. 4, the transmitted stress is roughly equivalent to the applied pressure, with a delay due to wave propagation and oscillations due to round trips for stress equilibrium.

The interaction between the moving sample interface and the blast wave is useful to understanding the stress transmission in PIR. The interface reaches speeds of 10 m/s, and its velocity is directly modulated by the reflected pressure from sensor C5 (Fig. 16). The synchronization
<figure><img src="image_16.png" /><figcaption>Fig. 13. Input and output pressures for a ALF sample under shock wave loading.</figcaption></figure>

of the interface speed with the pressure variations confirms a strong fluid-structure interaction (FSI), a behavior that aligns with the mechanism described by Kamboutchev for light plates [46]. The ~0.1 ms required for the interface to reach a plateau speed matches the delay observed in the back-face stress for low-pressure tests, confirming that the sample's own motion governs the stress transmission.

### 4.2.2. Sustained shock response

When subjected to sustained shocks, PIR experiences greater deformation than that of AAC and ALF. Fig. 17 shows deformation levels ranging from 55 % to 75 % strain, increasing with shock intensity. Specifically, deformation plateaus around 70 %, which can exceed the quasi-static densification strain of 60 %. Additionally, the strain rate is unsteady, increasing with shock pressure and reaching a maximum of 880 s⁻¹ for Curve 1, and 490 s⁻¹ and 430 s⁻¹ for Curves 2 and 3. Furthermore, recovery occurs beyond the recorded time frames. For stronger shocks, an additional reflected shock is produced at the end of compaction, as seen in Curve 1.

PIR's mechanical response is initially elastic when subjected to an incoming blast or sustained shock. As overpressure increases, a strain

<figure><img src="image_17.png" /><figcaption>Fig. 14. Input and mean output pressures for a ALF samples under shock waves loading. The tests shown correspond to IDs: 01/26/2023 04 for Strain 1, sample 01/26/2023 05 for Strain 2 from Table 2.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Fig. 15. Eng. strain of the PIR sample and pressure signal from sensor C5 versus time. After an initial deformation, the PIR releases all the accumulated energy and tends to return to its initial length. The three tests shown correspond to IDs 08/18/2022 01 for Strain 1, sample 08/17/2022 04 for Strain 2, and 08/18/2022 07 for Strain 3 from Table 2.</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>Fig. 16. The pressure signal from sensor C5 is corrected for time using the speed of the reflected blast wave and the displacement of the interface. Alongside it, we plot the speed of the interface, highlighting the correlation between both curves from 1.25 to 1.5 ms. The test shown correspond to ID 17/08/2022 08 from Table 2.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Fig. 17. Eng. strain for the PIR and overpressure recorded by sensor C5 versus time for three sustained shocks. The strain response to a shock wave is essential for this material with up to 70 %. The sample's strain rates range from 400 s⁻¹ to 860 s⁻¹. The three tests shown correspond to IDs 08/16/2022 05 for Strain 1, sample 08/16/2022 03 for Strain 2, and 08/16/2022 02 for Strain 3 from Table 2.</figcaption></figure>

localization plane forms orthogonal to the loading direction. As noted by El Yamani [33], and observed in this study, the position of the strain localization plane along the sample thickness is unpredictable. Once localization occurs, deformation propagates from this plane to the rest of the sample.

Fig. 18 illustrates the evolution of a PIR sample under sustained shock loading: Initially, the sample is at rest before loading (Fig. 18(a)). When the shock wave reaches the sample, the system has not yet reached equilibrium—the front face begins to move while the back face remains stationary, causing non-uniform strain (Fig. 18(b)). As strain reaches the back face and rebounds, a darker area (circle) indicates the beginning of compaction, and a second ellipse at the top of the sample shows air infiltration, creating a second weak point (Fig. 18(c)). The air infiltration area then expands, leading to a second compaction zone in the sample (Fig. 18(d)). Consequently, PIR exhibits strong fluid-material interactions, leading to increased deformation under sustained shock loading.

As with the aluminum foam, strain localization prevents an estimation of the transmitted pressure computed from the local accelerations (Fig. 19). The estimation of a mean transmitted pressure is again deduced from the mean Eng. strain shown in Fig. 9 taking into account the material behavior (Fig. 1). The results are shown in Fig. 20. The response can be divided into two or three parts. While the mean Eng.

strain remains lower than approximately a half of the strain at densification, the PIR mitigates the incident shock, limiting the transmitted stress to the plateau value. In a second part, since during the plateau stage there is a strain hardening, the mitigation gradually vanishes up to strain at densification. In a last part, only visible for the test with an incident loading greater than 0,4 MPa, due to the beginning of the densification process, the incident shock is amplified

### 4.3. Autoclaved aerated concrete (AAC)

Autoclaved Aerated Concrete (AAC) is a porous, lightweight cementitious material with thermal insulation and energy dissipation properties. Unlike ALF and PIR, AAC responds to shock waves through localized erosion at its extremities, rather than strain concentration in the middle of the sample. AAC also has the lowest yield stress among the three materials, measured at 0.22 MPa, which corresponds to a 1 kg TNT reflected overpressure at a scaled distance of 2.94 m/kg¹/³ [3].

#### 4.3.1. Image correlation and measurement challenges

AAC's dust generation and surface erosion create challenges in strain measurement during sustained shock tests. In particular, back-face crushing under blast loading disrupts standard digital image correlation (DIC) tracking. As a result, larger tracking thumbnails are required.
<figure><img src="image_21.png" /><figcaption>**Fig. 18.** Sample of PIR interacting with a sustained shock. The sequence is as follows: (a) *t* = 0 ms, before the shock arrival; (b) *t* = 0.4 ms, where the first visible interaction with the shock is outlined by an ellipse; (c) *t* = 0.68 ms, with an ellipse indicating the compaction zone where localization intensifies, and a dotted ellipse above showing air leakage; and (d) *t* = 0.9 ms, where the dotted ellipse highlights a second compaction area due to the air leak, while the compaction zone under the solid ellipse continues to grow. The test shown correspond to ID 08/16/2022 05 from Table 2.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>**Fig. 19.** Input and output pressures for an ALF sample under shock wave loading. The test shown correspond to ID 08/16/2022 06 from Table 2.</figcaption></figure>

**Fig. 21** illustrates this issue, where surface erosion removes material layers, making the affected thicknesses comparable to tracking thumbnail sizes (5 px). Moreover, the presence of dust interferes with image correlation, necessitating an increase in tracking thumbnail size to 15 × 15 px² (white square in Fig. 21).

Post-test measurements show length losses of 1–2 mm, these values exceed the DIC strain estimates (0.41 ± 0.15 mm below 0.41 MPa). This discrepancy complicates the identification of the pressure threshold for the elastic regime, as traditional DIC methods struggle to capture accurate strain values in eroding materials. A more effective approach for

live and post-mortem analysis applied to a denser AAC is demonstrated by Nian et al. (2016) [47], where cellular concrete is marked and maintained in a transparent tube, allowing visualization of the compaction length. The expelled dust also plays a role in the energy dissipation even though the expelled mass is negligible for this range of pressure loading.

### 4.3.2. Blast response

**Fig. 22** presents the strain response of AAC under blast loading, showing deformations ranging from 1 % to 3 %, despite consistent pressure signals. Moreover, the recorded strain rates vary between 20 and 60 s⁻¹, following a pattern similar to aluminum foams. This pattern includes an initial rapid strain increase, a plateau phase, and a final reduction.

The yield stress of AAC is exceeded by the reflected pressures. However, since most erosion occurs at the extremities, no permanent strain is visible in the image correlation measurements. AAC maintains an appearance of structural integrity. Post-test examination of the sample reveals how air eroded through the cube's volume. Few cavities were isolated; most cavities were interconnected, creating voids that led to structural failure of the sample. As a result, AAC exhibits strong air permeability, leading to the absence of sample deformation and significant erosion.

### 4.3.3. Erosion and fracture patterns

AAC primarily deforms through erosion. At reflected pressures up to 0.25 MPa, erosion remains relatively uniform across samples. However, beyond this threshold, some AAC specimens exhibit greater variability in erosion. **Fig. 23** illustrates a material-blast interaction. In the pre-blast state (Fig. 23a), the sample is positioned inside the shock tube. Once the shock wave impacts the sample (Fig. 23b), dust generation on the front
<figure><img src="image_23.png" /><figcaption>**Fig. 20.** Input and mean output pressures for PIR samples under shock waves loading. The three tests shown correspond to IDs 08/16/2022 05 for Strain 1, sample 08/16/2022 03 for Strain 2, and 08/16/2022 02 for Strain 3 from Table 2.</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>**Fig. 21.** AAC placed in the shock tube before the arrival of the blast wave. The white squares indicate a 5 × 5 px thumbnail and a 15 × 15 px thumbnail.</figcaption></figure>

face becomes visible. As the compression wave progresses in the sample (Fig. 23c), dust appears at the rear face, indicating localized crushing. Finally, after compression (Fig. 23d), the front face moves toward the shock tube, confirming the end of the blast loading.

For the level of blast wave overpressure we tested, erosion is hardly visible at the sample size. This erosion can be attributed to the material structure described by Kreft et al. [48]. Two distinct pore populations can be identified by size. The larger pores, resulting from gas expansion from aluminum in the slurry, are separated by membranes that include smaller pores. Some volumes contain a larger ratio of large pores compared to others. Consequently, in these areas, the membranes are thinner, leading to increased erosion along paths of random orientation, which can be orthogonal to the airflow. Additionally, erosion occurs at the sample's extremities [49]. Similar local crushing behavior has been reported in low-density AAC (<300 kg/m³), with material loss at the sample's extremities [49]. Under stronger blast waves, contact with the support erodes the material, leading to compaction from the back of the sample [47].

The first type of erosion increases AAC's permeability to the blast wave, resulting in small strain values, while the second type requires our stronger overpressure to be observed. Consequently, AAC experiences erosion localized on its extremities and along weakened material in the sample.

<figure><img src="image_25.png" /><figcaption>**Fig. 22.** The pressure signal compared with the AAC deformation response for three tests where the input pressure exceeded the yield stress. The three tests shown correspond to IDs 08/18/2022 15 for Strain 1, sample 08/18/2022 13 for Strain 2, and 08/18/2022 14 for Strain 3 from Table 2.</figcaption></figure>
<figure><img src="image_26.png" /><figcaption>**Fig. 23.** Sample of AAC interacting with a blast wave. The sequence is as follows: (a) *t* = 0 ms, before the blast arrival; (b) *t* = 0.58 ms, showing the beginning of blast compression with no equilibrium yet, and numerous particles in the area framed by the ellipse; (c) *t* = 0.98 ms, where equilibrium is reached, with light dust generation in the ellipse marking the back of the sample; and (d) *t* = 1.6 ms, indicating the end of compression. A comparison of (a) and (d) reveals the movement of the front face of the sample.</figcaption></figure>

# 5. Discussion

## 5.1. *Comparison of the blast results for the three tested materials*

In this section, results for three materials—ALF, AAC, and PIR—under blast and shock loading conditions are analyzed and compared. The objective is to understand their mechanical responses and identify key characteristics that differentiate their behavior. From our tests, we evaluate the response in terms of deformation and visible material damage. With increasing blast overpressure, the results highlight significant variations in deformation responses. Meanwhile, the sustained shock results underscore the strong interaction between the shock wave

and the materials, leading to large deformation and strain rates.

In Fig. 24, we compare all three materials under a low-amplitude blast load with a scale distance above 2.95 m/kg¹/³ for 1 kg eq.TNT. They show a similar deformation range of <1 %. While PIR returns to its initial length, ALF undergo a reduced permanent deformation. They also exhibit a brief plateau of constant strain over time. For PIR, the stress-strain curve in Fig. 1 begins with an elastic behavior, whereas the other two materials begin with pseudo-elasticity and show permanent deformation before reaching the yield point. Adapting the sample’s interface with the test apparatus induces local plasticization or crushing.

With higher peak pressure and a correspondingly smaller scale distance, deformation increases for all three materials. Specifically, in

<figure><img src="image_27.png" /><figcaption>**Fig. 24.** Comparison of the strain response of the three materials under blasts with a scale distance above 2.95 m/kg¹/³, resulting in a reflected overpressure of 0.20 MPa. The samples exhibit similar strain amplitudes. The three tests shown correspond to IDs 01/26/2023 01 for ALF, sample 08/18/2022 07 for PIR, and 01/26/2023 01 for AAC from Table 2.</figcaption></figure>
<figure><img src="image_28.png" /><figcaption>**Fig. 25.** Eng. Strain response of the three materials under blasts with a scale distance below $3.02 \text{ m/kg}^{1/3}$. With the higher peak pressure, the maximal strain varies among the materials. Moreover, the first plateau visible in Fig. 24 for ALF and AAC is no longer present. The three tests shown correspond to IDs 01/25/2023 06 for ALF, sample 08/17/2022 04 for PIR, and 08/18/2022 13 for AAC from Table 2.</figcaption></figure>

Fig. 25, the strain reaches 2 to 2.5 % for ALF and AAC, while PIR reaches 4 %. According to the stress-strain curves in Fig. 1, AAC is expected to exhibit the highest deformation, followed by PIR and ALF. However, Fig. 23 suggests that AAC interacts less with the blast wave. This reduced interaction can be attributed to the larger permeability of AAC.

Finally, Fig. 26 compares the maximal deformation induced by blast wave loading for the three materials. With similar yield strengths for the three materials, the recorded maximum deformation increases after the blast overpressure exceeds 0.37 MPa. While aluminum foam and PIR undergo significant deformation in the bulk of the sample, AAC exhibits an erosion behavior.

As Fig. 26 shows, closed-cell PIR may be less permeable to the shock wave. The thicker skin of aluminum foam provides a solid surface for interaction with the shock wave. In contrast, AAC's structure, through the erosion of its cells, allows more air circulation.

The compilation of those results can be fitted with an inverse power law and we can identify the blast wave interaction threshold for each material. Specifically, ALF starts interacting at $Z_{140} = 2.8 \text{ eq.TNT}$, PIR at $Z_{PIR} = 2.7 \text{ eq.TNT}$, and AAC at $Z_{AAC} = 2.5 \text{ eq.TNT}$.

## 5.2. Comparison of the sustained shock results for PIR and ALF

Under sustained shock loading, Fig. 27 compares aluminum foam with PIR. The 70 % deformation of PIR and the 30 % deformation of aluminum correspond to the same stress level in their stress-strain curves (Fig. 1). With a shock pressure of 0.17 MPa, the expected reflected shock pressure is 0.35 MPa. This pressure corresponds to a strain range of 40 to 45 % for ALF and 65 % for PIR.

## 5.3. Limits of the study

A series of limitations comes with this study:

* The lack of a force transducer at the rear of the sample restricts the determination of the material's constitutive law [50]. However, reflected shock pressure serves as an indicator of the force applied to the sample. The inertial-based method, as tested by Koohbor et al. [43,51], typically benefits from three rear force transducer for comprehensive assessment. To enhance the implementation of this method, our setup could benefit from two innovations. First, recently developed polymeric foam, doped with a conductive agent and sandwiched between plates, has been shown to provide stress information through piezoresistive effects [52]. Second, PVDF-based piezoelectric sensors, as used in Arrigoni et al. [53], could also be employed. This would allow the study of the amplification effect in AAC [47] and PIR [54,55].

* The inertial-based method, when applied to very low-density materials, appears to be highly sensitive to noise. The frame rate and spatial resolution are key parameters for reducing noise in the data. Moreover, during sustained shock interaction, sample compression leads to out-of-plane displacement. Therefore, upgrading the high-speed camera and lighting system would help reduce noise.

* The shock tube facility used in this work has a maximum pressure of 15 bar in the driver section. This limitation restricts the use of stronger positive impulses and peak pressures, thus preventing a full exploration of the absorption behavior of the three materials studied. However, it allows for windows in the test section, enabling monitoring through a high-speed camera. To study larger amplitudes

<figure><img src="image_29.png" /><figcaption>**Fig. 26.** For each blast test, this shows the maximal strain versus scaled distance, identified from the incoming blast wave overpressure reading for the three materials. This helps identify the threshold of blast wave interaction for each material by fitting an inverse power curve.</figcaption></figure>
<figure><img src="image_30.png" /><figcaption>Fig. 27. Eng. strain and strain rate response of ALF and PIR for sustained shock of comparable pressure. The aluminum foam accommodates 32 % Eng. strain at 400 s⁻¹ while the PIR reaches 74 % at 888 s⁻¹. The reflected over pressure from C5 is 0.42 - 0.43 MPa. The two tests shown correspond to IDs 01/26/2023 04 for ALF, sample 08/16/2022 05 for PIR from Table 2.</figcaption></figure>

<figure><img src="image_31.png" /><figcaption>Fig. 28. Identified overpressure and positive impulsion of all presented tests.</figcaption></figure>

needed to fully describe the absorption behavior, an alternative method should be implemented to monitor the sample's deformation.

* In Fig. 28, the shock tube generates blast waves along a limited path. With the driver's pressure being the only degree of freedom, peak pressure and impulse are inherently linked parameters by design.

## 6. Conclusion

This study provides a comparative dataset on the interaction of three different materials—polyisocyanurate foam (PIR), autoclaved aerated concrete (AAC), and aluminum lightweight foam (ALF)—with blast and shock loading conditions. The findings reveal distinct dissipative mechanisms in each material. Blast wave interaction threshold for each material were identified offering insights into their potential applications for building protection against blast effects.

PIR demonstrated the strongest interaction with blast and shock waves compared to AAC, effectively dissipating a larger portion of the blast. Combined with its effective thermal insulation properties, PIR is interesting for applications requiring both insulation and blast resistance. AAC exhibited characteristics of erosion-based dissipation. Under the levels of shock experienced, its porous structure allowed permeability to the blast wave. However, exposure of this fire-resistant insulator to higher shock levels might bypass the erosion response and trigger compaction instead [30]. As a reference material for shock absorption, ALF showed excellent mechanical dissipation capabilities.

These results contribute to the development of predictive tools and inform the design of larger-scale experiments, ultimately advancing

blast protection technologies. Future research should focus on enhancing the interaction between shock waves and these materials to improve their protective capabilities, particularly for PIR and AAC, which also offer thermal insulation benefits.

## Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work the author(s) used Mistral AI in order to improve the readability and language of the manuscript. After using this tool/service, the author(s) reviewed and edited the content as needed and take(s) full responsibility for the content of the published article.

## Annex: overview of mechanical tests

The full test matrix for this study is summarized in Table 2.

## CRediT authorship contribution statement

**David Drouet:** Writing – review & editing, Writing – original draft, Software, Investigation, Data curation. **Jean-Luc Hanus:** Writing – review & editing, Supervision, Project administration, Formal analysis, Data curation, Conceptualization. **Damien Laporte:** Writing – review & editing, Resources, Project administration. **Gaëtan Prod'homme:** Writing – review & editing, Supervision, Resources, Project administration. **Ludovic Blanc:** Writing – review & editing, Supervision, Investigation, Formal analysis, Conceptualization. **Steven Kerampran:** Writing – review & editing, Resources, Methodology, Investigation, Conceptualization. **Julien Le-Chanche:** Resources, Investigation,
Formal analysis, Data curation. Michel Arrigoni: Writing – review & editing, Validation, Project administration, Methodology, Investigation, Formal analysis, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors thank ANR (Agence Nationale pour la Recherche) for the
grant of the MAPSEA project number ANR-21-SIOM-0012 (MAteriaux
pour la Protection des Sites industriels contre les Explosions
Accidentelles).

Data availability

Data will be made available on request.

References

[1] Fu G, Wang J, Yan M. Anatomy of Tianjin Port fire and explosion: process and causes. Proc Saf Prog 2016;35:216–20. https://doi.org/10.1002/prs.11837.

[2] Sivarajan S, Varadharajan S. Investigative consequence analysis: a case study research of Beirut explosion accident. J Loss Prev Process Ind 2021;e04387. https://doi.org/10.1016/j.jlp.2020.104387.

[3] US Army Corps of Engineers. Structures to resist the effects of accidental explosions. Unified Facilities Criteria (UFC); 2008. https://www.wbdg.org/FFC/DOD/UFC/ARCHIVES/ufc_3_340_02.pdf.

[4] Maazoun A. Enhanced blast resistance of reinforced concrete slabs using carbon Fiber reinforced polymer as externally bonded reinforcement. Faculteit ingenieurswetschappen en architectuur. Universiteit Gent; 2019. https://rese archportal.vub.be/en/studentThesis/enhanced-blast-resistance-of-reinforced-conc rete-slabs-using-carb-2.

[5] Smith P. Blast walls for structural protection against high explosive threats: a review. Int J Prot Struct 2010;1(1):67–84. https://doi.org/10.1260/2041-4196.1.1.67.

[6] Matsagar VA. Comparative performance of composite sandwich panels and non-composite panels under blast loading. Mater Struct 2016;49:611–29. https://doi.org/10.1617/s11527-015-0523-8.

[7] Hussein AT. Blast protection systems: literature review. WIT transactions on the built environment. Edinburgh; 2020 Jun 9-11. https://doi.org/10.2495/SUS1200081.

[8] Breda C, Kerampran S, Sturtzer MO, Arrigoni M, Legendre JF. Analysis of planar and spherical shockwave mitigation by wet aqueous foams. editor. In: Kontis K, editor. Shock wave interactions. rainew 2017. Springer; 2018. p. 22. https://doi.org/10.1007/978-3-319-73180-3_22. Jul 4-8Glasgow.

[9] Monloubou M, Bruning MA, Saint-Jalmes A, Dollet B, Cantat I. Blast wave attenuation in liquid foams: role of gas and evidence of an optimal bubble size. Soft Matter 2016;12:8015–24. https://doi.org/10.1039/C6SM01281G.

[10] Ministry of Housing and Urban-Rural Development of the People's Republic of China. Gen Code Energy Efficient Renew Energy Appl Build (GB 55015-2021) 2021.

[11] European Parliament and Council. Directive (EU) 2024/1275 on the energy performance of buildings (recast). Off J Eur Union 2024.

[12] International Code Council. International energy conservation code. IL, USA: Inc.: Country Club Hills; 2021.

[13] Brekken KA, Reyes A, Berstad T, Langseth M, Bøvik T. Sandwich panels with polymeric foam cores exposed to blast loading: an experimental and numerical investigation. Appl Sci 2020;10:9061. https://doi.org/10.3390/app10249061.

[14] Gibson L, Ashby M. Cellular solids: structure and properties. 2nd ed. Cambridge University Press; 1997.

[15] Radford DD, McShane GJ, Deshpande VS, Fleck NA. The response of clamped sandwich plates with metallic foam cores to simulated blast loading. Int J Solids Struct 2006;43:7. https://doi.org/10.1016/j.ijsolstr.2005.07.006.

[16] Langdon GS, Cantwell WJ, Guan ZW, Nurick GN. The response of polymeric composite structures to air-blast loading: a state-of-the-art. Int Mater Rev 2014;59 (3):159–77. https://doi.org/10.1179/1743280413Y.0000000028.

[17] Galbraith C, Consultants IAL. Press release: the European Market for thermal insulation products. Available online: (accessed on 25 June 2025), https://www.ia lconsultants.com/media/1118/thermal-insulation-press-release-2023.pdf; December 2023 (accessed on 25 June 2025).

[18] Steineck S, Lange J. Material behavior of PIR rigid foam in sandwich panels: studies beyond construction industry standard. Mater (Basel) 2024;17(2):418. https://doi.org/10.3390/ma17020418.

[19] UK Ministry of Defence. In-Service and Operational Safety Management of OME. DSA03 OME. https://www.gov.uk/government/publications/dsa03-ome-part-2-in-service-and-operational-safety-management-of-ome; 2020.

[20] Mohamed AM, Tayeh BA, Majeed SS, Aisheh YIA, Salih MNA. Ultra-light foamed concrete mechanical properties and thermal insulation perspective: a comprehensive review. J CO2 Util 2024;83. https://doi.org/10.1016/j.jcou.2024.102827.

[21] Hanssen AG, Enstock L, Langseth M. Close-range blast loading of aluminium foam panels. Int J Impact Eng 2002;27(6):593-618. https://doi.org/10.1016/S0734-743X(01)00155-5.

[22] Liu H, Cao ZK, Yao GC, Luo HJ, Zu GY. Performance of aluminum foam-steel panel sandwich composites subjected to blast loading. Mater Des 2013;47:483-8. https://doi.org/10.1016/j.matdes.2012.12.003.

[23] Islam MA, Brown AD, Hazell PJ, Kader MA, Escobedo JP, Saadatfar ... M, Turner M. Mechanical response and dynamic deformation mechanisms of closed-cell aluminium alloy foams under dynamic loading. Int J Impact Eng 2018;114:111-22. https://doi.org/10.1016/j.ijimpeng.2017.12.012.

[24] Barthélémy R, Jacques N, Kerampran S, Vermeersch F. Modelling of micro-inertia effects in closed-cell foams with application to acoustic and shock wave propagation. Int J Solids Struct 2016;97-98:445-57. https://doi.org/10.1016/j.ijsolstr.2016.07.005.

[25] Hanssen AG, Hopperstad OS, Langseth M, Ilstad H. Validation of constitutive models applicable to aluminium foams. Int J Mech Sci 2002;44:359-406. https://doi.org/10.1016/S0020-7403(01)00091-1.

[26] Mespoulet J, Plassard F, Hereil PL. Strain rate sensitivity of autoclaved aerated concrete from quasi-static regime to shock loading. In: EPJ Web of Conferences; 2015 Sep 7-11. https://doi.org/10.1051/epjconf/20159401053.

[27] Liu C, Hou J, Hao Y, Hao H, Meng X. Effect of high strain rate and confinement on the compressive properties of autoclaved aerated concrete. Int J Impact Eng 2021; 156:103943. https://doi.org/10.1016/j.ijimpeng.2021.103943.

[28] UK Ministry of Defence. Ministry of Defence explosives regulations for the safe storage and processing of ordnance, munitions and explosives (OME). JSP 2013; 482. https://www.gov.uk/government/collections/jsp-482-mod-explosives-regulations.

[29] Aminou A, Belkassem B, Atoui O, Pyl L, Lecompte D. Numerical modeling of brittle mineral foam in sacrificial cladding under blast loading. Mech Ind 2023;24:27. https://doi.org/10.1051/meca/2023021.

[30] Mollaei S, Ghazijahani RB, Farsangi EN, Jahani D. Investigation of behavior of masonry walls constructed with autoclaved aerated Concrete Blocks under blast loading. Appl Sci 2022;12:8725. https://doi.org/10.3390/app12178725.

[31] Gibson LJ, Ashby M MF. The mechanics of foams: basic resultsCell. Solids struct, prop. Camb Univ Press 2014:175-234. https://doi.org/10.1017/cbo9781139878326.007.

[32] Li QM, Magkiriadis I, Harrigan JJ. Compressive strain at the onset of densification of cellular solidsJ. Cell Plast 2006;42(5):371-92. https://doi.org/10.1177/0021955 × 06063519.

[33] El Yamani. Caractérisation du comportement mécanique de matériaux isolants sous choc. INSA Cent Val Loire 2021. https://hal.science/tel-03843064.

[34] Jaminion S, Nelson NW, Chambard JP, Swiergel N, CorreliSTC Hild F. A global approach in digital image correlation. In: Proceedings of the First Annual Conference; 2017 Sep 7-10. https://doi.org/10.1007/978-3-319-51439-0-66.

[35] EN 1352 Standard, Determination of static modulus of elasticity under compression of autoclaved aerated concrete or lightweight aggregate concrete with open structure. 2001. https://www.boutique.afnor.org/fr-fr/norme/nf-en-1352/determination-du-module-delasiticiste-statique-en-compression-du-beton-cellul/fao14652/258.

[36] Belouettar R, Klepaczko J.R., Abadlia M.T. Etude du comportement mécanique du béton cellulaire autoclave: influence de la vitesse de déformation. 2001;5:667-75. https://doi.org/10.1080/12795119.2001.9692717.

[37] Belouettar R, Klepaczko JR. Study of the dynamic behavior of the autoclaved aerated concrete. In: EPJ Web of Conferences; 2009 Sep 7-11. https://doi.org/10.1051/dymat/2009072.

[38] Piezotronics®. Dynamic pressure sensors for high-frequency measurements. 2021. https://www.pcbpiezotronics.fr/produit/capteurs-de-pression/113b21/.

[39] National Instruments®. PXIe-1073 chassis. 2021. https://www.ni.com/fr-fr/sh op/model/pxie-1073.html.

[40] Photron®. Fastcam Nova S9. 2021. https://photron.com/fr/fastcam-nova-s/.

[41] André D. pydic, a python suite for local digital image correlation. 2023. https://gitlab.com/damien.andre/pydic.

[42] Aloui S, Othman R, Poitou A, Guegan P, El-Borgi S. Non-parametric identification of the non-homogeneous stress in high strain-rate un-axial experiments. Mech Res Commun 2008;35:392-7. https://doi.org/10.1016/j.mechrescom.2008.04.005.

[43] Koohbor B, Kidane A, Lu WY. Effect of specimen size, compressibility and inertia on the response of rigid polymer foams subjected to high-velocity direct impact loading. Int J Impact Eng 2016;98:62-74. https://doi.org/10.1016/j.ijimpeng.2016.08.006.

[44] Friedlander FG. The diffraction of sound pulses I. Diffraction by a semi-infinite plane. R Soc L 1946;186:322-44. https://doi.org/10.1098/rspa.1946.0046.

[45] Herezh++ Rio G. https://herezh.irdl.fr/; 2023.

[46] Kambouchev N, Noels L, Radovitzky R. Numerical simulation of the fluid-structure interaction between air blast waves and free-standing plates. Comput Struct 2007; 85:923-31. https://doi.org/10.1016/j.comprostruc.2006.11.005.

[47] Nian W, Subramaniam K, Andreopoulos Y. Experimental investigation on blast response of cellular concrete. Int J Impact Eng 2016;96:105-15. https://doi.org/10.1016/j.ijimpeng.2016.05.021.

[48] Kreft O, Hausmann J, Hubálková J, Aneziris C, Straube B, Schoch T. Pore size distribution effects on the thermal conductivity of light weight autoclaved aerated concrete. Cem-Wapno-Beton = Cem Lime Concr 2011;(16):49-52.
[49] Tan X, Chen W, Yang D, Liu H, Chan AHC. Experimental and theoretical studies on effect of height-to-diameter ratios on failure forms and mechanical characteristics of foamed concrete. J Mater Civ Eng 2019;31(1). https://doi.org/10.1061/(ASCE) MT.1943-5533.0002557.

[50] Kaviarasu K, Alagappan P. Blast impact on the density-based tri-layered polyurethane foam. Int J Impact Eng 2025;195:105108. https://doi.org/10.1016/j.ijimpeng.2024.105108.

[51] Koohbor B, Kidane A, Lu WY. Characterizing the constitutive response and energy absorption of rigid polymeric foams subjected to intermediate-velocity impact. Polym Test 2016;54:48-58. https://doi.org/10.1016/j.polymtesting.2016.06.023.

[52] Poirot A, Bedrici N, Walrick JC, Arrigoni M. Piezoresistive behavior of a conductive polyurethane based-foam for real-time structural monitoring. Sensors 2023;23: 5161. https://doi.org/10.3390/s23115161.

[53] Arrigoni M, Bauer F, Kerampran S, Le Clanche J, Monloubou M. Development of a PVDF pressure gauge for blast loading measurement. Hum Factors Mech Eng Def Saf 2018;2:2. https://doi.org/10.1007/s41314-018-0012-2.

[54] Ben-Dor G, Mazor G, Igra O, Sorek S, Onodera H. Shock wave interaction with cellular materials. Shock Waves 1994;3:167-79. https://doi.org/10.1007/BF01414711.

[55] Qi C, Yang S, Gao R. Numerical simulation of force enhancement by cellular material under blast load. Adv Mech Eng 2013;5:328651. https://doi.org/10.1155/2013/328651.