Repeated bending and indentation response of a bio-based sandwich panel with flax/epoxy skins and a palm-wood core

Abstract

This study investigates the mechanical behavior of bio-based sandwich panels (BBSP) composed of flax/epoxy skins and a palm wood core (PWC) under monotonic and repeated bending and indentation loading. PWC, sourced from northern and southern regions of Algeria, was prepared along three principal material directions to capture its anisotropic response. Three-point bending and indentation tests, including Repeated Progressive Loading (RPL), were conducted to assess both static and cyclic behavior. The bending results highlight the anisotropic nature of PWC, with fiber-aligned specimens particularly from the southern region, exhibiting superior mechanical performance. RPL tests reveal the onset of permanent deformation from early cycles; however, below a critical load threshold, the material maintains significant elastic recovery, with residual displacement remaining below 10% of the maximum. The main failure mechanisms identified include core crushing, skin cracking, and interfacial delamination. Acoustic emission analysis confirms that low-amplitude signals (Type A, ∼93%) are dominant and associated with microcrack initiation during the elastic phase. Indentation results show progressive plastic deformation and stiff degradation, accompanied by energy dissipation and permanent deformation. Under cyclic indentation, PWC exhibits a reduction in reduced modulus and hardness followed by stabilization around a normalized cycle ratio of 0.2 due to plastic compression. In contrast, BBSP does not reach stabilization, showing continuous degradation throughout the loading cycles, as reflected by the progressive increase in elastic and plastic energy components up to failure.

Keywords

bio-based sandwich flax/epoxy palm-wood core repeated indentation three-point bending cumulative damage

Highlights of the paper

(1) Evaluated bio-based sandwich panels (BBSP) with flax/epoxy skins and palm wood cores (PWC) under monotonic and Repeated bending and indentation Loads.

(2) PWC showed heterogeneous, anisotropic behavior with superior fiber-aligned performance.

(3) RPL tests tracked damage progression, energy dissipation, and plastic deformation in both PWC and BBSP.

(4) BBSP demonstrated mechanical efficiency and ecological potential for future industrial applications.

Introduction

Bio-based sandwich structures offer synergistic properties well suited for lightweight, high-performance, and sustainable applications. They typically consist of stiff face sheets bonded to a lightweight core, enabling efficient load transfer: the skins carry in-plane and bending stresses, while the core resists transverse shear and prevents buckling.^1–3 However, their performance depends on several critical factors, including the anisotropic and heterogeneous nature of bio-composites, optimization of structural parameters (such as skin-to-core thickness ratio and core density), and the control of manufacturing processes affecting interfacial bonding and defect formation. In addition, key mechanical responses include energy absorption and behavior under bending and indentation loads, which must be carefully evaluated as they directly influence structural integrity and damage tolerance.^4–6

Conventional core materials in sandwich structures, such as honeycombs and polymer foams, are widely used due to their proven performance but exhibit limitations, particularly in terms of durability, damage tolerance, and behavior under dynamic loading, like impacts, indentation, and vibration.^7,8 These constraints have driven the search for alternative core solutions with improved robustness and structural efficiency.^9,10 Among emerging options, natural materials with intrinsic cellular architectures have attracted increasing attention, as their optimized microstructures can provide unique property combinations difficult to achieve synthetically.^11,12 In this context, palm wood stands out as a promising bio-based core material due to its low density, high energy absorption capacity, excellent elastic recovery, and superior damping properties, enabling efficient shock and indentation dissipation.^13–17 These characteristics make it particularly suitable for enhancing impact resistance, damage tolerance, and sustainability of sandwich structures, aligning with current demands for eco-efficient materials and circular design approaches.^18–21

To address the complexity of sandwich structures with PWC and similar low-stiffness materials, several studies have examined their mechanical and tribological behavior.^22,23 However, hardness characterization remains challenging due to the combined elastic and inelastic deformations of wood and its intrinsic anisotropy, which lead to variability in indentation measurements.²⁴ To improve accuracy, conventional indentation models have been applied to estimate hardness from indentation depth, capturing both deformation components.²⁵ In parallel, friction and wear behavior, particularly for porous woods, has been investigated under various loading and sliding conditions,^26–28 while stress relaxation under compression follows linear logarithmic trends with distinct rates depending on stress levels.²⁹

Although indentation has been widely studied,^30,31 investigations focusing on wood as a sandwich core remain limited due to its natural heterogeneity and variability in mechanical properties.³² Moreover, the ability of repeated monotonic tests to reproduce failure mechanisms in multilayer sandwich structures is still debated.^33,34 Experimental tests carried out on a balsa core sandwich panel showed that local indentation represents 40% of the total deformation and that the response to indentation depends globally on the anatomical orientation, with lower penetration in the stiffest directions.^35–37 The role of permanent indentation in energy absorption, through plastic deformation and fracture, has also been quantified.³⁸

Research on sandwich structures under repeated low-velocity impacts or indentations is relatively recent, and key aspects such as energy absorption, stiffness degradation, and damage evolution remain insufficiently understood. Experimental studies have highlighted the influence of core materials on impact resistance and progressive damage under cyclic loading,³⁹ as well as the effects of core density and loading type on energy dissipation.⁴⁰ To emphasize the importance of loading conditions and structural configuration, investigations of monotone and repeated loading have identified dominant failure modes including local indentation, penetration, and perforation.⁴¹ Furthermore, residual strength analyses indicate that damage characterization is more accurately related to affected volume rather than indentation depth alone.⁴²

From the literature, the mechanical behavior of sandwich panels with polymer foam, metallic honeycomb, or PVC cores under bending, quasi-static indentation, and low-velocity impact under both single and repeated loading is relatively well documented. However, despite increasing interest in sustainable materials, sandwich panels incorporating wood, particularly PWC, remain insufficiently studied, especially under repeated indentation. This lack of data on damage evolution, energy absorption, and residual properties limits reliable comparison with conventional solutions and hinders their structural application. To address this gap and promote environmentally friendly materials through the valorization of local resources, this study presents an experimental investigation of a novel BBSP subjected to monotonic and repeated bending and indentation tests. Palm wood was sourced from two distinct regions of Algeria: A Mediterranean coastal area (North PWC) and a semi-arid region (South PWC). Specimens were prepared in accordance with relevant standards for bending and indentation testing.

For both PWC and BBSP, bending tests were conducted to determine the modules, failure modes, and the stress and strain at failure in the longitudinal, radial, and transverse directions. RPL loading was applied to reproduce the mechanical response observed under static conditions and to monitor damage accumulation during successive cycles. To further investigate damage evolution during three-point bending, RPL tests were instrumented with acoustic emission (AE), complemented by synchronized visual recording to correlate acoustic signals with observed damage. Due to the compliant and porous nature of PWC and the relatively low indentation loads (<50 N), monotonic and RPL indentation tests were performed using a Bruker UMT tribometer. In contrast, the higher stiffness and strength of BBSP samples required the use of an MTS 43 testing machine, which allows indentation loads up to 600 N. Overall, the experimental program was designed to assess the feasibility of using recycled PWC as a core material in BBSPs, with particular emphasis on mechanical performance, damage tolerance, energy absorption, and durability under static and cyclic loading.

Materials and methods

Preparation of specimens

Every year, palm tree maintenance generates large quantities of biomass waste, primarily palm leaves which are often disposed of by open burning, leading to environmental pollution and loss of valuable resources. However, these residues represent abundant lignocellulosic material with strong potential for use in bioenergy, biodegradable products, and fiber-reinforced composites within a circular economy framework. Their valorization can therefore contribute to both environmental protection and sustainable material development. In this study, date palm fronds were collected after the growing season from two regions in Algeria: Biskra (semi-arid climate) and Oran (Mediterranean climate). Following pruning, only the petiole, the structural base connecting the frond to the trunk, was retained due to its high lignocellulosic content and wood-like structure. The material was stored at room temperature, then selected, cleaned, and machined to obtain smooth, defect-free specimens suitable for mechanical testing. Each sample was identified according to its orientation and position. Bending specimens were prepared along the longitudinal, radial, and transverse directions with lengths exceeding 100 mm,³⁵ while smaller sections were used for monotonic and repeated indentation tests (Figure 1(a)).

The palm wood sections were aligned edge-to-edge and bonded using an epoxy adhesive (MEDAPOXY COLLE) to create a BBSP (Figure 2(a)). MEDAPOXY COLLE is indeed an epoxy-based material; however, it is specifically formulated as a structural adhesive rather than a laminating resin. It was therefore selected in this study for bonding purposes, namely for assembling the wood elements together and for bonding the wood core to the flax/epoxy skins of the sandwich structure. According to the manufacturer’s technical data sheet, MEDAPOXY COLLE, produced by Granitex and classified under AFNOR NF T30-006, is a two-component epoxy adhesive characterized by low shrinkage, a density of 1.15 g/cm³, an adhesion strength of 3 MPa, and a compressive shear strength exceeding 25,000 daN. The adhesive was prepared according to the manufacturer’s instructions, with a mixing ratio of 2/3 resin (component A) to 1/3 hardener (component B) to achieve optimal bonding properties.

The flax/epoxy composite sheets were manufactured using the hand lay-up technique. The reinforcement consisted of unidirectional flax fibers supplied by Eco-Technilin (L-FLAXDRY-UD180-30 m², 180 g/m²), while epoxy resin MEDAPOXY-STR was used as the matrix for stratification. The flax fabric was cut, resin-impregnated, and consolidated using a roller and bubble remover to obtain homogeneous laminate with reduced void content. The produced flax/epoxy sheets showed a Young’s modulus of 27.5 GPa, an ultimate tensile strength of 298 MPa, an ultimate strain of 1.69%, and a density of 1.22 kg/dm³.⁴³

After mixing, the adhesive was uniformly spread over the roughened surface of the flax/epoxy laminate (Figure 2(b)). The palm wood was then carefully placed onto the adhesive layer. A significant load was applied to ensure even pressure distribution and effective adhesion between the core and the skin (Figure 2(c)). The same bonding process was repeated on the opposite side to attach a second flax/epoxy sheet, thereby forming the sandwich structure. After curing, a large sandwich panel was obtained. This sandwich panel was subsequently cut into 30 mm-wide strips using a table saw to fabricate sandwich beams (Figure 2(d)). Each beam was then trimmed longitudinally to a final length of 300 m in accordance with the relevant standards. Monotonic and repeated indentation tests were conducted simply on the smaller square 30*30 mm² sections (Figure 2(e)).

Experimental setup

Three-point bending tests were conducted on both PWC and BBSP using an MTS 43 universal testing machine, in accordance with ASTM D143. Tests were performed under displacement control at a constant crosshead speed of 0.5 mm/min, with simply supported specimens loaded at mid-span. Multiple specimens were tested for each configuration to ensure repeatability, and load–displacement responses were continuously recorded, ensuring reliable and reproducible experimental conditions.

For indentation tests, specimens were prepared as shown in Figure 1(e) in accordance with ASTM E10-15. Testing was carried out using a Bruker UMT tribometer with computer-controlled data acquisition. A 9.5 mm diameter steel ball indenter was applied at loads ranging from 5 to 45 N. Due to the compliant and porous nature of PWC, partial recovery occurs upon unloading.⁴⁴ The loading response includes both elastic and permanent deformation, while only the elastic component is recovered during unloading. The hysteresis loop obtained from load/displacement curves, represents energy dissipation, where the enclosed area corresponds to dissipated plastic energy and the unloading curve reflects the recoverable elastic energy.⁴⁵

Results and discussion

Flexural and indentation tests were conducted under both monotonic and cyclic loading, as they provide complementary insight into the global and local mechanical responses of sandwich structures. Indentation testing, commonly associated with hardness evaluation, assesses the local resistance to concentrated contact loads and is particularly sensitive to mechanisms such as core densification, cell wall collapse, and skin–core interactions. In contrast, three-point bending tests evaluate the overall structural response by capturing the combined effects of skin stiffness, core shear modulus, and interfacial bonding on the global rigidity and strength of the sandwich structure. Although an increase in hardness is often correlated with enhanced flexural strength due to improved resistance to localized deformation, it may also result in reduced damage tolerance, increased brittleness, and earlier crack initiation under bending loads. Furthermore, under flexural loading, sandwich structures typically exhibit failure modes such as face sheet cracking, skin–core debonding, and, most prominently, core crushing, which is closely related to the compressive and indentation resistance of the core material. These considerations highlight the importance of achieving an optimal balance between hardness and flexural performance to ensure both strength and durability of bio-composite sandwich structures.

Three points bending tests

Due to the inherent variability of wood-like materials, specimens were tested along the three principal directions (X, Y, and Z). This variability arises from the heterogeneous and anisotropic nature of plant-based structures, influenced by factors such as moisture content, temperature, and growth conditions. Unlike most conventional materials, wood exhibits direction-dependent mechanical properties.³⁵ Accordingly, three-point bending tests were performed in all principal directions for both PWC and BBSP. The longitudinal direction (X) is aligned with the fibers, the in-plane transverse direction (Y) is perpendicular to the fibers within the cross-section, and the out-of-plane direction (Z) is normal to the thickness (Figure 1(a)).

Palm wood core

Figure 2(a) presents the load–mid-span deflection curves for five southern PWC specimens tested in the longitudinal (X) direction. All samples exhibit an initial linear elastic response followed by a nonlinear regime up to failure, with limited scatter, indicating good repeatability. Comparative bending tests performed in the X, Y, and Z directions for both northern and southern PWC (Figure 2(b)) highlight the anisotropic and nonlinear behavior of the material, with the highest stiffness and load-carrying capacity in the longitudinal (X) direction, corresponding to the fiber orientation, while significantly lower responses are obtained in the Y and especially Z directions. In all cases, southern PWC exhibits superior mechanical performance compared to northern PWC.

From Table1, the southern PWC exhibits superior mechanical performance compared to the northern PWC. In the longitudinal (X) direction, the flexural modulus (Eb) is 0.32 ± 0.09 GPa for the southern PWC and 0.21 ± 0.05 GPa for the northern PWC. These values are in good agreement with the data reported by Djoudi,⁴⁶ who reported a modulus of 0.585 ± 0.001 GPa for southern PWC in the X-direction. The improved mechanical performance of the southern PWC is consistently observed across all directions. This improvement is likely attributable to the previously reported difference in density,⁴⁷ with the southern PWC having a density of 211 kg/m³, compared to 143 kg/m³ for the northern PWC. As expected, PWC is a heterogeneous and anisotropic material, with significantly higher mechanical properties observed in the fiber (X) direction. For the southern PWC, the flexural modulus in the Y and Z directions is 0.07 ± 0.02 GPa and 0.03 ± 0.01 GPa, respectively, compared to 0.30 ± 0.09 GPa in the X-direction.

Table 1.

Mechanical properties of the tested PWC measured by bending test.

	North (ρ_n = 143 kg/m³)			South (ρ_s = 211 kg/m³)
	ε^U(%)	σ^U (MPa)	E_b (GPa)	ε^U (%)	σ^U (MPa)	E_b (GPa)
X	4.17 ± 0.59	4.71 ± 1.31	0.21 ± 0.05	5.05 ± 0.89	8.38 ± 1.73	0.32 ± 0.09
Y	1.88 ± 0.29	1.11 ± 0.43	0.07 ± 0.03	1.93 ± 0.21	1.60 ± 0.41	0.07 ± 0.02
Z	2.90 ± 0.18	0.69 ± 0.12	0.03 ± 0.003	2.68 ± 0.48	1.08 ± 0.48	0.03 ± 0.01

From Figure 3, failure modes strongly depend on loading orientation. In the transverse directions, damage is dominated by transverse cracking, parenchyma tearing, and fiber–matrix decohesion. In the longitudinal direction, southern PWC mainly exhibits interfacial decohesion followed by fiber rupture, whereas northern PWC shows limited fiber failure, suggesting weaker interfacial bonding. Microscopic observations further reveal more pronounced fiber decohesion in northern PWC compared to partial decohesion in southern PWC.

Biobased sandwich panel

Figure 4(a) compares the evolution of the applied load versus the mid-span deflection for the BBSP subjected to three-point bending and RPL. The load–displacement curves obtained from the RPL tests are presented alongside those from the corresponding static tests (SP1, SP2, and SP3). The results show that the RPL loading accurately reproduces the mechanical behavior observed in static tests, with particularly strong agreement for sample SP2.The static tests of the three samples exhibit an initial linear relationship between load and deflection. As the applied load increases, a transition to non-linear behavior occurs, which is associated with the onset of damage within the sandwich beams. This damage may include microcracking on the core, initiation of skin failure, or disbond between core and skins. Beyond the peak load, a gradual reduction in load is observed until complete failure, indicating the total damage of the BBSP. Analysis of the RPL loading curves reveals that, even during the early loading cycles, the material does not fully recover its original configuration upon unloading, indicating the presence of permanent deformation. However, below a certain load threshold, the residual displacement remains below 10% of the maximum displacement recorded in the cycle preceding failure, demonstrating a substantial capacity for elastic recovery within this loading range.

To investigate the damage mechanisms during three-point bending, sample SP3 was instrumented with an Acoustic emission (AE) monitoring was performed using an IL40D piezoelectric sensor (20–1000 kHz, 10 mm diameter) mounted on the specimen surface with silicone grease to ensure proper acoustic coupling (Figure 4(b)). The measurements were conducted with a PAC-type acquisition system (Physical Acoustics Corporation, Mistras Group), using AEwin software for signal acquisition at a sampling frequency of 5 MHz. A threshold of 38 dB was set to minimize background noise and avoid masking relevant damage-related events. The detected signals were reamplified with a gain of 40 dB and subsequently analyzed using Noesis software. The acoustic signal amplitudes recorded during testing range from 45 to 100 dB, with a marked increase in event activity as the applied load approaches failure. The AE analysis was complemented by synchronized visual monitoring using a camera, allowing correlation between acoustic signatures and observable damage. This combined approach improves the identification of damage mechanisms and enhances understanding of degradation progression in sandwich beams under three-point bending. The results indicate that type A signals are dominant, accounting for 93.28% of the emissions for SP3, with amplitudes between 45 and 87 dB. These signals are attributed to microcracking in the polycyclic composite (PWC) and occur mainly during the elastic phase, reflecting damage initiation without significant stiffness loss. Type B signals, representing 6.25% of the emissions and exhibiting amplitudes from 60 to 98 dB, are associated with the propagation of pre-existing cracks in the web. Their occurrence corresponds to the onset of non-linear behavior in the load–displacement response, marking the transition from elastic to plastic behavior and a progressive reduction in mechanical strength.

Static indentation loading

Palm wood is a porous and heterogeneous material, making accurate hardness evaluation using only static indentation tests challenging. Therefore, both quasi-static and repeated indentation tests were conducted in the three principal directions to better characterize its behavior and identify the most suitable material configuration for sandwich core applications. In such structures, particularly with thin skins, the core plays a key role in absorbing indentation loads and preventing perforation.

Palm wood core

For hard and rigid materials, the Brinell hardness based on plastic indentation is denoted HB_r and is given by⁴⁴:

H B_{r} = \frac{2 P}{π D (D - \sqrt{D^{2} - d_{r}^{2}})}

(1)

Where P (kGf) is applied load; D (mm) is the diameter of indenter and dr (mm) is diameter of indentation (mm). However, for PWC, which is generally porous, the total hardness (HB_t) is determined from the total indentation depth

h_{t}

(mm) and is given by:

H B_{t} = \frac{P}{π D h_{t}}

(2)

HB_r values include only plastic deformation, while HB_t values include both elastic and plastic deformation. The unloading stiffness (S) is given by:

S = {\frac{d P}{d h} |}_{h = h t}

(3)

When the hardness of the indenter is much greater than that of the specimen, the reduced modulus (E_r) of the indented specimen can be inferred as^48,49:

E_{r} = \frac{\sqrt{π} S}{2 β \sqrt{π (D h_{c} - h_{c}^{2})}}

(4)

With:

h_{c} = h_{t} - 0.75 \frac{P_{\max}}{S}

(5)

Where h_c is the contact depth, P_max in the maximal load and β = 1 for cylindrical indenters.⁴⁹ Figure 5 presents the load–depth responses from monotonic and RPL indentation tests southern PWC specimens. Figure 5(a) represents monotonic indentation tests on five southern PWC specimens (Sp1–Sp5) indented in the X-direction. In this Figure, all curves display a typical loading–unloading cycle, where the load increases nonlinearly with indentation depth up to 45 N, followed by unloading to zero. A significant scatter is observed among specimens: for the same maximum load, the indentation depth ranges from about 0.5 mm to nearly 1.0 mm. Specimens Sp2 and Sp3 reach 45 N at lower depths (0.5–0.6 mm), whereas Sp1 and Sp5 exhibit larger depths (0.8–1.0 mm). This variability reflects the heterogeneous and anisotropic nature of PWC, influenced by differences in density, porosity, and fiber arrangement. During unloading, partial recovery is observed, indicating permanent deformation. The presence of pronounced hysteresis loops further highlights substantial energy dissipation, typical of cellular materials. Figure 5(b) compares RPL indentation responses in the X- and Y-directions under incremental loading from 5 N to 45 N at the same location. At each load level, the indentation depth is consistently higher in the Y-direction (e.g., ∼0.05 mm vs 0.035 mm at 5 N, and ∼0.37 mm vs 0.28 mm at 45 N). This confirms anisotropic behavior, attributed to anatomical fiber orientation: fibers aligned along the X-direction enhance resistance in that direction, while offering less constraint in the Y-direction. By comparing both figures, the repeated loading induces local strain hardening due to microstructural changes and progressive compaction of the indented zone. As a result, the material becomes stiffer and more resistant, leading to reduced incremental indentation depths compared to the static case. Conversely, in static loading, the undeformed material offers less resistance, resulting in greater penetration at 45 N. Additionally, the hysteresis loop area increases with load during RPL testing, indicating progressive energy dissipation and damage accumulation.

For southern PWC specimens indented along the X and Y directions, the evolution of HB_r, HB_t, and the depth ratio (h_r/h_t) with RPL (Figure 6) reveals a clear indentation-size effect. Both hardness values increase with load, with a more pronounced increase at low loads followed by a tendency toward saturation around 30 N, indicating the approach to a predominantly plastic deformation regime and a more stable indenter–material contact.

For a given load, hardness values in the X direction are consistently higher than in the Y direction, reflecting the anisotropic nature of PWC, governed by anatomical fiber alignment and cellular structure orientation. In all cases, HB_r remains higher than HB_t because elastic recovery during unloading reduces the residual indentation depth. Since hardness is inversely proportional to indentation depth, this smaller residual depth leads to higher HB_r values.

This behavior is confirmed by the evolution of the depth ratio (h_r/h_t), which decreases with increasing load and eventually reaches a plateau, marking a transition in the dominant deformation mechanism. In the X direction, h_r/h_t drops rapidly at low loads and stabilizes near 25 N, indicating limited additional permanent deformation and a response dominated by elasticity. In contrast, the Y direction exhibits higher h_r/h_t values and a more gradual decrease up to35 N before stabilization, reflecting greater penetration and more pronounced plastic deformation. Overall, these results show that PWC undergoes significant plastic deformation at early loading stages, especially in the Y direction, before reaching a threshold where elastic behavior becomes dominant.

Biobased sandwich panel

Figure 7 presents the load–depth responses from indentation tests on BBSP specimens. For indentation tests performed on three specimens (Sp1–Sp3), all curves exhibit a nonlinear increase in load with increasing indentation depth (Figure 8(a)). An initial steep slope corresponds to quasi-elastic behavior, followed by a gradual reduction in slope as indentation increases, reflecting progressive damage evolution and stiffness degradation during loading. At P = 500N, multiple slope changes suggest successive damage events rather than a single catastrophic failure. During unloading, pronounced hysteresis loops appear in all curves, highlighting significant energy dissipation due to irreversible deformation. The residual indentation depths confirm permanent damage accumulation. Although slight variations exist among specimens due to the anisotropic nature and manufacturing variability of BBSP, the overall responses remain consistent, demonstrating stable load-bearing capacity up to the maximum applied load and good damage tolerance.

Figure 7(a) compares responses at three load levels (400 N, 500 N, and 600 N). Increasing the load leads to deeper indentation and more severe deformation, with substantially higher energy dissipation, as indicated by the enlarged hysteresis loops. At 400 N, penetration remains limited, whereas at 500 N and 600 N, indentation depths increase significantly. Notably, multiple damage events occur between approximately 0.4 and 0.6 mm for the higher loads, consistent with observed surface damage. These damage modes include local delamination and debonding between flax/epoxy skins and the palm-wood core, core crushing due to cell buckling, matrix cracking and flax fiber failure in the skins, and localized damage beneath the indenter. Overall, increasing load intensifies penetration and damage, with distinct points marking the progression from local damage to global failure of BBSP under indentation.

Repeated indentation loading

Palm wood Coe

Figure 8 shows the load–depth response in the X-direction and the corresponding energy evolution in both X- and Y-directions for southern PWC under repeated indentation. The load–depth curves (Figure 8(a)) reveal progressive stiffness degradation and accumulation of permanent deformation with increasing cycle number. Each cycle forms a hysteresis loop, whose area represents the energy dissipated through plastic deformation, while the unloading slope reflects the effective elastic stiffness. As cycling proceeds (from $N = 1$ to 100), incomplete recovery leads to increasing residual indentation depth, indicating cumulative plastic strain and damage, accompanied by a gradual reduction in unloading stiffness.

To assess cumulative damage, the plastic dissipation energy ( $W_{p}$ ) and elastic strain energy ( $W_{e}$ ) were evaluated as functions of the normalized number of cycles ( $N / N_{f}$ ) for both directions (Figure 8(b)). The elastic energy decreases progressively with cycling, reflecting stiffness degradation, with a more pronounced reduction in the X-direction, while the Y-direction maintains higher elastic energy due to anisotropic behavior. In contrast, the plastic energy increases rapidly during the initial cycles and then tends to stabilize at higher cycle numbers, with similar magnitudes in both directions. This indicates that, unlike the elastic response, plastic deformation and damage evolution are weakly affected by anatomical fiber orientation. Overall, cyclic indentation induces progressive elastic degradation and plastic accommodation, with anisotropy mainly influencing the elastic response.

Figure 9 illustrates the evolution of the reduced elastic modulus ( $E_{r}$ ) and hardness-related energies ( $H B_{t}$ and $H B_{r}$ ) as a function of $N / N_{f}$ for PWC samples tested in the X and Y directions. At the beginning, both directions show a sharp drop in $E_{r}$ , indicating rapid stiffness degradation during the first cycles due to early-stage damage. This is followed by a quasi-stable plateau with minor fluctuations up to failure ( $N / N_{f} \approx 1$ ), suggesting that damage evolves toward a predominantly plastic compression state. In this regime, the material beneath the indenter is already compacted and plastically deformed, so subsequent cycles mainly involve loading–unloading of a stabilized damaged zone rather than continuous stiffness degradation. The X-direction consistently exhibits higher $E_{r}$ than the Y-direction, reflecting elastic anisotropy linked to fiber orientation, which governs the absolute stiffness level rather than the degradation rate.

The evolution of $H B_{t}$ and $H B_{r}$ also reveals two phases: an initial transient phase ( $N / N_{f} \approx 0$ –0.2) and a stabilization phase ( $N / N_{f} \approx 0.2$ –1). In the first stage, hardness shows strong variations, with a rapid increase to peak values (up to 2.2 MPa in the X-direction) followed by a sharp decrease, indicating cyclic softening associated with early microstructural adjustments. Throughout this phase and the entire fatigue life, higher hardness values are consistently observed in the X-direction, confirming the anisotropic nature of PWC. As cycling continues, the reduction in hardness slows, and both $H B_{t}$ and $H B r$ gradually stabilize around 1.2–1.4 MPa near failure. This plateau reflects a saturated compressive microstructural state, where further cyclic loading produces minimal additional softening.

Biobased sandwich panel

Figure 10 presents the load–depth response, the reduced modulus ( $E_{r}$ ) and energies ( $W_{p}$ and $W_{e}$ ) obtained from an RPL indentation test up to $P = 600$ N. The curves (Figure 10(a)) show a progressive increase in load with each cycle, accompanied by deeper penetration of the indenter into the BBSP. Successive loading–unloading loops form pronounced hysteresis, indicating energy dissipation through plastic deformation. With increasing load, the response gradually departs from linearity, marking the transition from elastic to nonlinear behavior, while the incomplete recovery during unloading confirms the accumulation of permanent deformation. The increasing slope of the loading curves at higher loads suggests enhanced contact stiffness, likely due to material hardening or an expanding contact area. The final cycle reaches the maximum load and depth, reflecting the highest indentation level and the cumulative damage induced by repeated loading, including microcracking, core crushing, and permanent deformation of the outer skin.

Figure 10(b) shows the evolution of the $E_{r}$ as a function of $N / N_{f}$ during RPL indentation for three samples (Sp1–Sp3). The progressive decrease in $E_{r}$ with increasing cycles reflects a continuous degradation of BBSP stiffness due to the accumulation of microstructural damage. Arapid decrease during the initial cycles corresponds to the onset of damage, while the subsequent gradual decline indicates a reduced rate of stiffness loss as damage continues to develop. This behavior suggests a saturation effect, where damage mechanisms stabilize and the material beneath the indenter evolves toward a compressed state. Differences between samples are also observed, with Sp1 maintaining a higher modulus and slower degradation compared to Sp2 and Sp3, likely due to variations in manufacturing quality, local defects, or interfacial issues such as delamination or decohesion between the core and skins. The results highlight the progressive and irreversible nature of damage under repeated loading, leading to a reduction in elastic resistance and providing key insight into the durability and lifespan of BBSP under RPL conditions.

As $N / N_{f}$ maximal value both W_p and W_e increase quickly. However, W_e rises more rapidly and reaches higher values than W_p (Figure 10(b)). This indicates that, despite the progressive accumulation of irreversible deformation, the material’s ability to store and release W_e remains dominant throughout the cycles. The growth in W_e suggests a hardening effect with increasing deformation. The divergence between W_p and W_e reflects the balance between damage accumulation and energy recovery during cyclic indentation: the increase in W_p confirms ongoing fatigue damage and permanent deformation, while the higher W_e highlights the material’s resilience under repeated loading. Overall, the interplay between plastic dissipation and elastic recovery governs the mechanical response, providing key insight into the fatigue behavior, durability, and lifetime of BBSP.

Conclusion

This paper proposed a new material of a bio-based sandwich panel (BBSP) composed of flax/epoxy skins and a palm wood core (PWC), which was evaluated under repeated bending and indentation loads. Three-point bending tests revealed that PWC exhibited an initial linear elastic response, followed by nonlinear behavior until failure, with low dispersion between samples. These tests confirm that PWC displays heterogeneous and anisotropic behavior, with superior mechanical performance for southern samples oriented along the fiber direction.This is due to its higher density, better fiber alignment, improved interfacial bonding, more compact cellular structure, and a higher content of cellulose and hemicellulose, all of which enhance stiffness and delay damage initiation compared to northern PWC.Comparison between static and RPL tests demonstrates that the RPL technique accurately reproduces the mechanical response of BBSP, validating the RPL technique as an effective method for simulating static behavior while ensuring detailed monitoring of BBSP degradation mechanisms. Furthermore, although the RPL technique induces permanent deformation from the first cycles, the samples retain a high elastic recovery capacity below a critical load threshold. Combined monitoring of mechanical properties and acoustic emission (AE) allowed for better tracking of damage progression.

Indentation tests reveal that southern PWC exhibits a highly heterogeneous and anisotropic mechanical response, with significant dispersion in indentation depth and recovery between samples. This dispersion is due to variations in local stiffness and energy dissipation related to the PWC’s cellular structure, density fluctuations, and fiber arrangement. Partial recovery during unloading and pronounced hysteresis loops confirm the presence of permanent deformation and significant energy dissipation. Compared to static indentation, the RPL technique induces local work hardening through successive loading-unloading cycles, resulting in increased stiffness and reduced indentation depth at the same maximum load. The results of the RPL indentation tests show that the PWC’s hardness increases with loading and then stabilizes under plastic deformation. The higher residual hardness relative to the total hardness reflects significant elastic recovery after unloading.

The BBSP exhibits a nonlinear and consistent indentation response, characterized by a progressive degradation of its stiffness and the activation of several damage mechanisms. Significant hysteresis loops and residual indentation depths confirm substantial energy dissipation and continuous damage accumulation. The indentation results show that increasing load levels lead to deeper penetration, wider hysteresis loops, and greater energy dissipation within the BBSP, resulting in multiple damage phenomena associated with delamination, core crushing, and skin cracking.

Due to cumulative plastic deformation, repeated indentation on the PWC results in a progressive loss of stiffness, an increase in residual indentation, energy dissipation, and a decrease in the reduced modulus of elasticity (Er) and hardness in both directions. Hysteresis loops widen and unloading slopes decrease with the number of cycles, indicating fatigue-type damage. It is evident that repeated loading accelerated material degradation and reduced its load-bearing capacity compared to single-cycle indentation. This was reflected in a progressive degradation of We and a rapid increase in Wp during the first few cycles, stabilizing at higher cycles.

The RPL indentation of the BBSP also reveals progressive plastic deformation, energy dissipation, and cumulative damage. Hysteresis loops indicate irreversible deformation, with a transition from elastic to nonlinear behavior. Steeper load slopes at high cycles suggest contact hardening or an increase in the contact area. The RPL indentation of the BBSP causes a progressive degradation of elastic stiffness, with an initial sharp drop in the reduced modulus (Er). The increase in Wp indicates progressive degradation due to fatigue and permanent deformation, while We highlights resilience and hardening.

In conclusion, this study demonstrated the potential of BBSPs as eco-friendly materials for industrial applications by evaluating their structural response, failure mechanisms, and mechanical efficiency. Future work should also investigate the effects of environmental conditions (humidity, temperature, and aging) and employ advanced characterization techniques, such as digital image correlation, X-ray tomography, and in-situ microscopy, to better understand damage mechanisms. In addition, extending the study to dynamic, impact, and long-term fatigue loading would provide a more realistic assessment of durability and support the reliable design of high-performance, sustainable sandwich structures.

Footnotes

ORCID iDs

Rachid Benzidane

Zouaoui Sereir

Author contributions

Rachid BENZIDANE: Conceptualization, Data curation, Formal analysis, Investigation, Writing – Original Draft Preparation. Khamis HADJAZI: Visualization; Investigation; Formal analysis, Methodology. Mohammed Arezki BENZIDANE: Conceptualization, Data curation, Formal analysis, Investigation, Writing – Original Draft Preparation. Zouaoui SEREIR: Conceptualization, Data curation, Formal analysis, Methodology, Resources, editing, Supervision, Validation, Writing – Review & Editing. Bachir BOUHAMIDA: Visualization; Investigation; Formal analysis, Methodology. Christophe POILANE: Conceptualization; editing and Supervision; Data curation; Validation, Formal analysis, Resources, Methodology; Software.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.*

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