Parametric Design Investigation and Mechanical Performance of Laser-Cut Kerf Bending in Plywood Sheets

Abstract

Kerf bending, achieved through precisely patterned cuts, enables the transformation of rigid plywood into flexible, adaptive surfaces for advanced design and ergonomic applications. This preliminary, exploratory study systematically investigates 56 laser-cut kerf geometries—spanning both traditional and novel parametric patterns—in birch plywood sheets of two thicknesses. Mechanical performance was evaluated via standardised testing, with statistical analyses (including Weibull and coefficient of variation) employed to interpret the pronounced variability observed in maximum load (Fmax) values, even among geometrically similar patterns. Due to the limitation of single-specimen destructive testing per pattern, the results should be understood as indicative trends within this experimental set, not as definitive rankings. Observed results suggest that kerf geometry and arrangement—rather than thickness or gross material removal—are the primary determinants of flexibility and strength. Notably, specific parametric and meander-type patterns demonstrated promising balances of deformation capacity and mechanical reliability within this limited dataset. The inherent limitations of experimental replication and natural material heterogeneity are explicitly acknowledged, and the findings are intended as a foundation for future, more statistically robust investigations. This work provides a comparative framework and initial design guidance for kerf-based plywood structures and identifies key priorities for further research in replication, material selection, and real-world applications.

1. Introduction

Plywood is a widely used engineered wood product, valued for its favourable strength-to-weight ratio, dimensional stability, and versatility across architectural, furniture, and industrial applications. In recent years, there has been growing interest in expanding the functional and aesthetic possibilities of plywood through advanced fabrication techniques, particularly laser cutting. Conventional techniques to enhance flexibility, such as steam bending and lamination, are labour-intensive, material-demanding, and constrained by the physical characteristics of specific wood species [1]. These challenges have prompted researchers and designers to explore alternative fabrication methods that enhance the plasticity of wood without compromising its inherent properties [2].

One technique, known as kerf bending, utilises strategic patterns of cuts to enable the controlled deformation of rigid panels into complex, curved geometries. This approach has unlocked new opportunities for designers seeking to create dynamic, flexible wooden components while maintaining the desirable material properties of plywood. Kerf bending allows for controlled deformation by reducing stiffness along the cut direction. When applied to plywood, kerf patterns create hinge-like zones that enable the material to bend while maintaining overall continuity [3]. The geometry, spacing, and depth of kerf cuts significantly influence the achievable curvature, structural integrity, and aesthetic outcomes [4].

Despite these advances, the scientific understanding of the mechanical performance and reliability of kerf-bent plywood remains limited. Previous studies have primarily focused on the geometric parameters required to achieve desired curvatures or on the visual and functional outcomes of specific kerf patterns [2,4]. Among these technologies, laser cutting is particularly noteworthy due to its high accuracy and repeatability in generating intricate kerf patterns. Unlike traditional, manual or CNC router methods, laser cutters excel at rapid prototyping, facilitating the creation of complex kerf geometries with minimal tool wear [5,6]. Research indicates that the optimisation of laser cutting parameters directly affects kerf quality, which subsequently influences the edge finish and coherence of the cuts [7,8,9,10,11].

Previous studies have demonstrated the potential of kerf bending for developing flexible surfaces, architectural installations, and experimental design objects [12,13]. However, there is a lack of systematic research examining how variations in kerf geometry and laser processing parameters affect the structural integrity and bending strength of plywood panels. Moreover, the probabilistic characterisation of failure, particularly using reliability-oriented methods such as Weibull analysis, has not been thoroughly explored in this context.

Seating design requires a balance between comfort, structural stability, and aesthetic appeal. Ergonomic chairs often rely on materials that adapt to the user’s body while distributing load effectively [14]. The integration of kerf bending into seat construction provides a novel approach to achieving localised flexibility in otherwise rigid wooden components. This method enables the creation of forms that conform to ergonomic requirements without the need for additional upholstery or complex joinery [15].

Kerf bending offers a versatile method for inducing controlled curvature within planar materials. By introducing patterned separations in the form of kerf arrays, it enables adjacent regions to bend cohesively along defined boundaries. These kerfs act as flexible joints, giving rise to hinge-like behaviour that allows flat materials to assume complex, curved, or folded geometries.

Laser fabrication provides an exceptional level of precision in defining kerf geometry. The ability to finely control widths, spacings, and angles enables predictable deformation and consistent mechanical response. Consequently, laser kerfing extends the potential of traditional bending methods, ensuring repeatable structural performance and expanding design freedom for architectural and furniture applications.

Kerf bending represents a modern approach to wood deformation, relying on a network of fine, shallow cuts to locally reduce stiffness while maintaining material continuity. Each kerf functions as a mechanical hinge that governs bending direction and curvature.

Laser cutting is particularly effective for producing such precise arrays. It offers a high degree of accuracy and reproducibility in defining kerf geometry—parameters that ultimately dictate the bending behaviour and flexibility of the surface. Despite a growing body of literature on kerf performance, limited research has explored laser-based kerf creation for industrial-scale flexible wood applications. This study aims to bridge that gap through systematic experimentation and prototyping.

Although kerf bending appears contemporary, it is rooted in traditional wood-forming techniques such as kerf lamination—historically employed to create curved surfaces [16,17,18,19,20,21,22]. Over time, bending techniques have evolved alongside laminated and composite materials, including honeycomb and sandwich structures.

In furniture design, laser-crafted kerf arrays offer a promising path for achieving adaptable and ergonomic seating surfaces. Since the human body is dynamic and continuously adjusts posture, seating must respond flexibly to these micro-movements [23,24,25]. While traditional ergonomic design often relies on static anthropometric data, other design philosophies—such as those influenced by classical Chinese furniture—embrace flexibility and adaptability as key aesthetic and functional elements [26,27].

This study systematically investigates the influence of different kerf patterns and specimen thicknesses on the bending performance of laser-cut plywood. Our research is distinct in its combined use of classical statistical comparison methods and Weibull analysis to assess not only mean mechanical properties but also the distribution and reliability of strength values. By providing both comparative and reliability-based insights, this work advances the current state of knowledge and offers practical guidance for the design and engineering of flexible plywood structures. The objectives of this study are threefold: (1) to quantify the impact of various kerf geometries on the bending strength and stiffness of plywood, (2) to evaluate the reliability of kerf-bent specimens using Weibull statistical modelling, and (3) to establish design recommendations for the fabrication of structurally sound, flexible plywood components. The results presented here are intended to inform future applications in adaptive furniture, architectural installations, and other domains where wood flexibility and strength are critical.

2. Materials and Methods

Based on an understanding of the kerf bending technique and the relevant studies reviewed above, this research links the need for a deeper exploration of a diverse measurement approach. The objective was to compile a comprehensive and systematic table that brings together all kerf patterns currently available, along with the measurement data derived from experimental testing.

The experimental process for the specimens was structured in three consecutive stages (Figure 1). In the first stage, all kerf patterns accessible online were identified, then carefully screened to eliminate any clearly unsuitable examples, and subsequently organised according to the criteria and classifications outlined in the previous chapter. The second stage focused on the fabrication of the selected specimens using a laser cutter. Finally, the third stage involved mechanical evaluation using a universal testing machine and material testing equipment at the Department of Forestry, Wood Sciences, and Design, University of Thessaly, Greece. These tests provided accurate measurements of the specimens’ properties. Additional conventional non-destructive testing methods complemented them.

2.1. First Stage of Experiments: Pattern Collection

One of the most widely used linear patterns was designed by Aaron Porterfield, consisting of horizontal parallel lines with interruptions at two or three points. This design is valued for its ability to provide both high curvature and strength. As noted in a study [28], modifying the discontinuities in such patterns affects material flexibility: fewer interruptions yield greater curvature but reduced structural strength due to increased material removal.

Alternative variations were created where discontinuities alternated left and right, resulting in highly flexible samples capable of bending up to 180°. Increasing line density enhanced curvature and elasticity but reduced mechanical strength.

In contrast, “wave” and “zigzag” patterns replace straight lines with polygonal, diagonal, or curved chains (Figure 2). This modification disrupts wood fibres at multiple points, thereby maximising curvature capacity.

“Perforated” or “cut-out” patterns, such as “bowling-pin-shaped” perforations, involve complete removal of material in geometric forms, producing transparency and significantly increased flexibility. However, this comes at the cost of reduced structural integrity. The distribution of bending forces in these shapes is more even, preventing sharp angles and concentration of local stress.

“Offset” patterns, composed of shifted triangles, squares, or hexagons, demonstrated high strength and the ability to generate double curvature (Figure 2b). However, points of discontinuity in triangular or square offsets often coincided with fracture locations, while intersections marked zones of maximum curvature. The “honeycomb” pattern, though also involving material removal, was classified as an offset pattern due to its curvature performance depending on the external offset cuts.

The “meander” pattern (Figure 2c), developed by Scott Austin, consists of labyrinth-like continuous lines that combine flexibility and resilience. Variations demonstrated that smaller-scale meanders increased flexibility but decreased strength. Parametric modifications of meanders, including rounded corners or triangular/hexagonal adaptations, generated new behaviours ranging from single to double curvature.

Finally, “parametric” patterns (Figure 2d) were developed using algorithmic design, incorporating adjustable parameters such as line density, spacing, length, orientation, and discontinuity. These produced complex double-curvature behaviours, with densification at specimen centres enabling maximum curvature.

The first experimental stage concluded with the final selection of 56 unique patterns, including original designs and their variations.

The patterns were collected following extensive online research, as the kerf-bending technique with laser cutting primarily relies on digital files for fabrication. This reliance on digital resources makes it challenging to find such patterns within conventional bibliographic references.

During the collection process, several widely used designs were identified, including parallel line patterns and meander-type patterns. However, some patterns that were initially presented as suitable proved incompatible as their cutting would have segmented the piece completely, eliminating structural cohesion and thereby preventing curvature. In certain cases, this limitation was not immediately apparent; for instance, some sample files failed to bend when cut at their original scale, requiring further modification.

To process the collected patterns and prepare them for final cutting, the software “Rhinoceros 6” and “AutoCAD 2019” were employed. Using both software, variations of existing patterns were created by adjusting scale, line spacing, and line morphology (e.g., replacing sharp corners with filleted curves), as well as by altering density (parametric density variations). Through this process, new patterns with distinct bending capabilities were generated.

Patterns were initially divided into two major categories: those enabling single curvature and those capable of double curvature. A more detailed classification was then developed, combining both previously established typologies and newly observed or designed patterns. The final categorisation is as follows (with corresponding numbering as listed below (

Table 1. Design pattern categorisation.

Type of Pattern	Pattern Numbers
Linear (parallel lines)	1–5
Wave or zigzag	6–11
Perforated/cut-out (closed shapes with material removal)	12–26.2
Offset	27–34
Meander	35–41.2
Parametric	42–42.3

):

2.2. Second Stage of Experiments: Pattern Cutting

Following the collection and preparation of the digital designs, the second stage involved the fabrication of test specimens. Laser cutting was performed using a Bodor (Jinan, China) CO₂ CNC laser cutting machine (150 W), operated at 70% power output (105 W) and a cutting speed of 30 mm/s. The focus distance was set to 8 mm, and air, at 1.5 bar, was used as the assist gas. Each kerf was cut in a single pass. All processing was conducted under ambient laboratory conditions (20 ± 2 °C temperature, 55 ± 5% relative humidity). Birch plywood sheets (3 mm and 4 mm thick, 12% moisture content, 0.70 g/cm³ density) were cut to standardised dimensions, and kerf patterns were exported as vector files from Rhinoceros/AutoCAD. Specimens were aligned with the wood grain parallel to their long axis. Cutting parameters were optimised in preliminary trials to achieve clean edges with minimal charring. The kerf width: 150 µm (0.15 mm—standard deviation: ±0.01 mm), was measured using a portable optical measuring microscope (50×–160×), directly at the surface of the specimen after focusing the laser (Figure 3). The measured kerf width was used for all quantitative analyses. This kerf width represents the effective width of material removed during each laser pass and is a key parameter influencing the precision and mechanical characteristics of the fabricated patterns. The primary material selected was Russian birch plywood. The main components of the materials used in this study are thin birch wood veneers (plies), phenolic resin adhesive (WBP type) to bond the layers, and a sanded surface finish. The birch plywood used in this study was industrial-grade (EN 636-2S) [29] with a standard cross-laminated structure. For the 3 mm thick panels, there were 3 veneer layers; for the 4 mm panels, 5 layers. The grain direction of each veneer alternated at 90°, with the outermost layers’ grain running parallel to the specimen’s long axis. The adhesive used was phenolic resin (WBP type), providing water and weather resistance. The original panels measured 2500 × 1250 mm, with a density of 0.70 g/cm³ and a moisture content of 12% at the time of cutting. The specimens were cut into standardised dimensions for consistency across tests. Natural defects such as knots, voids, or seams, as well as variations in adhesive layers, were noted as potential sources of structural irregularities.

Cutting times were recorded for each specimen and are summarised in the consolidated table, ranging from 1 to 9 min, depending on the pattern lines’ density.

During initial cutting trials, several errors were observed. Some collected patterns, due to scale or dimensional issues, produced excessively rigid specimens. This necessitated a second round of design modifications. Additional issues arose from inherent material defects such as knots, seams, voids, or variations in adhesive layers, which occasionally caused localised cutting failures and required reprocessing.

In total, 112 specimens were fabricated: 56 from 3 mm birch plywood and 56 from 4 mm birch plywood. For the supplementary bending angle experiment (a non-destructive method measuring the degree of curvature in single-bend specimens), an additional 56 specimens were cut with extended material tabs on one side to allow secure clamping. These later served as reference samples for the final catalogue presentation.

2.3. Third Stage of Experiments: Measurement Methods

2.3.1. Mechanical Testing (Destructive)

After specimen fabrication, the third and final stage involved evaluating mechanical and bending properties using both conventional and advanced measurement methods. Regarding the mechanical properties, the initial modulus of elasticity in bending (E) of the solid material without processing is estimated to be approximately 8000 N/mm² (≈8000 MPa) for the 3 mm thickness and approximately 9000 N/mm² (≈9000 MPa) for the 4 mm thickness. The baseline mechanical reference for comparing the behaviour of the specimens after the application of the kerf bending technique is based on these values, which are within the typical range for high-quality birch plywood.

It should be noted that while EN 301 [30] pertains to the testing of adhesive joints in load-bearing timber structures, our mechanical evaluation followed the principles of EN 310 [31], which is the standard for determining the bending strength and modulus of elasticity of wood-based panels. However, due to the discontinuous nature and unique deformation behaviour of kerf-bent specimens, we adapted the standard three-point bending test by employing a custom fixture to assess both single and double curvature patterns. This adaptation was necessary to obtain meaningful comparative data for the modified panels, as traditional EN 310 methods presuppose a continuous, homogeneous cross-section not present in kerf-bent samples. In this test, the specimen is supported at two points and loaded vertically at the midpoint of the span until failure occurs. Loading was applied at a constant rate of 5 mm/min until failure. The maximum load recorded during the test (Fmax) is expressed in Newton (N) and is used to calculate the bending strength, which is expressed as stress in Megapascal (MPa). The double curvature of the Kerf was used to highlight the samples’ properties by creating four support points in a square frame using the specimens coming from flat sheets.

The primary method involved measuring the fracture point and modulus of elasticity of the 112 specimens using a Zwick/Roell Z020 (ZwickRoell GmbH & Co. KG, Ulm, Germany) universal testing machine (Figure 4).

A custom wooden frame (150 × 150 mm) was constructed to hold specimens at four points, simulating a seating frame (Figure 5a). A plunger was used to apply force to the specimen centre until it failed, while also recording load values in Newtons (N) and creating stress-strain graphs (Figure 5b). This approach was particularly suitable for double-curvature patterns, though single-curvature specimens were also measured to provide a complete dataset.

2.3.2. Conventional Testing (Non-Destructive)

In addition to destructive testing, a non-destructive bending angle method was employed. This method focuses on (i) measuring the bending angle of specimens (in degrees) under single curvature, (ii) applying loads with weights on single-curvature patterns, allowing for comparison of flexibility across patterns without compromising structural integrity, and (iii) assessing double-curvature patterns by applying localised force.

The angle measurement experiment was particularly suitable for specimens with single curvature and was also performed on all double-curvature patterns to investigate whether these designs could function along a single axis. For this test, a custom protractor was designed and mounted onto a vertical base, enabling the specimens to be clamped securely on one side (Supplementary Table S1). The free side was then allowed to bend along one axis, and the resulting angle was recorded using the protractor.

In the weight-loading experiment, specimens were fixed along two edges, allowing bending exclusively along a single axis (single curvature). Weights were applied incrementally until the specimens approached their fracture threshold. For double-curvature patterns, the method was modified: the four corners of the specimen were supported on independent bases, leaving them free, while force was applied at the centre. This configuration allowed the surface to form a convex double curvature.

Some specimens elongated during this process, while others did not approach fracture even under maximum applied load. In total, up to four weights of 200 g each (maximum load: 800 g) were applied to certain single-curvature specimens. For other cases, manual surface pressure was applied until resistance was encountered during bending (Supplementary Table S2).

2.4. Kerf Patterns

Based on an extensive collection, modification, and classification process, 56 kerf patterns were selected and tested. These patterns were grouped into six main categories:

The first category was the “linear” patterns (1–5). Parallel straight cuts, including widely used designs such as Aaron Porterfield’s interrupted-line pattern, are capable of bending up to 180° with variations in density and discontinuities. These provide high curvature but reduced strength as kerf density increases.

The second category was the “wave/zigzag” patterns (6–11). These patterns are derived from linear patterns by replacing straight cuts with diagonal, polygonal, or wavy lines. They disrupt fibres in multiple directions, enhancing flexibility and enabling greater curvature.

The third category was “perforated/cut-out” patterns (12–26.2). They consist of geometric cut-outs (e.g., bowling pin shapes) that fully remove material. These result in transparency and uniform elasticity but reduce overall structural integrity.

The fourth category was the “offset” patterns (27–34). They are formed by shifted shapes (triangles, squares, hexagons), including honeycomb structures. These designs provide high strength and can achieve double curvature, though stress points often appear at discontinuities.

The fifth category was the “meander” patterns (35–41.2). A labyrinth-like continuous line design (Scott Austin’s model) is valued for its balance of flexibility and resilience. Smaller-scale meanders increase curvature but reduce strength. Variations with rounded corners, triangles, and hexagons expand their performance from single to double curvature.

The sixth category was the “parametric” patterns (42–42.3). Those were generated through algorithmic design, with adjustable variables such as line density, spacing, and curvature direction. These patterns concentrate flexibility in specific regions (often at the centre), enabling double curvature and highly controlled bending performance.

3. Results

The combined results from both destructive and non-destructive tests were consolidated into a comparative database, enabling systematic evaluation and selection of the most suitable kerf patterns for subsequent application in the seating prototype.

Patterns were organised into a digital library of 56 designs, categorised by curvature type and geometry. Visual inspection of kerf patterns focused on curvature smoothness, absence of cracks, and reduction of burn marks from laser cutting.

The combined results from destructive and non-destructive methods allowed the creation of a comprehensive database of kerf pattern performance, used to select the most suitable designs for the seating prototype.

Following the acquisition of all necessary measurements with the universal testing machine, the results were compiled in a consolidated table (Annex:

Table 2. Potential application groups for “double curvature” patterns based on the Fmax.

Application Groups	Pattern Numbers
Decorative and visual applications	27, 28, 41
Interior cladding and surface coverings	29, 34, 36, 39, 41.1, 41.2
Load-bearing surfaces (e.g., seats and backrests)	30, 31, 32, 38, 42, 42.2
Curved cladding or backrest panels	33, 35, 37, 40, 42.1, 42.3

) and further analysed comparatively. The analysis examined values across patterns and material thicknesses, while the relationship between kerf geometry, percentage of material removal, and their combined influence on curvature and mechanical strength was reviewed. Special emphasis was given to double-curvature patterns to identify indicative applications for each and select the most suitable candidates for subsequent application (in a flexible seating prototype).

3.1. Comparison of Fmax Values by Thickness

From the comparative analysis of Fmax (N) values for all patterns at the two tested thicknesses (3 mm and 4 mm), it was observed that the 3 mm specimens consistently achieved higher Fmax values than their 4 mm counterparts. The thinner plywood offered better deformation capacity before fracture and more efficient distribution of internal stresses.

The kerf bending process introduces a series of cuts that create local stress concentrations. As a result, the mechanical behaviour of the specimens is highly sensitive to the presence and location of internal defects, which may not be visible on the surface. A small defect or irregularity in a critical region can drastically reduce the maximum load a specimen can withstand, leading to a wider spread in Fmax values.

Specifically, patterns No. 30, 32, 38, and 42.2 at 3 mm thickness exhibited significantly high Fmax values, maintaining stable curvature and thus proving ideal for applications requiring a balance of strength and elasticity (Annex:

Table 3. Descriptive statistical analysis (Fmax), using IBM SPSS Statistics 31.0.1.0 software.

Statistics	4 mm (N)	3 mm (N)
Mean	172.16	211.16
Standard deviation	138.27	175.15
Minimum	19.10	26.80
Median	138.53	145.16
Maximum	587.47	765.61

). In contrast, patterns such as No. 27 and No. 41 recorded particularly low Fmax values, rendering them suitable only for non-structural or decorative uses. A bar chart was produced to visualise Fmax values per thickness and collectively across all patterns (Figure 6).

3.2. Influence of Material Removal Percentage

Analysis of the percentage of material removed (as calculated per pattern and reported in the consolidated Table 3) revealed notable variations in how geometry impacts mechanical and ergonomic behaviour. Percentages ranged from approximately 3% to nearly 60%, offering a wide diversity of kerfing approaches (Figure 7).

However, the ratio of removed to retained material was not always a strict determinant of flexibility. Certain geometries with low removal percentages (e.g., “parametric” patterns) achieved high deformation due to efficient structural distribution, while others with high removal percentages demonstrated reduced strength because of diminished cross-sectional resistance to stress. These results highlight the importance of geometry over raw material removal.

3.3. Performance of Double-Curvature Patterns

For double-curvature patterns (No. 27–42.3), force–deformation diagrams obtained from the mechanical performance tests indicated that several designs achieved high Fmax values along with favourable elastic–plastic behaviour. Once again, 3 mm specimens outperformed 4 mm specimens, combining larger bending capacity with higher peak loads (Figure 8). Patterns No. 32, 35, 38, 40, 42, 42.1, 42.2, and 42.3 showed the best overall mechanical behaviour.

3.4. Indicative Applications of Double-Curvature Patterns

Based on their Fmax values, “double curvature” patterns were categorised into four indicative application groups (Table 2). From this classification, the most suitable candidates for seating applications were determined as those combining progressive deformation, high Fmax values, and the ability to generate double curvature. These included patterns No. 32, 35, 38, 40, 42, 42.1, 42.2, and 42.3.

Notably, patterns No. 42 and 42.2 exceeded 125 N Fmax at 3 mm thickness, allowing smooth loading without permanent deformation. Patterns No. 38 and 40 demonstrated gradual force increases with steady curvature. Although pattern No. 42.3 did not record the highest Fmax, it exhibited strong elasticity and recovery capacity, making it valuable for ergonomic surfaces.

The analysis confirmed that geometry plays a more decisive role than thickness or removal percentage in determining kerf-bent performance.

The experimental results confirmed that kerf geometry plays a decisive role in determining the flexibility of plywood panels. Linear kerfs with dense spacing (≈3 mm) achieved a bending radius as low as 50 mm, enabling significant curvature. By contrast, wider spacings (>6 mm) reduced flexibility and restricted the bending angle. “Wave” and “zigzag” patterns offered higher adaptability, as the angled or sinusoidal kerfs disrupted fibres along multiple directions. “Parametric” designs concentrate curvature in specific regions, allowing controlled deformation and, in some cases, achieving double curvature, which is not possible with traditional linear cuts. Generally, thinner specimens (3 mm plywood) consistently exhibited greater curvature than 4 mm specimens, demonstrating that thickness reduction enhances flexibility without catastrophic loss of stability.

Mechanical testing with the Zwick/Roell Z020 revealed that while kerf bending inevitably reduces the load-bearing capacity of the birch plywood, certain patterns maintained 60–70% of the original strength. Patterns with balanced material removal, such as offset or meander designs, exhibited the best trade-off between flexibility and strength.

The maximum force values (Fmax) for 3 mm specimens were generally higher than those of 4 mm specimens, as the thinner panels distributed stresses more effectively under bending. Notably, patterns No. 32, 35, 38, 40, 42, 42.1, 42.2, and 42.3 combined high Fmax values with progressive, non-brittle failure modes, making them strong candidates for structural furniture applications. Patterns with excessive material removal (up to 60%) exposed reduced mechanical resistance, confirming that while flexibility increases, the cross-section resistance is diminished. Conversely, “parametric” geometries demonstrated that efficient kerf arrangements can achieve satisfactory strength even at relatively low removal percentages.

In addition to mechanical performance, the kerf patterns were evaluated for their visual and tactile qualities. Excessive burn marks were minimised by adjusting laser settings (lower power and higher cutting speed), resulting in clean kerfs with smooth edges. From a design perspective, “linear” and “parametric” patterns provided the most visually seamless transitions, producing organic and flowing surfaces that enhanced the aesthetic quality of the bent panels. “Perforated cut-out” designs added transparency and visual lightness, although their reduced strength limited their functional applications. The evaluation confirmed that kerf patterns not only modify the mechanical properties of wood but also act as decorative design elements, contributing to both functional and aesthetic qualities in furniture applications.

3.5. Statistical Analysis

Statistical comparison between different groups was conducted using ANOVA and t-tests, as these methods are appropriate for detecting significant differences in mean mechanical properties when data are approximately normally distributed, and sample sizes are adequate. In addition, Weibull analysis was performed to model the probability of failure and assess the reliability of the kerf-bent specimens. The Weibull distribution is particularly suitable for materials like plywood, where strength properties are influenced by natural variability and flaw distribution. This dual approach provides both comparative and reliability-based insights, supporting a comprehensive understanding of the mechanical performance of the tested specimens.

IBM’s SPSS Statistics software was used to process and analyse experimental data. A descriptive statistical analysis of the maximum bending strength values (Fmax) was performed, calculating the mean, standard deviation, median, minimum and maximum values for the 3 mm and 4 mm thick specimens (Table 3). Using the Shapiro-Wilk and Kolmogorov-Smirnov tests, the normality of the data was assessed. Since the data were not normally distributed (

Table 4. The Shapiro-Wilk normality test.

Variable	W Statistic	p-Value	Normality
Fmax/4 mm	0.880	p < 0.001	Not normal
Fmax/3 mm	0.821	p < 0.001	Not normal

and

Table 5. The Kolmogorov–Smirnov normality test.

Variable	D Statistic	p-Value	Normality
Fmax/4 mm	0.134	0.243	Cannot reject normality
Fmax/3 mm	0.215	0.009	Not normal

), the nonparametric Mann-Whitney U test was used to compare the two groups (Table 4). For completeness, a parametric t-test of independent samples was also performed with Welch’s correction. Relative variability of the results was assessed using the coefficient of variation (CV), while the magnitude of the effect of thickness was estimated using Cliff’s delta, which is suitable for nonparametric data. Lastly, a two-parameter Weibull analysis was applied to evaluate the reliability and the fracture behaviour of the specimens. In all statistics, the level of statistical significance was set at 0.05. Both datasets significantly deviate from normality (p < 0.05).

The Kolmogorov–Smirnov test demonstrated that the 3 mm specimens’ data clearly violate normality, and the 4 mm specimens’ results are mixed; hence, the Shapiro–Wilk is considered more reliable. The Shapiro–Wilk test indicated that Fmax datasets deviate significantly from normality (p < 0.001). Therefore, a non-parametric Mann–Whitney U test was used to compare the maximum force between 3 mm and 4 mm specimens.

The analysis revealed no statistically significant difference between the two thicknesses (U = 1355, p = 0.216). Parametric t-test results led to the same conclusion (p = 0.194) but were considered secondary due to violation of normality assumptions.

To undertake a comparison between 3 mm and 4 mm specimens, a parametric test was also undertaken: Independent samples t-test (Welch)

H₀: 

Mean (Fmax 3 mm) = Mean (Fmax 4 mm).

t = −1.31, p = 0.194

No statistically significant difference between means (α = 0.05). The non-parametric test: Mann–Whitney U test, makes the hypothesis:

H₁: 

The distributions of Fmax are equal.

U = 1355, p = 0.216

The test showed no statistically significant difference between 3 mm and 4 mm (α = 0.05). In conclusion, both distributions were strongly right-skewed, with the majority of values concentrated below approximately 250 N for the 4 mm specimens and below 300 N for the 3 mm specimens, while several high-force outliers exceeded 500 N. This behaviour suggested that the data were unlikely to follow a normal distribution.

Normality was assessed using the Shapiro–Wilk test, which indicated significant deviation from normality for both thicknesses (p < 0.001). Although the Kolmogorov–Smirnov test produced mixed results—failing to reject normality for the 4 mm specimens but rejecting it for the 3 mm specimens—the Shapiro–Wilk test was considered more reliable for the given sample size. Consequently, both datasets were treated as non-normally distributed. Given the violation of normality assumptions, a non-parametric Mann–Whitney U test was employed to compare the Fmax values between thicknesses (Figure 9). The test revealed no statistically significant difference between the 3 mm and 4 mm specimens (U = 1355, p = 0.216). For completeness, a Welch independent-samples t-test was also performed and yielded a consistent result (t = −1.31, p = 0.194), although it was considered secondary due to the lack of normality.

The coefficient of variation (CV) was calculated to assess relative variability and reliability (

Table 6. Coefficient of Variation (CV %).

Thickness	Mean Fmax (N)	Std. Dev. (N)	CV (%)
4 mm	172.16	138.27	80.3
3 mm	211.16	175.15	82.9

). The coefficient of variation quantifies relative variability and is crucial for reliability assessment. Both thicknesses exhibited extremely high CV values, exceeding 80%, which indicates substantial scatter and low repeatability. The 3 mm specimens showed slightly higher variability, suggesting marginally lower consistency despite their higher mean strength. This high scatter explains why numerical differences in mean Fmax did not translate into statistically significant results.

As shown in Table 6 and discussed in Section 3.5, both 3 mm and 4 mm thick specimen groups exhibited very high coefficients of variation (over 80%), indicating substantial scatter and low repeatability. This high variability persisted despite the use of standardised fabrication and testing protocols. The Weibull analysis (

Table 7. Weibull reliability analysis.

Thickness	Shape β (Weibull Modulus)	Scale η (N)	Interpretation
4 mm	1.3	187	Lower characteristic strength
3 mm	1.32	231	Higher characteristic strength

, Figure 10) further confirmed that failure is controlled by defect sensitivity, resulting in a highly scattered distribution of Fmax values.

Because normality is violated, Cliff’s delta is the correct effect size. Cliff’s δ = 0.136, which shows a negligible practical effect. Although the 3 mm specimens exhibited a higher mean maximum force compared to the 4 mm specimens, both datasets showed extremely high coefficients of variation (>80%), indicating significant scatter and low repeatability.

A Mann–Whitney U test revealed no statistically significant difference between thicknesses (p = 0.216), and the effect size measured by Cliff’s delta (δ = 0.136) was negligible. These results suggest that thickness alone does not govern bending strength, and failure behaviour is dominated by material variability and defect sensitivity rather than nominal geometry. A two-parameter Weibull distribution was fitted to the maximum force (Fmax) data for both specimen thicknesses (3 mm and 4 mm), assuming a zero-threshold load. Weibull reliability analysis revealed that both 3 mm and 4 mm specimens exhibit low Weibull modulus (β ≈ 1.3), indicating highly scattered, defect-controlled failure behaviour (Figure 10, Table 7). Although the 3 mm specimens demonstrated a higher characteristic strength (η = 231 N) compared to the 4 mm specimens (η = 187 N), the similarity of Weibull moduli and the strong overlap of reliability curves indicate comparable reliability levels. Consequently, the observed increase in mean strength for thinner specimens does not translate into a statistically or practically significant reliability improvement.

4. Discussion

This study systematically assessed the mechanical performance of laser-cut kerf patterns in birch plywood, focusing on how geometric parameters, material removal, and thickness affect flexibility, localised stress distribution, and ultimate bending strength (Fmax). The findings confirm that kerf geometry is a key driver of bending behaviour, yet significant variability in mechanical results underscores the influence of both natural material defects and process-induced imperfections.

The results (Section 3.1, Figure 6, Table 3) show that specific kerf geometries—most notably the parametric and meander patterns (e.g., No. 42, 42.2)—outperform others in terms of mean Fmax and deformation capacity. These geometries combine high load resistance with progressive, non-brittle failure modes, making them promising for applications requiring both flexibility and structural integrity (Section 3.4, Table 2). Conversely, patterns with excessive material removal, such as perforated or cut-out designs, consistently exhibited the lowest Fmax values and reduced structural reliability, a finding in line with prior research [4,8,10].

The custom mechanical testing setup was designed to reflect real-world use (e.g., seating applications) by applying force at the specimen centre. However, minor misalignments or local weaknesses due to kerf geometry and cut precision may also introduce additional variability in peak load measurements. While pattern geometry and material removal percentage were controlled variables, their interaction with the plywood’s natural variability can amplify differences in observed Fmax values among nominally identical specimens.

Analysis of material removal percentage (Section 3.2, Figure 7) further demonstrates that flexibility and strength are largely dictated by the efficiency of the geometric arrangement rather than the absolute volume of material removed. For instance, parametric patterns with relatively low removal ratios still achieved superior mechanical performance due to optimised stress distribution—supporting conclusions from earlier studies on the importance of kerf geometry [3,4,6].

Despite these clear trends, mechanical performance exhibited substantial scatter, as reflected by high coefficients of variation (>80%, Table 6) and a low Weibull modulus (β ≈ 1.3, Table 7; Figure 10). This indicates that specimen failure is primarily defect-controlled, with local weaknesses such as knots, veneer seams, or adhesive inconsistencies—potentially aggravated by the laser’s heat-affected zone—acting as fracture initiation sites. This pattern of defect sensitivity and reliability-limited strength is well documented in engineered wood literature [8,20], and is particularly pronounced in thin, highly processed laser-cut panels.

The Weibull reliability analysis (Section 3.5, Table 7, Figure 10) emphasises the need for caution when recommending particular patterns for load-bearing applications. Even among the highest-performing geometries, the probability of encountering a critical defect remains significant, underscoring the necessity of incorporating safety factors and robust quality control in practical implementations.

The implications for design and manufacturing are as follows:

Pattern Selection: Patterns such as No. 42 and 42.2 are recommended based on their consistent relative performance (Section 3.4, Table 2). However, their use in critical applications should always be accompanied by stringent material selection and manufacturing oversight to minimise defect incidence.

Process Optimisation: As laser kerf width and thermal effects can vary with process parameters, precise control over cutting conditions (Section 2.2, Figure 3) is crucial for repeatability and mechanical reliability. Future work should include direct microscopic analysis of the kerf region to assess the extent of the heat-affected zone and adhesive degradation.

Quality Assurance: Designers should plan for batch-to-batch variability and employ statistical or reliability-based design methods, particularly for safety-critical or load-bearing uses.

The systematic exploration of 56 kerf patterns with destructive and non-destructive testing (Section 2.3, Section 3.1, Section 3.2, Section 3.3 and Section 3.4) adds to the body of work on digital fabrication in wood [2,4,6]. While prior studies have demonstrated the potential for parametric kerfing to achieve tailored flexibility [3,4], our findings highlight both the promise and the practical challenges—especially the need to address inherent material variability and the effects of localised thermal damage.

Future research should apply microscopic and spectroscopic techniques to characterise the kerf region and quantify the impact of the heat-affected zone and adhesive degradation on mechanical properties. Also, more tests should be conducted using alternative engineered wood panels or composite materials with reduced heterogeneity to further isolate geometric effects. Moreover, larger sample sizes and long-term cyclic or environmental testing should be integrated to better predict real-world performance and durability.

This study’s limitations include the natural variability of plywood, the absence of direct microstructural analysis of the kerf and adhesive regions, and the moderate sample size for statistical confidence. Despite these, the results provide a robust comparative framework for kerf geometry optimisation and application. Kerf geometry is indeed a dominant factor influencing the mechanical and ergonomic behaviour of laser-cut plywood panels, but its advantages can only be fully realised when combined with careful material selection, process control, and quality assurance. Recommendations for specific patterns should be interpreted as context-specific, with due consideration for the variability inherently present in wood-based composites and digital fabrication processes.

While this study employed standardised laser processing parameters and default pattern-derived scanning paths for all kerf designs, future research should investigate the optimisation of cutting sequences and parameter adaptation for each pattern type. Tailoring the scanning path and dynamically adjusting laser settings based on local geometry may further improve cutting quality, minimise heat-affected zone effects, and enhance the mechanical performance and durability of kerfed plywood components

5. Conclusions and Future Steps

This research presents a preliminary, systematic, investigation of laser-cut kerf bending in plywood, integrating digital fabrication with ergonomic furniture design. By experimentally testing and classifying a comprehensive set of kerf patterns, this exploratory study identifies trends in how kerf geometry—not just material thickness or removal percentage—affects both flexibility and structural integrity. Due to the methodological limitation of single-destructive trial per pattern, the results should be interpreted as indicative of general trends rather than as definitive evaluations of pattern performance. The findings provide initial guidelines for applying kerf bending in adaptive, load-bearing wooden components, and offer a digital pattern library to support future research and industrial exploration. Within the tested set, “parametric” and “meander” patterns showed promising combinations of high curvature capacity, gradual deformation, and load resistance. However, all recommendations are context-specific and reflect performance within this limited experimental framework. This work sets a new benchmark for combining computational design with mechanical performance in sustainable wood structures without the need for steam bending or lamination. Geometry dominates performance: “parametric” and “meander” patterns, particularly design numbers: 32, 35, 38, 40, 42, 42.1, 42.2, and 42.3, achieved the best combination of high curvature capacity, gradual deformation, and load resistance. Moreover, thinner plywood (3 mm) consistently outperformed the 4 mm sheets in terms of flexibility and Fmax but requires reinforcement in practical applications. The material removal percentage alone is not predictive of flexibility or strength; efficient geometries can achieve high performance even at lower removal ratios.

As for aesthetic value, it is an intrinsic outcome of kerf bending: the cut patterns function as both structural solutions and expressive visual elements. In conclusion, kerf bending merges digital precision, ergonomic adaptability, and aesthetic expression, reinforcing its potential as a technique for contemporary furniture and architectural applications.

While this study provides a comprehensive balance, several areas require further exploration. Future studies should investigate kerf bending in alternative wood species, engineered panels, and even bio-based composites to broaden the applicability of this technique. Also, it should include specimen-level replication for each pattern to enable more rigorous statistical analysis and to support more robust conclusions regarding the influence of kerf geometry on mechanical performance.

Another area of investigation refers to the performance of kerf-bent panels under cyclical loading, humidity changes, and wear, which should be evaluated to determine their reliability in daily use. Parametric and algorithmic design approaches could be developed further, enabling automated generation of kerf geometries optimised for specific curvature and load conditions. In addition, combining kerf bending with lamination, fabric backings, or embedded composites could enhance strength without compromising flexibility.

While the study did not directly quantify the HAZ or adhesive degradation, these effects are inherently included in the mechanical test results (Fmax and variability analyses). The high variability and defect sensitivity observed suggest that thermal effects (including HAZ and adhesive degradation) do locally influence stress distribution and failure but are not the primary determinant of ultimate strength, which is more strongly governed by kerf geometry and pattern efficiency. Explicit quantification of the HAZ’s effect remains an important area for future investigation.

A limitation of the present study is the lack of microstructural and compositional analysis of the laser-processed surface and heat-affected zone. Future research should employ techniques such as scanning electron microscopy (SEM), optical profilometry, or spectroscopic analysis to characterise surface morphology, adhesive integrity, and potential chemical changes in the kerf area. Such investigations will provide a more comprehensive understanding of how laser processing quality influences the mechanical performance and reliability of kerfed plywood structures.

The reliability analysis highlights substantial variability and defect-controlled failure behaviour across all tested patterns, with high coefficients of variation and low Weibull modulus. These findings underscore the strong influence of natural material heterogeneity and local fabrication imperfections. Accordingly, any recommendations regarding specific patterns—such as Nos. 42 and 42.2—are not absolute but reflect relative performance in the current cohort. For future work and critical applications, larger sample sizes, systematic experimental replication, and advanced microstructural analysis are essential to strengthen the statistical basis and reliability of conclusions. These recommendations should be interpreted as context-specific and comparative, rather than absolute. For critical applications, improved control of material and process variables, larger sample sizes, and direct reliability-based design approaches are advised to minimise variability and maximise structural safety. This balanced perspective acknowledges the primacy of kerf geometry among design factors, while also recognising the inherent limitations imposed by natural material variability and process sensitivity.

The major limitation of this study is the lack of experimental replication for each kerf pattern, due to resource constraints. As a result, conclusions about pattern performance are indicative, and trends should be interpreted with caution. The pronounced variability observed further highlights the need for larger sample sizes and statistical replication in future work. This work provides an initial comparative framework and identifies research priorities for advancing kerf-based plywood design. The results are intended as a foundation for further, more rigorous studies, and should not be viewed as conclusive evaluations of individual patterns. We strongly encourage future research to address experimental replication, alternative materials, microstructural effects, and real-world performance to build on these preliminary findings.