Sustainable cocoon waste epoxy composite solutions: Novel approach based on the deformation model using finite element analysis to determine Poisson’s ratio

2.1 Procedure

The structured workflow procedure is designed to achieve specific objectives efficiently through the systematic integration of various components and adherence to established protocols. This organized approach facilitates the effective completion of tasks. A thorough explanation of the process requires identifying its key phases and dependencies, which is essential for improving both understanding and operational efficiency. Initially, the deformation curve of CWEC was determined through tensile testing. Subsequently, the study utilized LHS implemented via MATLAB software (The MathWorks, Inc., Natick, MA, USA) to calculate key mechanical properties, including the modulus of elasticity and Poisson’s ratio. In the third phase, detailed CWEC structural models were generated using PowerShape software, developed by Autodesk Inc. (San Rafael, CA, USA). Following model generation, the simulation process was conducted using ANSYS Workbench, a sophisticated computational tool developed by ANSYS Inc. (Canonsburg, PA, USA). The research placed particular emphasis on FEA and its consistency with experimentally validated data from CWEC, as demonstrated in Figure 1.

Figure 1

Workflow for the novel methodology based on the deformation model and utilizing FEA.

2.2 Tensile testing

The cocoon waste used in this study, sourced from the Nang Noi Sisaket-1 silkworm breed in Sisaket Province, consists of discarded or defective cocoons unsuitable for reeling due to irregular morphology. Typically, the waste has a pointed end, blunt head, a fibrous texture, and averages 3 cm in length and 1.5 cm in width, as shown in Figure 2(a). Its average weight is 6.47–6.55 g per 10 cocoons, with silk lengths ranging from 280 to 950 m. The epoxy resin (CYD-128) used as the matrix has a density of 1,200 kg/m³, and the hardener, EPAMINE PA53, was sourced locally in Thailand. The cured epoxy composites exhibit a hardness exceeding 85 Shore A. The composite plate was fabricated using compression molding. Epoxy resin and hardener were mixed in a 4:1 ratio, producing 50 g of matrix solution, which was degassed to remove air bubbles. Initially, 10 g of the solution was poured into the base of a 15 cm × 15 cm × 20 cm mold. Approximately 50 g of cocoon waste was then evenly distributed, and the remaining resin was poured to fully cover the material. The mold was sealed and compressed at 1.5 MN for 2 h at 25°C. After compression, the specimen was removed and cured at 25°C for 72 h, resulting in fully formed composite panels, as shown in Figure 2(b).

Figure 2

The general macroscopic view of (a) raw cocoon waste materials and (b) CWEC panels.

Tensile testing was conducted at a displacement rate of 5 mm/min until the specimen reached the load cutoff, in accordance with ASTM D638 standards [36]. The experiment utilized the Bluehill software, version 3 (INSTRON Co., Ltd., High Wycombe, Bucks, UK). In experimental tensile tests, the load–extension relationship plays a crucial role in determining the mechanical properties of materials. This method consists of applying tensile force to the specimen and accurately recording the resulting elongation or displacement, as illustrated in Figure 3. These measurements provide the foundation for evaluating the material’s behavior under external forces, contributing to a deeper understanding of its mechanical properties. The experimental deformation curve, derived from these measurements, is subsequently employed to validate the deformation curve generated through FEA models, ensuring consistency between empirical and simulated results. The deformation curve was derived through testing a set of ten specimens in the experimental setup.

Figure 3

The configuration for the tensile testing of CWEC panels.

2.3 LHS

LHS is a valuable tool in materials science for investigating the properties and behavior of CWEC structures [37]. When applying LHS to CWEC structures, the goal is to systematically explore the parameter space, encompassing design variables and manufacturing conditions that influence the material’s properties. This process begins with identifying the key design variables, such as geometric parameters, material properties, or manufacturing conditions, that affect the CWEC structure. Crucial to this step is defining the ranges and discretization levels for each variable, including the minimum and maximum values for parameters such as cell size and the number of intervals within each range. Based on this defined parameter space, a Latin hypercube design is generated. The LHS algorithm ensures that the sampling of design variables is both even and representative, allowing for a diverse exploration of CWEC structure configuration.

For each experimental run or simulation, specific values are assigned to the design variables according to the Latin hypercube design, creating unique combinations of design parameters for each trial. These parameter sets are then used to either simulate the behavior of CWEC structures through computational methods or to fabricate physical prototypes with varying parameter combinations. Once the physical prototypes are fabricated, measurements of material properties, such as mechanical strength, stiffness, or thermal conductivity, are conducted. In parallel, simulations provide relevant material property data derived from computational results. The collected data from both experiments and simulations are analyzed to assess the material properties corresponding to each set of design variables. Statistical analysis and data visualization techniques are then employed to identify trends and correlations between the design parameters and material properties. By utilizing LHS in the study of CWEC structures, researchers can efficiently explore the influence of various design variables, optimize structural performance, balance trade-offs between different properties, and gain valuable insights into the behavior of these unique cellular materials.

The exit is divided into M sub-intervals, resulting in the occurrence of the jth sub-interval for the ith design variable X _i :

The points within each sub-range were subsequently generated through uniform random sampling of a point X _ij within the jth sub-interval corresponding to the ith design variable, employing the Monte Carlo method:

After obtaining X ij , which represents the elements of the design matrix, the elements X are randomly swapped within the rows to generate the final design matrix using the LHS method. Here, L ij represents the lower bound of the jth sub-interval for design variables, while U ij denotes the upper bound of the same sub-interval. The term rand refers to a random number sampled from a uniform distribution over the interval [0, 1].

2.4 Finite element analysis (FEA)

FEA is a powerful numerical technique widely used in engineering to simulate the physical behavior of structures and materials [34]. This approach involves dividing complex geometries into smaller, more manageable elements, which facilitates detailed analysis of behavior under various conditions. FEA has demonstrated effectiveness in predicting stress, strain, and deformation, providing engineers with critical insights into structural performance prior to the construction of physical prototypes. Moreover, this methodology is applicable across a diverse range of engineering disciplines, including mechanical, civil, aerospace, and biomedical engineering. When applying FEA to model the CWEC structure, it is essential to establish an appropriate mathematical framework. This framework is characterized by specific equations that depend on key model details, including material properties, geometry, and loading conditions. A simplified representation of the finite element formulation for the CWEC structure can be articulated through a general structural equation based on force equilibrium, particularly within the context of linear elastic analysis:

In this discussion, K (N/mm) is referred to as the stiffness matrix, U (mm) represents the displacement vector, and F (N) signifies the force vector. The stiffness matrix encompasses material properties, such as the modulus of elasticity (E), measured in MPa, and Poisson’s ratio ( υ ), which are crucial for understanding how the material reacts under various loading scenarios. The constitutive matrix (D), also expressed in MPa, for isotropic, linear elastic materials is represented by the subsequent expression:

2.5 Verification of experimental results

To validate the simulation results, an experimental investigation of Poisson’s ratio was conducted in accordance with the ASTM D3039 standard [38]. The experiment involved testing ten specimens, and the standard error was calculated to compare the experimental findings with the simulation data. For fiber-reinforced polymer composite materials, the determination of Poisson’s ratio follows the ASTM D3039 standard, which outlines the procedures for assessing the tensile properties of reinforced polymer composites under controlled conditions. In this study, an Instron Electropulse E10000 (INSTRON Co., Ltd., High Wycombe, Bucks, UK) was used, equipped with a dynamic extensometer featuring a 12.5 mm gauge length, ±5 mm travel, and 0.01 mm accuracy. Poisson’s ratio testing process comprised several steps. First, dog-bone-shaped test specimens were fabricated from the composite material according to specific dimensions and geometry. Second, strain gauges or extensometers were attached to the specimen in both axial (loading) and transverse directions to measure longitudinal and lateral strains during the tensile loading process. Next, the prepared specimen was mounted in a tensile testing machine and subjected to uniaxial tensile loading until failure, with load and strain data continuously recorded throughout. Finally, Poisson’s ratio was determined by calculating the negative ratio of lateral strain to axial strain, focusing on the elastic region of the stress–strain curve.

3.1 LHS modulus of elasticity and Poisson’s ratio

The LHS method has gained widespread adoption in research due to its effectiveness and ease of implementation. To support this approach, an experimental program was developed in MATLAB, allowing for the assignment of 20 distinct values to each design variable. The range for modulus of elasticity was set between 300 and 600 MPa, while Poisson’s ratio was defined between 0.3 and 0.5. These values were derived from the deformation analysis of the tensile test conducted on CWEC, in conjunction with the findings reported by Gere and Goodno [16] and Chowdary et al. [17]. These values were subsequently analyzed using the FEA to calculate the deformation for the 20 models presented in Figure 5. In this figure, the modulus of elasticity is plotted on the vertical axis, and Poisson’s ratio is plotted on the horizontal axis, offering a clear visual representation of the normal data distribution within the specified ranges. The randomization process employed in this study is based on a uniform data distribution.

Figure 5

The findings obtained using the LHS technique, utilizing 20 pairs of input variables.

The results obtained from incorporating the modulus of elasticity and Poisson’s ratio parameters into the computation of 20 FEA models are presented in Table 1.

3.2 FEA simulation

The boundary conditions applied during the tensile testing of CWEC are critical for accurately capturing the material’s mechanical behavior. At the fixed end of the specimen, displacement is constrained to zero, while at the moving end, the applied force is either controlled or measured, providing essential input load data for the tensile test. This configuration ensures that the test reliably reflects the actual mechanical response of the CWEC material. Figure 6 illustrates the boundary conditions employed in the simulation. The finite element mesh consists of 9,000 elements and 46,602 nodes. The element size in finite element models of specimens varies depending on the region of interest. Accurate stress analysis in the gauge and fillet transition areas, where stress gradients peak, necessitates the use of fine mesh elements with edge lengths near 0.5 mm. Conversely, in less critical regions such as the grip sections, a coarser mesh with element edge lengths of 1.0 mm is generally sufficient. To ensure numerical accuracy and minimize distortion, it is essential to maintain an element aspect ratio close to unity. The use of a structured mesh with a gradual transition between fine and coarse regions is recommended to achieve an optimal balance between computational efficiency and solution fidelity. In particular, localized mesh refinement should be applied in the fillet regions, where geometric discontinuities can lead to elevated stress concentrations. Capturing these localized effects accurately is crucial for evaluating mechanical performance and predicting failure. To ensure the reliability of simulation results, mesh convergence studies should be systematically performed. This involves refining the mesh and monitoring the variation in stress or strain at key locations within the model. A variation of less than 3% between successive mesh refinements is accepted as an indicator of adequate mesh convergence and model stability.

Figure 6

Boundary conditions applied in the analysis: (a) distributed load with a fixed support, and (b) meshing of the tensile model using the quadratic hexahedral element.

FEA will be performed on each model, applying load values ranging from 10 to 300 N to calculate the corresponding elongation distances. The results from the elongation phase tests for each model will then be compared with data obtained from actual tensile test experiments. To validate the tensile test results for CWEC using FEA, the root mean square error (RMSE) will be used as a key statistical measure to evaluate how accurately the simulation represents the material’s deformation behavior. RMSE quantifies the discrepancies between experimental data and simulated results by assessing the differences between observed and predicted values. A lower RMSE indicates a closer alignment between FEA predictions and experimental observations [39], suggesting that the simulation effectively reflects the real-world deformation behavior of CWEC under tensile loading, as illustrated in Figure 7. Calculating RMSE allows for the evaluation of agreement between experimental and simulated results. For example, a low RMSE value indicates that the FEA model successfully captures the deformation patterns observed in physical tests. Therefore, RMSE is a reliable metric for comparing deformation behavior in tensile testing with FEA predictions [39]. Minimizing RMSE is essential for validating the FEA model and ensuring its accuracy in representing the mechanical performance of CWEC under tensile stress [40]. This validation is critical for both material research and design applications. The minimum RMSE observed for Model 5 is 0.2181, as shown in Table 1, with corresponding modulus of elasticity and Poisson’s ratio values of 565.57 MPa and 0.4564, respectively.

Figure 7

Deformation comparison between the results of the experiment and some simulation data.

A total of ten specimens were employed in the experimental procedure. Given the limited sample size, the confidence interval (CI) for RMSE of CWEC was calculated using the t-distribution rather than the normal distribution due to the increased statistical uncertainty inherent in small datasets. For a 95% confidence level with a sample size of ten, the CI is computed using the following equation:

where X ̅ represents the sample mean, s is the sample standard deviation, n is the sample size, and t α 2 , n − 1 is the critical t-value corresponding to the desired confidence level.

This approach is widely adopted in the analysis of composite materials due to its robustness in handling small sample sizes. The calculated CI values are presented in Table 1, with SEM ranging from 0.0694 to 0.0824. The relatively wide CI indicates a higher degree of uncertainty in the mechanical behavior of the material. This variability is attributed to the natural heterogeneity of plant-based fibers, including variations in fiber diameter, cellulose content, and fiber–matrix interfacial bonding, which contribute to broader CIs compared to those observed in synthetic fiber composites [41,42,43].

The validation of numerical simulations was performed by comparing the simulation outcomes with the experimental results. Specifically, Poisson’s ratio of CWEC was measured in both the numerical simulations and the experimental tests. The findings indicate a high degree of correlation between the two approaches, with a similarity of 94.21%, corresponding to an error margin of 5.79%.

FEA simulations are critical for understanding the mechanical behavior of CWEC during tensile testing. These simulations provide detailed insights into stress distribution, deformation patterns, and strain energy within the material. Several factors affect the accuracy of FEA results, including boundary conditions, material properties, geometric configuration, and the time-dependent behavior of the composite. By analyzing these variables, FEA reveals the formation of complex stress fields, especially in cases of significant deformation. Accurately modeling stress distribution is essential for predicting the mechanical performance of CWEC, identifying potential failure points, and optimizing designs that rely on its tensile properties. For example, as illustrated in Figure 8, the maximum recorded stress reached 18.98 MPa, while the peak observed deformation was 1.89 mm.

Figure 8

(a) Stress distribution and (b) deformation in CWEC subjected to load extension.