Crown pear drop impact damage prediction model based on EPE net cover density and aperture

Abstract

The invention discloses a crown pear drop impact damage prediction model based on density and aperture of an expanded polyethylene (EPE) net cover. Comprising the following steps: S1, carrying out a quasi-static tensile experiment on an EPE net cover material; s2, carrying out a compression experiment on the crown pear pulp, and determining a critical damage stress value; s3, establishing a geometric model of the EPE net cover packaged crown pears; s4, establishing constitutive models of the EPE net cover material and the crown pear pulp material; s5, dividing grids and endowing material parameters; s6, performing a crown pear drop experiment to obtain a crown pear drop impact maximum load; s7, performing crown pear drop finite element simulation to obtain a crown pear drop impact maximum load under simulation; s8, comparing the experiment with finite element data, and verifying the validity of the model; and S9, establishing a damage prediction model of the EPE net cover packaged crown pears based on the density and the aperture. According to the method, the damage condition of the EPE net cover packaged crown pears at the specific height can be quickly and accurately predicted, and guidance is provided for reducing the impact damage of the crown pears.

Description

Technical Field

[0001] This invention relates to the field of transport packaging simulation technology, specifically to a predictive model for drop impact damage of Crown Pear based on EPE mesh density and pore size. Background Technology

[0002] Driven by modern materials, information, and artificial intelligence technologies, e-commerce has developed rapidly, greatly promoting the progress of the logistics industry. After harvesting, fruits need to go through sorting, transportation, and other stages to reach consumers. To reduce post-harvest losses, fruits are generally packaged before entering the logistics process. During loading, unloading, handling, and sorting, fruits are prone to drop and impact damage. In my country, post-harvest logistics losses of fruits are significant each year, resulting in huge resource waste and economic losses. Therefore, packaging protection design and damage prediction are crucial for reducing post-harvest fruit losses during logistics. Crown pears are popular for their good taste and high nutritional value. However, their thin skin and juicy texture make them highly susceptible to mechanical damage during post-harvest logistics. Therefore, scientifically effective cushioning packaging design is essential. Furthermore, damage to Crown pears affects their nutritional and commercial value; damage prediction is crucial for post-harvest loss reduction and optimized packaging design.

[0003] There are three ways to assess and predict fruit damage: (1) On-site transportation measurement. This requires measuring fruit damage during actual transportation. (2) Laboratory simulation experiments. This involves recreating the actual transportation process in the laboratory, simulating fruit damage under static pressure, drops, and vibrations. (3) Simulation. Using relevant simulation analysis software, such as ANSYS, simulations are conducted to analyze situations that fruit may encounter during logistics, such as static pressure, drops, and vibrations, to predict fruit damage. The first two methods are time-consuming and labor-intensive, resulting in resource waste. Simulation methods can reduce fruit loss, shorten the experimental cycle, and save costs.

[0004] Patent CN107543801A discloses a hyperspectral-based method for predicting the hardness of mangoes after impact damage. This invention uses hyperspectral imaging and mathematical modeling techniques to detect changes in mango hardness after impact damage, providing a framework for revealing the damage mechanism of fruits and non-destructively assessing their mechanical damage. Patent CN111289463A discloses a hyperspectral non-destructive method for predicting the area of ​​impact damage to apples. This invention can non-destructively quantify and predict the area of ​​impact damage to apples, providing a means for non-destructively assessing the mechanical damage of fruits. While these two methods offer some reference value for predicting fruit impact damage, there has been no research or report on predicting the critical impact damage height of fruits during transportation.

[0005] EPE mesh sleeves are widely used in fruit cushioning packaging due to their lightweight and excellent mechanical properties. Currently, most Crown pears transported over long distances use EPE mesh sleeves for individual fruit cushioning. The density and pore size of the EPE mesh sleeve affect its mechanical properties, resulting in varying cushioning performance for the fruit. Researchers have begun to focus on how to achieve better protection through optimized design of the density and pore size of the EPE mesh sleeve. This invention proposes a method for predicting damage to Crown pears using EPE packaging with different parameters, based on mathematical modeling and finite element simulation technology. This method can accurately predict the drop damage of Crown pears, providing a reference for fruit packaging design, damage assessment, and post-harvest loss reduction. It is expected to promote fruit transport packaging design and damage assessment technology, and improve economic efficiency. Summary of the Invention

[0006] The purpose of this invention is to provide a predictive model for drop impact damage of Crown pears based on EPE netting density and pore size. This model aims to assess and predict the impact damage of Crown pears under different EPE netting packaging conditions, thereby optimizing the design of fruit cushioning packaging and achieving better protection. The invention is implemented as follows:

[0007] S1. Quasi-static tensile tests were conducted on EPE mesh material samples with different densities and pore sizes using a universal testing machine. The tensile speed was 5-15 mm / min. Stress-strain curves of EPE mesh materials with different densities and pore sizes were obtained, and material parameters such as elastic modulus were obtained.

[0008] S2. A universal testing machine was used to conduct compression tests on the flesh of the Crown pear. The compression speed was 5–15 mm / min. The stress-strain curves of the Crown pear flesh were obtained, and the critical damage stress value σ of the Crown pear flesh was determined. l This value serves as the basis for determining whether the Crown Pear fruit has been damaged.

[0009] S3. Use SolidWorks software to create a three-dimensional geometric model of the Crown Pear packaged with EPE mesh sleeves of different aperture sizes. Model the Crown Pear and the mesh sleeve at a 1:1 scale according to their size, shape and dimensions.

[0010] S4. Import the three-dimensional geometric model of the EPE mesh-wrapped Crown pears described in step S3 into the Hypermesh software. Input the stress-strain curve mechanical data of the EPE mesh material obtained in step S1 into the finite element software Hypermesh to establish a constitutive model of the EPE mesh material including material density, stress-strain curve, and elastic modulus parameters; input the stress-strain curve mechanical data of the Crown pear pulp material obtained in step S2 into the finite element software Hypermesh to establish a constitutive model of the Crown pear pulp elastoplastic material including pulp density, stress-strain curve, and elastic modulus parameters.

[0011] S5. Perform mesh generation and assign the material parameters of the mesh sleeve and the crown pear to their respective 3D models. Apply a downward constraint load of one times the gravitational acceleration. Build a rigid wall at a distance downward from the bottom of the EPE mesh sleeve-packaged crown pear model to simulate a rigid ground.

[0012] S6. Select the density and pore size of EPE-packaged Crown pears and conduct a drop test at a specific height to obtain the drop acceleration-time curve of the Crown pears. Calculate the maximum impact load.

[0013] S7. The drop height, EPE density, and pore size are kept consistent with those in step S6. A drop impact simulation is performed on the Crown Pear packaged in EPE mesh to obtain the maximum impact load of the Crown Pear in the finite element simulation.

[0014] S8. The maximum impact load of the Crown Pear obtained through finite element method and experiment will be compared to verify the effectiveness of the model.

[0015] S9. Drop simulations were conducted on Crown Pears packaged in EPE mesh sleeves with different densities and pore sizes at specific drop heights. Based on multiple simulation data, the maximum von Mises equivalent stress σ of Crown Pears packaged in EPE mesh sleeves with different densities and pore sizes at a specific drop height was established. max Database, based on which the EPE mesh density and pore size are established in relation to σ max Predictive models between them.

[0016] S10. Using the prediction model established in step S9, predict the maximum von Mises equivalent stress of Crown pears packaged in EPE mesh sleeves of different densities and pore sizes at a specific drop height, and compare it with the critical damage stress value σl to determine whether the Crown pears have been damaged.

[0017] 2. The Crown Pear Impact Damage Prediction Model based on EPE mesh density and pore size according to claim 1, characterized in that step S6 includes the following steps:

[0018] S61, with an EPE mesh density of 17.0 kg / m 3 A drop test of the crown pear was conducted under the condition of an aperture of 6 mm.

[0019] 3. The drop impact damage prediction model for Crown pears based on EPE mesh density and aperture as described in claim 1, characterized in that, in step S2, a static compression test is performed on the Crown pear pulp to obtain a stress-strain curve, and the stress at which the pulp begins to undergo plastic deformation is taken as the critical damage stress value σ of the Crown pear pulp. l .

[0020] 4. The impact damage prediction model for Crown pear based on EPE netting density and pore size according to claim 1, characterized in that, in step S9, nonlinear surface fitting is performed using Origin software to construct the equivalent stress σ of the maximum von Mises stress of the Crown pear fruit for different EPE netting densities and pore sizes. max The mathematical model uses EPE mesh thickness and aperture as independent variables, maximum von Mises equivalent stress as the dependent variable, and the fitting function is the Parabolic 2D function, with the following formula:

[0021] σ max =C + aρ + bD + cρ 2 +dD 2

[0022] In the formula, C is a constant, a, b, c, and d are constants, D is the aperture of the EPE mesh, ρ is the density of the EPE mesh material, and σ max The maximum von Mises equivalent effect of Crown Pear fruit.

[0023] The beneficial effects of this invention are:

[0024] This invention proposes a method for predicting damage to Crown pears packaged in EPE with different parameters based on mathematical modeling and finite element simulation technology. This method can quickly and accurately predict the damage of Crown pears packaged in EPE mesh sleeves with different densities and apertures at a specific height. It can provide a reference for fruit packaging design and damage assessment, effectively reduce fruit losses during logistics and transportation, and thus generate considerable economic benefits. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the three-dimensional geometric model of the EPE mesh packaging of crown pears in this invention;

[0026] Figure 2 This is a schematic diagram of a three-dimensional geometric model of the EPE mesh sleeve with different apertures in this invention;

[0027] Figure 3 This is a schematic diagram of the stress-strain curve of the Crown Pear pulp in this invention;

[0028] Figure 4 This is a schematic diagram of the maximum von Mises equivalent stress surface of the Crown Pear with different densities and pore sizes in this invention;

[0029] Figure 5 This is a schematic diagram of the XY-axis projection of the fitting surface for the maximum von Mises equivalent stress of the EPE mesh sleeves with different densities and pore sizes used in the present invention for packaging Crown Pears. Detailed Implementation

[0030] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, provides a further detailed explanation of the Crown Pear Drop Impact Damage Prediction Model based on EPE mesh density and aperture according to the present invention. The scope of protection of the present invention is not limited to the following specific embodiments.

[0031] A drop impact damage prediction model for Crown Pear trees based on EPE mesh density and pore size, the steps of which are as follows:

[0032] S1. Pre-treat the EPE mesh material samples with temperature and humidity for more than 24 hours, under the conditions of 23℃ and 50% humidity. Use a universal testing machine to conduct quasi-static tensile tests on EPE mesh material samples with different densities and pore sizes. The tensile speed is 5-15 mm / min, preferably 15 mm / min. Set up 10 parallel tests and take the average value to obtain the stress-strain curves of EPE mesh materials with different densities and pore sizes, and obtain material parameters such as elastic modulus.

[0033] S2. A universal testing machine was used to conduct compression tests on the flesh of the Crown Pear to obtain the stress-strain curve of the Crown Pear flesh, obtain parameters such as the elastic modulus of the Crown Pear flesh, and determine the critical damage stress value σ of the Crown Pear flesh. l This value is used to determine whether the Crown Pear fruit has been damaged. The specific steps are as follows:

[0034] S21. Determine the critical damage stress value σ of the Crown Pear pulp. l In this step, a static compression test was conducted on the Crown pear pulp at 23℃ and 50% relative humidity. Ten parallel tests were set up to obtain the average stress-strain curve. The stress at which the pulp began to undergo plastic deformation was used as the basis for judging whether damage had begun to occur in the Crown pear pulp. Figure 3 The static average stress-strain curve for a Crown pear with a diameter of 81 mm is shown. The OA stage approximates linear elasticity; after point A, the material enters the plastic stage, undergoing irreversible deformation. Therefore, point A is used as the criterion for judging pear damage. l =0.26 MPa, therefore, when the maximum von Mises equivalent stress of the Crown pear exceeds 0.26 MPa, the pear is considered to have been damaged. Crown pear damage stress σ l The σ value is related to the maturity and size of the Crown pear, and is determined based on actual experiments. l The range is approximately 0.21 MPa to 0.27 MPa.

[0035] S3. Establish the finite element model of the EPE-packaged Crown Pear. The specific steps are as follows:

[0036] S31. Use Solidworks software to create geometric models of EPE mesh for packaging crown pears with different apertures (4, 6, 7.2, 8, 9 mm) and different densities (15, 21, 28, 36 kg / m3), and import them into LS-DYNA software for material assignment, mesh generation and calculation.

[0037] S32. Based on the stress-strain curve of the fruit pulp obtained in step S2, input it into the LS-DYNA software and use the *MAT_PIECEWISE_LINEAR_PLASTICITY constitutive model to establish a multilinear elastoplastic material model of the Crown Pear pulp, and assign relevant material parameters to the Crown Pear.

[0038] S32. Based on the EPE mesh material sample parameters obtained in step S1, input the relevant parameters of the EPE mesh into the LS-DYNA software.

[0039] S33. Mesh the geometric model and set the contact settings. Perform tetrahedral meshing on the EPE mesh-packaged crown pear model, selecting tetrahedral elements. Frictional contact is used between the EPE mesh-packaged crown pear and the rigid plate, as well as between the EPE mesh and the crown pear. In LS-DYNA, select the default tetrahedral element type ELFORM=10 in the keyword *SECTION_SOLID, using the tetrahedral formula with single-point integration. Frictional contact is used between the EPE mesh-packaged crown pear and the rigid plate, as well as between the EPE mesh and the crown pear. Select the contact keyword *CONTACT_AUTOMATIC_SINGLE_SURFACE for automatic single-surface contact. The program will search all external surfaces in the model to check for mutual penetration.

[0040] S34. Add a rigid wall to simulate the ground during an actual impact.

[0041] S35. Submit calculation; analysis time is 0.02s.

[0042] S4. Finite Element Model Verification. A drop impact test with a height of 100mm was conducted with an EPE mesh density of 17.0 kg / m³ and a mesh diameter of 6 mm. The impact load from the test and the load on the rigid wall in the simulation were obtained. Using the method of this embodiment, the following data were obtained:

[0043]

[0044] The impact loads from the experiment and the impact loads from the simulation were compared and analyzed to verify the finite element model. The data in the table above show that the impact loads from the experiment and the finite element model are 176.11N and 182.92N, respectively, with a relative error of 3.72%. The error between the finite element simulation and the experimental value is small, indicating that the finite element model is accurate.

[0045] S5. Finite element simulation analysis of drop impact on Crown pears packaged in EPE mesh sleeves, and establishment of a damage prediction model for Crown pears. Drop impact simulations of Crown pears packaged in EPE mesh sleeves with different densities and pore sizes were conducted at specific heights. Based on multiple simulation data, a von Mises equivalent stress database of Crown pears packaged in EPE mesh sleeves with different densities and pore sizes was established. Based on this database, a prediction model was established between the pore size and density of the EPE mesh sleeve and the maximum von Mises equivalent stress of the Crown pear. Specific steps are as follows:

[0046] S51. Crown pears packaged in EPE mesh sleeves with preferred aperture sizes of 4mm, 6mm, 7.2mm, 8mm, and 9mm, and preferred densities of 15kg / m³, 21kg / m³, 28kg / m³, and 36kg / m³, were subjected to drop impact simulation at a specific height, with a preferred drop height of 100mm. A database of the maximum von Mises equivalent stress of Crown pears under EPE packaging with different densities and aperture sizes was obtained. Using the method of this embodiment of the invention, the following data were obtained:

[0047]

[0048] The data in the table above shows that as the aperture and density of the EPE mesh increase, the maximum stress inside the Crown Pear fruit gradually decreases, and the buffering effect gradually increases.

[0049] S52. Based on the database, a predictive model was established for the relationship between EPE mesh density, pore size, and damage in Crown pears. A three-dimensional relationship diagram was created between different EPE mesh densities and pore sizes and the maximum von Mises equivalent stress in Crown pears. Figure 4 As shown, the relationship between the maximum von Mises equivalent stress of Crown pear fruit and the density and pore size of the EPE mesh is intuitively demonstrated.

[0050] S53. Using Origin software, a nonlinear surface fitting was performed to construct a mathematical model of the relationship between different densities and pore sizes of EPE netting and the maximum von Mises equivalent stress of Crown pear fruit: the thickness and pore size of the EPE netting are the independent variables, and the maximum von Mises equivalent stress σ is the independent variable. max The dependent variable is the Parabolic 2D function, and its formula is:

[0051] σ max =C + aρ + bD + cρ 2+dD 2

[0052] In the formula, C is a constant, a, b, c, and d are constants, D is the aperture of the EPE mesh, ρ is the density of the EPE mesh material, and σ max The maximum von Mises equivalent effect of Crown Pear fruit.

[0053] The fitted 3D surface plot, such as Figure 5 As shown in the figure, it can be seen that as the density and pore size of the EPE netting increase, the maximum von Mises equivalent stress of the Crown Pear fruit gradually decreases, and the rate of decrease in the curvature gradually flattens out. This indicates that if the density and pore size of the EPE netting continue to increase, the buffering performance of EPE will not increase indefinitely but will gradually stabilize.

[0054] In this step, the values ​​of the fitted parameters are obtained using the method of this embodiment of the invention, resulting in the following data:

[0055]

[0056] The R² of the fitted surface is 0.938, which is greater than 0.9, indicating that the formula has a high degree of fit and can describe the relationship between different densities and pore sizes of EPE netting and damage to Crown pear fruit.

[0057] S54. Using a damage prediction model for Crown pears packaged with EPE mesh of different thicknesses and pore sizes, the EPE size and structural regions of Crown pears at the time of damage are obtained, and von Mises equivalent stress contour maps projected onto the three-dimensional curved surface along the XY axis are drawn, such as... Figure 5 As shown, when the stress exceeds σ l At that time, it was believed that the Crown Pear packaged with EPE mesh thickness and aperture in this area would be damaged when dropped from a height of 100mm.

[0058] The above description is merely an embodiment of the present invention and is not intended to limit the present invention in any other way. Any equivalent modifications made using the technical content of the present invention, or direct or indirect applications in related technical fields, shall still fall within the protection scope of the technical solution of the present invention.

Claims

1. A predictive model for drop impact damage of Crown Pear fruit based on EPE mesh density and pore size, characterized in that, Includes the following steps: S1. Quasi-static tensile tests were conducted on foamed polyethylene (EPE) mesh material samples with different densities and pore sizes using a universal testing machine. The tensile speed was 5-15 mm / min. Stress-strain curves of EPE mesh materials with different densities and pore sizes were obtained, and material parameters such as elastic modulus were obtained. S2. A universal testing machine was used to conduct compression tests on the flesh of the Crown pear. The compression speed was 5–15 mm / min. The stress-strain curves of the Crown pear flesh were obtained, and the critical damage stress value σ of the Crown pear flesh was determined. l This value serves as the basis for determining whether the Crown Pear fruit has been damaged. S3. Use SolidWorks software to create a three-dimensional geometric model of the Crown Pear packaged with EPE mesh sleeves of different aperture sizes. Model the Crown Pear and the mesh sleeve at a 1:1 scale according to their size, shape and dimensions. S4. Import the three-dimensional geometric model of the EPE mesh-wrapped Crown pears described in step S3 into the Hypermesh software. Input the stress-strain curve mechanical data of the EPE mesh material obtained in step S1 into the finite element software Hypermesh to establish a constitutive model of the EPE mesh material including material density, stress-strain curve, and elastic modulus parameters; input the stress-strain curve mechanical data of the Crown pear pulp material obtained in step S2 into the finite element software Hypermesh to establish a constitutive model of the Crown pear pulp elastoplastic material including pulp density, stress-strain curve, and elastic modulus parameters. S5. Perform mesh generation and assign the material parameters of the mesh sleeve and the crown pear to their respective 3D models. Apply a downward constraint load of one times the gravitational acceleration. Build a rigid wall at a distance downward from the bottom of the EPE mesh sleeve-packaged crown pear model to simulate a rigid ground. S6. Select the density and pore size of EPE-packaged Crown pears and conduct a drop test at a specific height to obtain the drop acceleration-time curve of the Crown pears. Calculate the maximum impact load. S7. The drop height, EPE density, and pore size are kept consistent with those in step S6. A drop impact simulation is performed on the Crown Pear packaged in EPE mesh to obtain the maximum impact load of the Crown Pear in the finite element simulation. S8. The maximum impact load of the crown pear during the drop process obtained by finite element method and experiment will be compared to verify the effectiveness of the model. S9. Drop simulations were conducted on Crown pears packaged in EPE mesh sleeves with different densities and pore sizes at specific drop heights. Based on multiple simulation data, the maximum von Mises equivalent stress σ of Crown pears packaged in EPE mesh sleeves with different densities and pore sizes at a specific height was established. max Database, based on which the EPE mesh density and pore size are established in relation to σ max Predictive models between them. S10. Apply the prediction model established in step S9 to predict the maximum von Mises equivalent stress of Crown Pears packaged in EPE mesh sleeves with different densities and pore sizes at a specific drop height, and compare it with the critical damage stress value σ. l Compare the results to determine if the Crown pears have been damaged.

2. The Crown Pear Drop Impact Damage Prediction Model based on EPE Mesh Density and Aperture as described in claim 1, characterized in that, Step S6 includes the following steps: S61, with an EPE mesh density of 17.0 kg / m 3 A drop test of the crown pear was conducted under the condition of an aperture of 5 mm.

3. The Crown Pear Drop Impact Damage Prediction Model based on EPE Mesh Density and Aperture as described in claim 1, characterized in that, In step S2, a static compression test is performed on the Crown Pear pulp to obtain a stress-strain curve. The stress at which the pulp begins to undergo plastic deformation is taken as the critical damage stress value σ of the Crown Pear pulp. l .

4. The Crown Pear Impact Damage Prediction Model based on EPE mesh density and pore size as described in claim 1, characterized in that: In step S9, nonlinear surface fitting is performed using Origin software to construct the equivalent stress σ of the maximum von Mises stress of the Crown pear fruit for different densities and pore sizes of the EPE mesh. max The mathematical model uses EPE mesh thickness and aperture as independent variables, maximum von Mises equivalent stress as the dependent variable, and the fitting function is the Parabolic 2D function, with the following formula: s max =C+aρ+bD+cρ 2 +dD 2 In the formula, C is a constant, a, b, c, and d are constants, D is the aperture of the EPE mesh, ρ is the density of the EPE mesh material, and σ max The maximum von Mises equivalent effect of Crown Pear fruit.

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