Nut shell heterogeneity numerical model construction method

By constructing a numerical model of the heterogeneity of nut shells, and using the Weibull distribution and finite element method to simulate the cracking process of nut shells, the problem of inaccurate crack prediction in existing modeling methods is solved, and high-precision simulation of fracture behavior is achieved, reducing research costs and difficulties.

CN121637909APending Publication Date: 2026-03-10TARIM UNIV
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-12-08
Publication Date
2026-03-10

AI Technical Summary

Technical Problem

Existing modeling methods fail to accurately represent the heterogeneity of nut shells, leading to distorted crack path prediction and inaccurate energy threshold assessment, which limits the design and optimization of nut processing equipment.

Method used

By introducing the mechanical parameters of the Weibull distribution, a numerical model of the heterogeneity of nut shells is constructed. The finite element method is used to simulate the cracking process of nut shells, distinguishing between internal elastic elements and bonding elements, and assigning different strength levels to reflect the heterogeneity inside the shell.

Benefits of technology

This study improved the accuracy of predicting nut shell cracking behavior, captured the actual cracking mechanism of the shell, reduced research costs and difficulties, and provided an efficient and reliable technical approach for the design of shell-breaking devices.

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Abstract

The invention relates to a numeric model construction method for nut shell heterogeneity, and belongs to the technical field of numerical simulation in the food processing process. The method comprises the following steps: establishing a three-dimensional geometric model of the nut shells and dividing grids; inserting a zero-thickness bonding unit between adjacent elastic units and defining a bilinear constitutive model, wherein the bilinear constitutive model comprises a traction-separation stage, a damage starting stage and an evolution stage; calibrating a mechanical parameter expected value through a test; randomly distributing mechanical parameters of the elastic unit based on Weibull distribution so as to simulate the heterogeneity of the material; mechanical parameters are given to the bonding units according to the average expected coefficient value of the adjacent elastic units; distinguishing a shell internal bonding unit and a suture line interface bonding unit, and setting a strength difference; finally, a heterogeneous fracture model is constructed, fracture behavior prediction is achieved, and the accuracy is verified through tests. According to the method, the limitation of traditional homogeneous modeling is broken through, the prediction precision of the crack propagation path and the cracking mode is remarkably improved, and an efficient technical means is provided for design and optimization of a nut shell breaking device.
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Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of numerical simulation of food processing, and particularly relates to a numerical model construction method for non-homogeneity of nut shell. BACKGROUND

[0002] In the research and development of nut processing equipment, how to accurately predict the shell cracking behavior and the critical stress condition is a long-standing bottleneck problem. Nut shell is a typical natural non-homogeneous material, and its non-homogeneity comes from the difference in structural organization, which makes the nut cracking behavior more random.

[0003] In recent years, with the continuous development of computers and numerical simulation technology, this technology has been widely used in engineering research and equipment development because it can reveal the micro information of the internal mechanical behavior of the material. However, the existing modeling methods are generally based on the ideal assumption of material homogenization. For example, the modeling ideas adopted in patents CN113821926A and CN110414139A and related literature (Testing and simulation of the three point bending anisotropic behaviour of hazelnut shells, Optimization of technical parameters of breaking Macadamia nut shell and finite element analysis of compression characteristics, and Experimental characterization and numerical modeling of the compressive mechanical behavior of hazelnut kernels) and the like, all regard the material as isotropic and uniform as a whole. Although this simplification reduces the complexity of modeling to a certain extent, it objectively ignores the inherent non-homogeneous characteristics of the material. Due to the failure to reflect the actual distribution of the internal mechanical properties of the material, such simplified models show obvious limitations in predicting the cracking and breaking behavior, such as distortion of crack path prediction and inaccuracy of energy threshold evaluation, and many other systematic deviations from objective experimental observation results, which directly restricts the effect of equipment design and optimization based on numerical simulation. The reason is that the existing simulation technology cannot represent the spatial distribution of the internal mechanical parameters of the material, thereby limiting its prediction accuracy in the cracking process. Therefore, developing a numerical modeling method that can truly represent the non-homogeneous structure of the shell has become the key to improving the simulation accuracy of nut cracking behavior.

[0004] To this end, the present invention proposes a numerical model construction method for the non-homogeneity of nut shells. This method can realistically simulate the cracking process of nut shells by introducing the non-homogeneity of the shells, which helps to deeply analyze the cracking mechanism in the processing process, thereby providing an efficient and reliable technical approach and method for the design and testing of nut shell breaking devices. According to the existing patent and literature research, from the perspective of considering the non-homogeneity of the shells, there is no report on the modeling method for the non-homogeneity of nut shells. SUMMARY

[0005] The present invention aims to overcome the shortcomings of existing modeling methods that fail to characterize the heterogeneous distribution characteristics of nut shell materials, and provides a numerical model construction method for the non-homogeneity of nut shells. This method introduces the mechanical parameters of Weibull distribution into the model, breaking through the difficulty of not being able to characterize the internal heterogeneity of the shells, making the simulation model more realistically reflect the mechanical behavior of the shells, thereby improving the prediction accuracy of the cracking strength and crack propagation of the shells.

[0006] The technical solution adopted by the present invention is as follows: A numerical simulation modeling method for the non-homogeneity of nut shells, characterized by the following steps: S10, selecting a typical nut sample, measuring its geometric size parameters and establishing a three-dimensional geometric model of the nut shell through conventional three-dimensional technology, discretizing the geometric model through mesh division, and generating a finite element mesh model composed of elastic elements; S20, inserting zero-thickness cohesive elements along the interface of adjacent elastic elements in the mesh model of S10, reading the node and element information of the initial mesh through a self-defined program, copying and renumbering the nodes shared by adjacent elastic elements to disconnect the original topological connection; S30, defining a bilinear constitutive model for the cohesive elements, including the traction-separation stage, damage initiation and damage evolution stage, and setting the initial stiffness of the cohesive elements; S40, using a conventional physical and mechanical testing machine to calibrate the expected values of the mechanical parameters of the elastic elements and the cohesive elements, including the elastic modulus, tensile strength, shear strength, and type I and type II fracture energy, and through the global force-displacement curve fitting method, the simulation results are matched with the experimental macroscopic mechanical behavior as the benchmark for non-homogeneous distribution; S50, calculating the expected coefficient values of all elastic elements according to the Weibull cumulative distribution function, and randomly assigning values to all elastic elements.

[0007] S60, according to the expected coefficient average value of the adjacent elastic elements and , the mechanical parameters are assigned to the cohesive elements used for connection, and all cohesive elements are assigned values through this rule.

[0008] S70, according to the structure of the walnut shell characteristics distinguished two types of cohesive elements: one is the shell inside the general cohesive elements CIEs1, the second is along the natural seam (upper and lower shell joint surface) distribution of the interface cohesive elements CIEs2. And CIEs2 strength parameters set lower than CIEs1; S80, based on the finite discrete element method, and according to the above, the construction of heterogeneous nut shell cracking model. Using numerical simulation method to solve the model, realize the nut shell under the load of fracture behavior simulation, and through the experiment comparison and verification of the accuracy of heterogeneous modeling.

[0009] Preferably, the S10 in the establishment of geometric model when using three-dimensional X-ray CT scan to obtain the internal structure information of the nut shell, through image segmentation and reconstruction technology to get the fine shell geometry, and using spherical harmonic function and other methods to simplify the complex surface, to improve the grid quality and calculation efficiency.

[0010] Preferably, the S20 in the initial thickness of the cohesive element is zero, in the initial state of the model to maintain geometric continuity, and the cohesive element does not affect the position relationship of adjacent elastic elements when not under stress.

[0011] Further, the S30 in the definition of the bilinear constitutive model for cohesive elements, including traction-separation phase, damage initiation and damage evolution stage: S31, traction-separation model is: In the formula, The traction force, And Respectively along the normal stress and shear stress of the cohesive element; And Corresponding elastic modulus and stiffness matrix, Indicates the strain, Constitutive thickness, Indicates the displacement; S32, damage initiation criterion is: In the formula, Macaulay symbol indicates that the compression traction force will not affect the initial state of failure, And The maximum normal stress and shear stress can be borne respectively; S33, damage evolution stage introduces damage variable Describe the stiffness attenuation process: Where The current maximum relative displacement, the initial displacement of damage, the displacement of complete fracture, and The type I and type II fracture energy is calculated by the BK criterion.

[0012] Preferably, in the S40, the desired parameter calibration adopts a conventional physical mechanics testing machine to measure the mechanical properties under compression load, and the secant modulus, slope and peak load at the half peak strength are fitted and corresponded.

[0013] Further, in the S50, the mechanical parameters are randomly assigned according to the Weibull cumulative distribution function, including: S51, obtaining the elastic modulus of any elastic unit according to the Weibull cumulative distribution function is: In the formula, E represents the expected value of the elastic modulus, m is the homogeneity index, and f is a uniform distribution function between 0 and 1.

[0014] S52, randomly assigning values to all elastic units through the expected coefficient value .

[0015] Further, in the S60, the parameters are reasonably assigned to the bonding units for connection by averaging the expected coefficient values of adjacent elastic units, including: S61, calculating the respective expected coefficient values of the adjacent elastic units that have been assigned values , and averaging them . The average expected coefficient value is set as the expected coefficient value of the bonding unit .

[0016] S62, obtaining the Weibull strength distribution model with adjacent continuous position relationship through the expected coefficient value of the bonding unit : In the formula, , , and respectively represent the compressive strength, shear strength, type I fracture energy and type II fracture energy of the connected unit ; , , and These represent the expected tensile strength, expected shear strength, expected Type I fracture energy, and expected Type II fracture energy, respectively.

[0017] S63 assigns different mechanical parameters to all bonded elements using the Weibull strength distribution model.

[0018] S64, elastic modulus ,tensile strength and shear strength It is set to follow a Weibull distribution law, while other parameters (such as viscous damping) are... The fracture energies (such as Type I and Type II fracture energies) also follow a Weibull distribution because they depend on the elastic modulus and tensile strength, and remain stable for other fixed conventional parameters. Compared with the prior art, the beneficial effects of the present invention are: This invention introduces a Weibull random distribution to heterogeneously assign values ​​to the parameters of nut shell materials, successfully constructing a numerical model that reflects the discreteness of the internal properties of the shell. Compared to traditional homogeneous models, the elastic modulus, strength, and toughness parameters in this invention's model are spatially randomly distributed, thus more realistically reproducing the crack propagation path and failure mode within the material, significantly improving the accuracy of the simulation in predicting actual nut shell fracture behavior. For example, cracks preferentially propagate along the weak-strength regions in the model, with energy release and dissipation concentrated in the low-toughness regions, consistent with the fracture mechanism of real nut shells. By distinguishing the bonding units within the shell matrix and the suture interface and assigning them different strength levels, the model further captures the crack-prone characteristics of special structural parts of the shell (natural sutures), making the simulated fracture mode (the main crack surface separating along the suture line) consistent with experimental observations. This heterogeneous numerical simulation modeling method effectively solves the problem of inaccurate crack prediction in homogeneous models and can be used for in-depth research on the fracture mechanism of nut shell materials. Furthermore, while achieving high-precision simulation, this invention eliminates the need for extensive repeated experiments to obtain material micro-parameters, reducing research costs and difficulties. It provides new ideas and innovative technical means for the study of nut shell cracking mechanisms in food processing and the structural optimization design of shell-breaking devices. Attached Figure Description

[0019] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart of a method according to an embodiment of the present invention; Figure 2 elastic modulus Depending on A schematic diagram of the probability distribution function of the value; Figure 3 The number of elastic units under different expectation coefficients; Figure 4 Adjacent elastic units , and adjacent bonding units A schematic diagram of the spatial structure; Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the following detailed description of this invention is provided in conjunction with a specific example of numerical simulation modeling of heterogeneous walnut shells and with reference to the accompanying drawings.

[0021] Figure 1 This is a flowchart of a numerical simulation modeling method for heterogeneous walnut shells according to the present invention. The example walnut variety used is a walnut sample with an initial moisture content of 6.5%–8% (wet basis) at a temperature of 185°C. The example simulation software used is the commercial ABAQUS. Based on... Figure 1 The flowchart shown illustrates the steps involved in establishing a numerical simulation modeling method for heterogeneous walnut shells: S10, Obtain the geometric size distribution characteristics of walnut shells. A large number of walnut samples are randomly selected, and the major axis (L), minor axis (W), and thickness (T) of each walnut are measured, and the equivalent diameter is calculated. Statistical analysis revealed that the equivalent spherical diameter approximately follows a normal distribution, ranging from 30 to 44 mm. A 36 mm walnut was selected as the most representative for modeling. Simultaneously, to obtain shell thickness information, a subset of walnuts from the measured samples were selected, and the thickness at different locations of their half-shells was measured and statistically analyzed. The results showed that the average shell thickness was approximately 1.15 mm, and the thickness values ​​also exhibited a normal distribution among the samples. Based on these statistical data, a walnut with an equivalent diameter of approximately 36 mm, an average shell thickness of approximately 1.2 mm, and a regular shape without obvious defects was selected as the modeling prototype. An industrial CT scanner was used to perform 3D scanning of the selected walnuts, acquiring shell structure information and obtaining 2D tomographic images. A seed-point-based watershed image processing algorithm was used to segment these CT slices, and a 3D reconstruction algorithm was used to reconstruct the point cloud model of the walnut shell. A smooth 3D surface was obtained by fitting a spherical harmonic function. Discrete mesh generation was performed using HyperMesh software. Mesh sensitivity analysis was conducted during mesh generation to select the optimal mesh size that balances computational accuracy and efficiency, generating a discrete element mesh model. S20, in the obtained finite element mesh model, using our developed ABAQUS secondary development interface program, zero-thickness bonding elements are inserted along the interface of adjacent elastic elements to give the model the ability to simulate crack initiation and propagation. The bonding elements are only placed between adjacent elastic elements and are not generated within individual elements. A custom program reads the node and element information of the initial mesh, copies and renumbers the nodes shared by each pair of adjacent elastic elements to break the original topological connections, and inserts zero-thickness bonding elements at the corresponding positions to ensure the initial geometric continuity between adjacent elastic elements and that forces are transmitted through the bonding elements. After this processing, the model consists of elastic elements and bonding elements, where the elastic elements are used to simulate the elastic deformation of the material bulk, and the bonding elements are used to simulate potential crack surfaces within the material. In the initial state of the model, each bonding element is tightly bonded to the elastic elements, maintaining the continuity of the model. S30, To simulate the cracking behavior of walnut shells, a reasonable mechanical constitutive relationship needs to be assigned to the bonding elements. This embodiment uses a bilinear constitutive model to establish the constitutive model of the bonding elements, including the traction-separation stage, damage initiation stage, and damage evolution stage: S31, where the linear elastic stage uses a traction-separation model: In the formula, Indicates traction force. and These represent the normal stress and tangential stress along the cohesive unit, respectively; and Corresponding elastic modulus and stiffness matrix, Indicates strain, Refers to constitutive thickness. This represents displacement. In the elastic stage, the bonded element behaves like a linear spring. When the normal tensile stress or tangential shear stress it bears reaches the material limit, damage occurs, and it enters the softening stage. Finally, when the stress drops to zero, the bonded element fractures and is removed from the model. It is important to emphasize that the initial thickness of the bonded element is zero, and its stiffness is set very high, making it almost rigidly connected before damage and not affecting the overall elastic response of the structure. However, once damage occurs, its stiffness decreases sharply, eventually completely releasing the constraint force between adjacent elements, allowing cracks to form.

[0022] S32, the damage initiation criterion is the maximum nominal stress criterion, that is, failure begins when the normal or tangential stress of the bond element reaches the material's ultimate strength. The criterion is as follows: In the formula, the symbol "Macaulay" indicates that the compressive traction force does not affect the initial failure state. and These are the maximum normal stress and shear stress that the stress can be withstood, respectively. S33, the damage evolution stage introduces damage variables. Describes the decrease in stiffness of the bonded elements. The evolution from 0 to 1 corresponds to the process of the bonding unit going from intact to completely broken, and its damage model is as follows: In the formula, This represents the current maximum relative displacement. The initial displacement of the damage. For complete fracture displacement, and The fracture energies of Type I and Type II fractures were calculated using the Benzeggaggh-Kenane (BK) criterion. Simultaneously, the critical displacement of the bonded element at complete failure was calculated based on the Benzeggaggh-Kenane (BK) hybrid fracture criterion to determine the energy condition for bonded element fracture. To avoid the bonded element introducing additional stiffness into the model after loading due to its zero initial thickness, the initial stiffness of the bonded element was set to be much higher than that of the adjacent elastic element; that is, the normal and tangential stiffness of the bonded element were increased, making its influence on the overall structural stiffness negligible. This ensures that the mechanical response of the model before damage occurs is consistent with that of a homogeneous material.

[0023] S40. After determining the constitutive relation of the bonding elements, it is first necessary to set the equivalent homogeneous parameters of the model as the basis for assigning heterogeneous values. In this embodiment, these parameters are determined by combining experimental calibration with simulation iteration: uniaxial compression tests are conducted on walnut shell samples with regular shapes, and the force-displacement curves and fracture modes are recorded; at the same time, the finite element model is simulated under the same loading conditions. By adjusting parameters such as elastic modulus, Poisson's ratio, bond strength, and fracture energy, the simulation curves are made to match the experimental curves in key features such as the slope of the elastic segment, peak load, and the shape of the curve after the peak. Finally, a set of reliable model material parameters is obtained, including average elastic modulus, tensile strength, shear strength, and fracture energy.

[0024] S50, mechanical parameters are randomly assigned according to the Weibull cumulative distribution function, including: S51, Obtain the elastic modulus of any elastic element based on the Weibull cumulative distribution function. for: In the formula, This represents the expected value of the elastic modulus, which is approximately equal to the average value of all elastic element material parameters. This is the uniformity index; a higher value indicates greater uniformity in the nut sample. Elastic modulus. Depending on The cumulative distribution function of the value is as follows Figure 2 As shown. The elastic modulus of the elastic element is... in It is a uniform distribution function between 0 and 1.

[0025] S52, the above formula ensures that the expected coefficient value is obtained according to the Weibull distribution law. All elastic elements are randomly assigned values. Furthermore, by assigning arbitrary random numbers to the markers, it can be ensured that elastic elements with different elastic moduli exhibit a random spatial distribution, thus simulating the random distribution of micro-defects, vascular bundles, and fibers, such as... Figure 3 As shown; S60, by using the average expected coefficient value of adjacent elastic elements, reasonably assigns parameters to the bonding elements used for connection, including: S61, for connecting elastic units and bonding unit ,like Figure 4 As shown. Based on adjacent particles of the material. and Parameters such as tensile strength and shear strength are directly proportional to the elastic modulus, with the specific relationship being: Through the adjacent elastic units that have already been assigned values. and Calculate their respective expected coefficient values And calculate the average value. The average expected coefficient value is set as the bonding unit. The expected coefficient value.

[0026] S62, via adhesive unit The expected coefficient values ​​are used to obtain the Weibull intensity assignment model with adjacent continuous positional relationships: In the formula, , , and Representing connection units respectively The compressive strength, shear strength, Type I fracture energy, and Type II fracture energy; , , and These represent the expected tensile strength, expected shear strength, expected Type I fracture energy, and expected Type II fracture energy, respectively.

[0027] S63 assigns different mechanical parameters to all bonded elements using the Weibull strength distribution model.

[0028] S64, elastic modulus ,tensile strength and shear strength It is set to follow a Weibull distribution law, while other parameters (such as viscous damping) are... The fracture energies (such as Type I and Type II fracture energies) also follow the Weibull distribution because they depend on the elastic modulus and tensile strength, and remain stable for other fixed conventional parameters.

[0029] S70 distinguishes two types of bonding units based on the structural characteristics of walnut shells: one is the general bonding unit CIEs1 inside the shell, whose parameters are directly derived from the material properties of adjacent units; the other is the interface bonding unit CIEs2 distributed along the natural suture line (the joint surface between the upper and lower halves of the shell). Since the suture line joint of actual walnut shells is often more prone to cracking than other areas of the shell, we set the strength parameters of CIEs2 to be lower than those of CIEs1 in the model. The expected strength of CIEs2 can also be calibrated by comparing the force-displacement curve. By combining the set heterogeneous elastic units and heterogeneous bonding units (CIEs1 and CIEs2), a heterogeneous nut shell model is formed. S80. After establishing a numerical model of the walnut shell that incorporates the heterogeneous properties of the material, it was imported into ABAQUS / Explicit to simulate the compressive fracture process. The loading conditions were consistent with the experiment: the upper pressure plate was pressed down at a speed of 0.02 mm / s, the bottom was fixed, and quasi-static equilibrium was ensured by introducing viscous damping. The simulation recorded the force-displacement response and the damage evolution of the bonded elements. The results showed that cracks first appeared in weak areas such as the suture line, and due to the spatial inhomogeneity of the material parameters, they propagated along low-strength paths, eventually forming a main crack running along the suture line and multiple secondary cracks, and the shell fractured into irregular fragments. Comparison with the experiment showed that the simulation curves were consistent with the measured values ​​in terms of stiffness, peak load, and post-peak softening trend. The fracture morphology also reproduced the actual phenomenon that cracking along the suture line was the main characteristic, verifying the reliability of this heterogeneous modeling method in effectively reproducing the real fracture process through a statistical equivalence strategy.

[0030] The above embodiments are only used to illustrate the present invention. Each step can be varied, and the scope of protection of the present invention is not limited thereto. Any person skilled in the art who makes equivalent substitutions or changes to the inventive concept based on the technical solution of the present invention within the scope of the technology disclosed in the present invention should be covered within the scope of protection of the present invention.

Claims

1. A numerical model construction method of nut shell heterogeneity, characterized in that The method comprises the following steps: S10, selecting a typical nut sample, measuring its geometric size parameters, and establishing a three-dimensional geometric model of the nut shell by a conventional three-dimensional technique, discretizing the geometric model by meshing, and generating a finite element mesh model composed of elastic elements; S20, inserting zero-thickness cohesive elements along the interfaces of adjacent elastic elements in the mesh model of S10, reading the node and element information of the initial mesh by a self-defined program, copying and renumbering the nodes shared by adjacent elastic elements to disconnect the original topological connection; S30, defining a bilinear constitutive model for the cohesive elements, including a traction-separation stage, a damage initiation stage, and a damage evolution stage, and setting the initial stiffness of the cohesive elements; S40, calibrating the expected values of the mechanical parameters of the elastic elements and the cohesive elements, including the elastic modulus, the tensile strength, the shear strength, and the type I and type II fracture energy, by using a conventional physical mechanics testing machine, matching the simulation results with the experimental macroscopic mechanical behavior by a global force-displacement curve fitting method, and taking the non-homogeneous distribution as a benchmark; S50, calculating the expected coefficient values of all elastic elements according to the Weibull cumulative distribution function, and randomly assigning values to all elastic elements according to the expected coefficient values; S60, the assigned adjacent elastic element with the expected coefficient average value assigns mechanical parameters to the cohesive elements for the connection and assigns values to all cohesive elements by this rule; S70, distinguishing two types of cohesive elements according to the structural characteristics of the walnut shell: one is the general cohesive element CIEs1 inside the shell, and the other is the interface cohesive element CIEs2 distributed along the natural suture line (the upper and lower shell joint surface) of the walnut, and the strength parameters of CIEs2 are set to be lower than those of CIEs1; S80, constructing a non-homogeneous nut shell cracking model based on the finite discrete element method and according to the above content, solving the model by a numerical simulation method, realizing the simulation of the fracture behavior of the nut shell under load, and verifying the accuracy of the non-homogeneous modeling by experiments; In S30, the bilinear constitutive model for the cohesive elements includes a traction-separation stage, a damage initiation stage, and a damage evolution stage: S31, the traction-separation model is: ; wherein represents the traction force, and represent the normal and tangential stresses along the cohesive element, respectively; and correspond to the elastic modulus and stiffness matrix, represents the strain, refers to the constitutive thickness, represents the displacement; S32, the damage initiation criterion is: ; where is the Macaulay symbol, indicating that the compressive tractions do not affect the initial state of failure, and are the maximum normal and shear stresses that can be sustained, respectively. S33, introducing damage variable in damage evolution stage Describe the stiffness degradation process: ; wherein is the current maximum relative displacement, is the damage initiation displacement, is the full fracture displacement, and are calculated according to the BK criterion from the type I and type II fracture energies. In S50, the mechanical parameters are randomly distributed according to the Weibull cumulative distribution function, including: S51, obtaining the elastic modulus of any elastic unit according to the Weibull cumulative distribution function is: ; ; wherein E is the expected value of the elastic modulus, is the homogeneity index, is a uniform distribution function between 0 and 1; S52, by the expected coefficient value randomly assign all elastic units; In S60, the parameters are reasonably assigned to the cohesive elements for connection by the average expected coefficient values of the adjacent elastic elements, including: S61, through the assigned adjacent elastic unit With The respective expected coefficient values are calculated and averaged The average expected coefficient value is set as the expected coefficient value of the bonding unit ; S62, by the bonding unit The expected coefficient value obtains the Weibull strength distribution model with adjacent continuous position relationship: ; wherein , and respectively represent compressive strength, shear strength, mode I fracture energy and mode II fracture energy of the connecting unit ; , , and then respectively represent expected tensile strength, expected shear strength, expected mode I fracture energy and expected mode II fracture energy; S63, different mechanical parameters are assigned to all cohesive elements by the Weibull strength distribution model; S64, the elastic modulus , tensile strength and shear strength are set to obey Weibull distribution law, while other parameters (such as viscous damping , type I and type II fracture energy, etc.) also follow Weibull distribution due to the dependence on elastic modulus and tensile strength, and remain stable and unchanged for other fixed conventional parameters.

2. The numerical model construction method for the heterogeneity of nut shell according to claim 1, characterized in that: In S40, the mechanical performance curve of the nut shell sample under compression load is determined by a conventional physical mechanics testing machine, the slope of the elastic section, the secant modulus at the half peak strength, and the peak load of the curve are fitted to calibrate the expected parameters of the model, such as the elastic modulus, the tensile strength, the shear strength, and the fracture energy.

3. The method according to claim 1, wherein: In S40 and S80, the conventional physical mechanics testing machine can be any one of a universal testing machine, a texture analyzer, a drop hammer impact testing machine, etc.

4. The method of claim 1, wherein In the S50, the elastic modulus of each elastic element is obtained according to the Weibull cumulative distribution function . And through the expected coefficient value , the elastic modulus of each elastic element is randomly assigned. In addition, by assigning an arbitrary random number to the marker, it can be ensured that the elastic elements with different elastic moduli are randomly distributed in space to simulate heterogeneity.

5. The method of claim 1, wherein, In the step S60, the adjacent elastic units with the assigned values are calculated and averaged . The average expected coefficient value is set as the expected coefficient value of the bonding unit . The Weibull strength distribution model with the adjacent continuous position relationship is obtained through the expected coefficient value of the bonding unit , and the compressive strength, shear strength, type I fracture energy and type II fracture energy of all the bonding units are obtained according to the model.

6. The method of claim 1, wherein, In S70, two types of cohesive elements are distinguished according to the structural characteristics of the walnut shell, and the strength of the suture interface cohesive element is less than that of the matrix cohesive element.

Citation Information

Patent Citations

  • Simulation calculation method for hot processing of granular nuts in roller

    CN110414139A

  • Discrete element numerical simulation method for nut shell crushing

    CN113821926A