Mold flow behavior virtual simulation design system integrating multi-field characteristics

Abstract

The invention relates to the technical field of mold design and manufacturing, and discloses a mold flow behavior virtual simulation design system integrating multi-field characteristics, which comprises a multi-modal data acquisition module, a multi-field coupling simulation module, a material gene spectrum library, an intelligent optimization engine module and a physical verification closed loop module, by arranging a multi-modal data acquisition module, a multi-field coupling simulation module, an intelligent optimization engine module and a physical verification closed loop module, interaction between a temperature field and a stress field of a mold can be dynamically simulated through a thermal-force coupling equation, so that error accumulation of traditional separated simulation is avoided; the coupling effect of melt flow and mold deformation is predicted through a fluid-solid coupling equation to solve the problem of flow instability in traditional single-field simulation, and millimeter-scale and micron-scale cross-scale correlation is achieved by coupling a thermal field and a flow field and coupling a force field and a thermal field. Error accumulation of traditional separated simulation is avoided through a thermal-mechanical coupling equation and a fluid-solid coupling equation.

Description

Technical Field

[0001] This invention relates to the field of mold design and manufacturing technology, and more specifically to a virtual simulation design system for mold flow behavior that integrates multiple field characteristics. Background Technology

[0002] Publication document CN119647290A discloses a parametric simulation model design method and system for plastic molds. The method includes the following steps: finely preparing the target plastic raw material to obtain a homogeneous dried material; performing multi-field rheological property scanning on the homogeneous dried material and extracting viscosity model parameters to obtain initial parameters for the viscosity model; accurately measuring the thermodynamic properties of the plastic material on the homogeneous dried material and analyzing its crystallization kinetics to obtain crystallization kinetic model parameters; and integrating the material gene spectrum based on the initial viscosity model parameters and the crystallization kinetic model parameters to obtain the material gene spectrum. This invention significantly improves the efficiency and quality of mold manufacturing and reduces manufacturing costs through performance-driven parameter optimization based on material properties and microenvironment and the generation of an "intelligent mold blueprint."

[0003] However, in existing mold design, virtual simulation technologies such as UG motion simulation and injection filling simulation are mostly focused on a single physical field, such as fluid or structural stress. They lack comprehensive analysis of the coupling effects of multiple fields, resulting in data silos and failure to achieve dynamic data fusion. This leads to large deviations between simulation and physical mold testing, and the simulation results lack real-time interactive verification with physical experiments, making dynamic correction difficult and lacking closed-loop verification. Summary of the Invention

[0004] To overcome the aforementioned deficiencies of the prior art, the present invention provides a virtual simulation design system for mold flow behavior that integrates multiple field characteristics, thereby solving the problems existing in the background art.

[0005] This invention provides the following technical solution: a virtual simulation design system for mold flow behavior integrating multi-field characteristics, including a multi-modal data acquisition module, a multi-field coupling simulation module, a material gene library, an intelligent optimization engine module, and a physical verification closed-loop module; The multimodal data acquisition module integrates multiple types of sensors to collect physical signals of key areas of the mold in real time, and performs data fusion after data preprocessing; The multi-field coupled simulation module uses thermo-mechanical coupling equations and fluid-solid coupling equations to simultaneously simulate melt flow, mold deformation and temperature field distribution, and acquire simulation data. At the same time, it introduces latent heat of phase change to construct a real-time heat exchange model. The material gene library constructs a cross-scale correlation model through the viscosity-temperature-shear rate relationship, establishes a database to store material parameters, and receives data from the physical verification closed-loop module to update the parameters of the cross-scale correlation model. The intelligent optimization engine module uses an improved genetic algorithm to generate the optimal mold design scheme. The physical verification closed-loop module uses 3D printing to create a mold prototype, uses a 3D scanner to acquire measured data, calculates deformation, and drives the actuator to perform compensation.

[0006] Preferably, the multiple types of sensors include temperature sensors, pressure sensors, strain sensors, and vibration sensors; the key areas of the mold include mold cavities, flow channels, and pressure rings; the real-time acquisition is based on a dynamic high-speed sampling frequency according to the dynamic compensation sampling method of the mold motion state; the data fusion adopts a time alignment algorithm to map the scattered data to a unified coordinate system and generate a gridded feature dataset.

[0007] Preferably, the time alignment algorithm is expressed by the formula: ;in, express Data features after time-mapping; Indicates the first The weights of each sensor are dynamically allocated based on the signal-to-noise ratio; Indicates the exponential decay coefficient; Indicates the first The time it takes for each sensor to acquire data; Indicates the first One sensor The characteristics of data collected at any time.

[0008] Preferably, the thermo-mechanical coupling equation is expressed as: ;in, Indicates the material density of the mold; This indicates the specific heat capacity of the mold; Thermal conductivity indicates the ability of the mold material to conduct heat. This indicates the conversion of mechanical work into heat energy, representing the heat energy converted due to mechanical action or other reasons. Indicates temperature; Represents the Hamiltonian operator; The fluid-structure interaction equation is expressed as follows: ;in, Represents the melt velocity field; This represents the pressure acting on the melt; Indicates dynamic viscosity; Represents the thermal buoyancy term; This represents the Laplace operator.

[0009] Preferably, the real-time heat exchange model is expressed by the formula: ;in, Represents the latent heat term of phase transition. Indicates latent heat; Indicates the liquid phase fraction.

[0010] Preferably, the material parameters include the material's elastic modulus and viscosity-temperature relationship parameters; the viscosity-temperature-shear rate relationship is used to construct a cross-scale correlation model, expressed by the formula: ;in, Viscosity represents the viscosity of a material and is a function of temperature and shear rate; Indicates the shear rate; Indicates reference viscosity; Indicates activation energy; Represents the gas constant; This represents the shear rate parameter; This represents a variable parameter, with values ​​ranging from 1 to 2. .

[0011] Preferably, the step of generating the optimal mold design scheme using the improved genetic algorithm specifically includes: Step 1: Initialize the population; set the population size as follows: , decision variables Encode as a real number vector, , Indicates the first Each design parameter and decision variable corresponds to a mold design scheme; an initial population is generated. , , Indicates the first in the initial population The individual, that is, the first individual One decision variable; Step 2: Set the objective function and sort the objective functions by numerical value; Step 3: Perform non-dominated sorting based on non-dominated levels; Step 4: Calculate the congestion level; Step 5: Generate offspring populations through binary tournament selection, crossover, and mutation operations; Step 6: Merge the current population with the offspring population to form a mixed population, and then form a new generation of parent population from the mixed population; Step 7: Repeat steps 3 to 6. Stop iterating when the number of iterations reaches the maximum number of iterations or the fixed convergence condition is met. Output the first non-dominated layer in the final population as the optimal solution. The optimal solution is the optimal mold design scheme.

[0012] Preferably, the objective function is expressed as: ;in, Indicates the first The objective function corresponding to each individual; Let represent the first objective function, which is the th objective function. The filling pressure corresponding to each individual; Let represent the second objective function, which is the th objective function. The residual stress of the filling pressure corresponding to each individual; .

[0013] Preferably, the non-dominated sorting specifically involves: Individuals in the population are divided into different dominance levels; for any two individuals and If satisfied Then it is called Dominate , recorded as ; Form the first layer of individuals in the population that are not dominated by any other individual. Remove the individuals in the first layer from the population. Repeat this process to find the remaining individuals that are not dominated by any other individual and form the second layer. Repeat this process until all individuals are classified into a certain layer.

[0014] Preferably, the calculation of congestion degree specifically involves: ;in, Indicates the first The first layer The degree of crowding of individuals; Indicates the first The normalized range of each objective function. Indicates the number of objective functions; and Indicates the first In the layer Two adjacent individuals.

[0015] The technical effects and advantages of this invention are as follows: This invention, by incorporating a multimodal data acquisition module, a multi-field coupled simulation module, an intelligent optimization engine module, and a physical verification closed-loop module, facilitates the dynamic simulation of the interaction between the temperature and stress fields of the mold through thermo-mechanical coupling equations, thus avoiding the error accumulation of traditional separate simulations. It addresses the flow instability problem in traditional single-field simulations by predicting the coupling effect between melt flow and mold deformation through fluid-structure interaction equations. Overcoupling the thermal and flow fields, and the force and thermal fields, achieves cross-scale correlations at the millimeter and micrometer levels. Simultaneously solving the melt velocity, pressure, and temperature fields through thermo-mechanical and fluid-structure interaction equations avoids the error accumulation of traditional separate simulations. A real-time heat exchange model describes the exothermic effect during melt solidification, solving the problem of large temperature prediction deviations during the solidification stage in traditional methods. The physical verification closed-loop module interactively verifies the simulation results with physical experiments and dynamically corrects them through deformation compensation for closed-loop verification. Attached Figure Description

[0016] Figure 1 This is a structural diagram of the virtual simulation design system for mold flow behavior integrating multi-field characteristics according to the present invention. Detailed Implementation

[0017] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. In addition, the forms of the various structures described in the following embodiments are merely illustrative. The virtual simulation design system for mold flow behavior integrating multiple field characteristics involved in the present invention is not limited to the structures described in the following embodiments. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] like Figure 1 As shown, this invention provides a virtual simulation design system for mold flow behavior integrating multi-field characteristics, including a multimodal data acquisition module, a multi-field coupled simulation module, a material gene library, an intelligent optimization engine module, and a physical verification closed-loop module; the modules interact with each other through a data hub. The multimodal data acquisition module integrates multiple types of sensors to collect physical signals of key areas of the mold in real time, and performs data fusion after data preprocessing; the multimodal data acquisition module transmits data to the multi-field coupling simulation module, the physical verification closed-loop module, and the material genome library to provide real-time working condition data for reference and storage; The multi-field coupled simulation module uses thermo-mechanical coupling equations and fluid-solid coupling equations to simultaneously simulate melt flow, mold deformation, and temperature field distribution, and acquire simulation data. At the same time, it introduces latent heat of phase change to construct a real-time heat exchange model, accurately simulating the exothermic effect of melt solidification during injection molding. The multi-field coupled simulation module receives data from the multimodal data acquisition module and transmits simulation data to the intelligent optimization engine module and the physical verification closed-loop module. The material gene library constructs a cross-scale correlation model using viscosity-temperature-shear rate equations, establishes a database to store material parameters, and receives data from the physical verification closed-loop module to update the parameters of the cross-scale correlation model. By establishing a quantitative relationship between the microstructure and macroscopic properties of materials, the simulation accuracy is improved. The material gene library provides material-related parameters to the multi-field coupled simulation module and receives data from the multi-modal data acquisition module for storage. The intelligent optimization engine module uses an improved genetic algorithm to generate the optimal mold design scheme. The mold design scheme consists of mold design parameters, including but not limited to mold temperature, injection speed, and holding time. The mold design scheme can be obtained by collecting historical mold design schemes and improving them by those skilled in the art based on actual mold design requirements using professional knowledge or books. The intelligent optimization engine module receives data from the multi-field coupling simulation module and transmits the optimal mold design scheme data to the physical verification closed-loop module. The physical verification closed-loop module creates a mold prototype through 3D printing, acquires measured data using a 3D scanner, calculates deformation, and drives the actuator for compensation to solve the lag problem of post-correction in traditional methods. The measured data includes, but is not limited to, measured deformation data and measured temperature data. The physical verification closed-loop module feeds back the measured data to the intelligent optimization engine module and to the multi-field coupling simulation module.

[0019] In this embodiment, it should be specifically noted that the various types of sensors include, but are not limited to, temperature sensors, pressure sensors, strain sensors, and vibration sensors; the key areas of the mold include, but are not limited to, mold cavities, flow channels, and pressure rings; the real-time acquisition uses a dynamic compensation sampling method based on the dynamic high-speed sampling frequency of the mold's motion state to avoid data loss during high-speed movement; the data preprocessing specifically uses Kalman filtering to eliminate data noise and extract data features; the data features include, but are not limited to, temperature gradient and strain rate; the data fusion uses a time alignment algorithm to map scattered data to a unified coordinate system to generate a gridded feature dataset, thereby solving the data silo problem of traditional systems; the dynamic compensation sampling method specifically adaptively adjusts the sampling frequency based on the mold's motion state.

[0020] In this embodiment, it should be specifically noted that the time alignment algorithm is expressed by the following formula: ;in, express Data features after time-mapping; Indicates the first The weights of each sensor are dynamically allocated based on the signal-to-noise ratio to address the issue of varying importance among multiple data sources. This represents the exponential decay coefficient, reflecting the timeliness of the signal. Recent data has a higher weight, thus avoiding interference from outdated data. Indicates the first The time it takes for each sensor to acquire data; Indicates the first One sensor The characteristics of data collected at any time.

[0021] In this embodiment, it should be specifically noted that the thermo-mechanical coupling equation is expressed as: ;in, Indicates the material density of the mold; This indicates the specific heat capacity of the mold; Thermal conductivity indicates the ability of the material used in the mold to conduct heat; the higher the thermal conductivity, the easier it is for the material to conduct heat. This indicates the conversion of mechanical work into heat energy, representing the heat energy converted due to mechanical action or other reasons. Indicates temperature; The Hamiltonian operator is used to describe the spatial variation of physical quantities; the interaction between the temperature field and stress field of the mold is dynamically simulated to avoid the accumulation of errors in traditional separate simulations. The fluid-structure interaction equation is expressed as follows: ;in, Represents the melt velocity field; This represents the pressure acting on the melt; This indicates dynamic viscosity, reflecting the magnitude of the melt's viscosity; Represents the thermal buoyancy term; This represents the Laplace operator; it solves the flow instability problem in traditional single-field simulation by predicting the coupling effect between melt flow and mold deformation. By coupling the thermal field with the flow field and the force field with the thermal field, the cross-scale correlation between millimeter and micrometer scales is achieved. The melt velocity field, pressure field and temperature field are solved simultaneously through the thermo-mechanical coupling equation and the fluid-solid coupling equation, so as to avoid the error accumulation of traditional separate simulation. The real-time heat exchange model is expressed by the following formula: ;in, Represents the latent heat term of phase transition. Indicates latent heat; It represents the liquid phase fraction; the exothermic effect during melt solidification is described by a real-time heat exchange model, thus solving the problem of large temperature prediction deviations during the solidification stage in traditional methods.

[0022] In this embodiment, it should be specifically noted that the material parameters include, but are not limited to, the elastic modulus of the material, viscosity-temperature relationship, and other parameters; the viscosity-temperature-shear rate relationship is used to construct a cross-scale correlation model, which is expressed by the following formula: ;in, Viscosity represents the viscosity of a material and is a function of temperature and shear rate. It describes the properties within the material that impede its relative flow and reflects the magnitude of the material's viscosity. Indicates the shear rate; The reference viscosity, which can be obtained through nonlinear fitting of experimental data, is a parameter that affects the viscosity. This represents the activation energy, which affects the relationship between viscosity and temperature. Interatomic potential energy parameters are obtained through molecular dynamics simulations. Represents the gas constant; The shear rate parameter can be obtained by nonlinear fitting of experimental data. It is related to the shear rate and affects how viscosity changes with the shear rate. This represents a variable parameter, with values ​​ranging from 1 to 2. The reference viscosity is used to describe the characteristics of viscosity as a function of shear rate. ,activation energy Shear rate parameters and changing parameters The model can be corrected quickly based on experimental data to ensure its generalization ability. The cross-scale correlation model establishes a cross-scale correlation between "atomic-mesoscopic-macroscopic" scales, which more accurately describes the nonlinear changes in material viscosity.

[0023] In this embodiment, it should be specifically noted that the step of generating the optimal mold design scheme using the improved genetic algorithm specifically includes: Step 1: Initialize the population; set the population size as follows: , decision variables Encode as a real number vector, , Indicates the first Each design parameter and decision variable corresponds to a mold design scheme; an initial population is generated. , , Indicates the first in the initial population The individual, that is, the first individual One decision variable; for example ,in, For mold temperature, For injection speed, For the holding time, the encoding is as follows: , That is , That is , That is ; Step 2: Set the objective function and sort the objective functions by numerical value; Step 3: Perform non-dominated sorting based on non-dominated levels; Step 4: Calculate the congestion level; Step 5: Generate offspring populations through binary tournament selection, crossover, and mutation operations; Step 6: Merge the current population with the offspring population to form a mixed population, and then form a new generation of parent population from the mixed population; Step 7: Repeat steps 3 to 6. Stop iterating when the number of iterations reaches the maximum number of iterations or the fixed convergence condition is met. Output the first non-dominated layer in the final population as the optimal solution. The optimal solution is the optimal mold design scheme.

[0024] In this embodiment, it should be specifically noted that the objective function is expressed as: ;in, Indicates the first The objective function corresponding to each individual; Let represent the first objective function, which is the th objective function. The filling pressure corresponding to each individual; Let represent the second objective function, which is the th objective function. The residual stress of the filling pressure corresponding to each individual; .

[0025] In this embodiment, it should be specifically explained that the non-dominated sorting specifically refers to: Individuals in the population are divided into different dominance ranks; the lower the rank, the higher the quality of the individual's solution. For any two individuals... and If satisfied Then it is called Dominate , can be written as ; Form the first layer of individuals in the population that are not dominated by any other individual. Remove the individuals in the first layer from the population. Repeat this process to find the remaining individuals that are not dominated by any other individual and form the second layer. Repeat this process until all individuals are classified into a certain layer.

[0026] In this embodiment, it should be specifically explained that the calculation of congestion degree is as follows: ;in, Indicates the first The first layer The degree of crowding of individuals; Indicates the first The normalized range of each objective function. This represents the number of objective functions, in this embodiment. ; and Indicates the first In the layer Two adjacent individuals; The crowding degree is used to measure the distribution density of individuals within the same dominance level, so as to avoid the algorithm from converging to a local optimum too early. The larger the crowding degree, the sparser the solution in the region where the individual is located. Step 6 specifically involves: Individuals from each non-dominant level are added to the new generation parent population in descending order of their non-dominant level, until adding individuals from the next level would cause the new generation parent population to exceed [a certain size]. Stop when the population is full. Sort the last layer that cannot be fully added in descending order of crowding, and select individuals in turn to add to the new generation of parent population, until a population of a certain size is formed. The new generation of parental population.

[0027] In this embodiment, it should be specifically noted that in the process of calculating the deformation and driving the actuator for compensation, the calculated deformation is expressed by the formula: ;in, Indicates the amount of deformation compensation; This indicates the measured temperature. This indicates the measured temperature change. Indicates the measured strain. Indicates strain change; This represents the change in mold displacement caused by a unit change in temperature. This indicates the change in mold displacement caused by a unit change in strain.

[0028] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0029] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A virtual simulation design system for mold flow behavior integrating multiple field characteristics, characterized in that: It includes a multimodal data acquisition module, a multi-field coupling simulation module, a materials genome library, an intelligent optimization engine module, and a physical verification closed-loop module; The multimodal data acquisition module integrates multiple types of sensors to collect physical signals of key areas of the mold in real time, and performs data fusion after data preprocessing; The multi-field coupled simulation module uses thermo-mechanical coupling equations and fluid-solid coupling equations to simultaneously simulate melt flow, mold deformation and temperature field distribution, and acquire simulation data. At the same time, it introduces latent heat of phase change to construct a real-time heat exchange model. The material gene library constructs a cross-scale correlation model through the viscosity-temperature-shear rate relationship, establishes a database to store material parameters, and receives data from the physical verification closed-loop module to update the parameters of the cross-scale correlation model. The intelligent optimization engine module uses an improved genetic algorithm to generate the optimal mold design scheme. The physical verification closed-loop module uses 3D printing to create a mold prototype, uses a 3D scanner to acquire measured data, calculates deformation, and drives the actuator to perform compensation.

2. The virtual simulation design system for mold flow behavior integrating multi-field characteristics according to claim 1, characterized in that: The various types of sensors include temperature sensors, pressure sensors, strain sensors, and vibration sensors; the key areas of the mold include the mold cavity, flow channel, and pressure ring; the real-time acquisition uses a dynamic compensation sampling method based on the dynamic high-speed sampling frequency of the mold's motion state; the data fusion uses a time alignment algorithm to map the scattered data to a unified coordinate system, generating a gridded feature dataset.

3. The virtual simulation design system for mold flow behavior integrating multi-field characteristics according to claim 2, characterized in that: The time alignment algorithm is expressed by the following formula: ;in, express Data features after time-mapping; Indicates the first The weights of each sensor are dynamically allocated based on the signal-to-noise ratio; Indicates the exponential decay coefficient; Indicates the first The time it takes for each sensor to acquire data; Indicates the first One sensor The characteristics of data collected at any time.

4. The virtual simulation design system for mold flow behavior integrating multi-field characteristics according to claim 3, characterized in that: The thermo-mechanical coupling equation is expressed as: ;in, Indicates the material density of the mold; This indicates the specific heat capacity of the mold; Thermal conductivity indicates the ability of the mold material to conduct heat. This indicates the conversion of mechanical work into heat energy, representing the heat energy converted due to mechanical action or other reasons. Indicates temperature; Represents the Hamiltonian operator; The fluid-structure interaction equation is expressed as follows: ;in, Represents the melt velocity field; This represents the pressure acting on the melt; Indicates dynamic viscosity; Represents the thermal buoyancy term; This represents the Laplace operator.

5. The virtual simulation design system for mold flow behavior integrating multi-field characteristics according to claim 4, characterized in that: The real-time heat exchange model is expressed by the following formula: ;in, Represents the latent heat term of phase transition. Indicates latent heat; Indicates the liquid phase fraction.

6. The virtual simulation design system for mold flow behavior integrating multi-field characteristics according to claim 5, characterized in that: The material parameters include the material's elastic modulus and viscosity-temperature relationship parameters; the viscosity-temperature-shear rate relationship is used to construct a cross-scale correlation model, expressed by the following formula: ;in, Viscosity represents the viscosity of a material and is a function of temperature and shear rate; Indicates the shear rate; Indicates reference viscosity; Indicates activation energy; Represents the gas constant; This represents the shear rate parameter; This represents a variable parameter, with values ​​ranging from 1 to 2. .

7. The virtual simulation design system for mold flow behavior integrating multi-field characteristics according to claim 6, characterized in that: The method of generating the optimal mold design scheme using the improved genetic algorithm specifically includes: Step 1: Initialize the population; set the population size as follows: , decision variables Encode as a real number vector, , Indicates the first Each design parameter and decision variable corresponds to a mold design scheme; an initial population is generated. , , Indicates the first in the initial population The individual, that is, the first individual One decision variable; Step 2: Set the objective function and sort the objective functions by numerical value; Step 3: Perform non-dominated sorting based on non-dominated levels; Step 4: Calculate the congestion level; Step 5: Generate offspring populations through binary tournament selection, crossover, and mutation operations; Step 6: Merge the current population with the offspring population to form a mixed population, and then form a new generation of parent population from the mixed population; Step 7: Repeat steps 3 to 6. Stop iterating when the number of iterations reaches the maximum number of iterations or the fixed convergence condition is met. Output the first non-dominated layer in the final population as the optimal solution. The optimal solution is the optimal mold design scheme.

8. The virtual simulation design system for mold flow behavior integrating multi-field characteristics according to claim 7, characterized in that: The objective function is expressed as: ;in, Indicates the first The objective function corresponding to each individual; Let represent the first objective function, which is the th objective function. The filling pressure corresponding to each individual; Let represent the second objective function, which is the th objective function. The residual stress of the filling pressure corresponding to each individual; .

9. The virtual simulation design system for mold flow behavior integrating multi-field characteristics according to claim 8, characterized in that: The specific steps of performing non-dominated sorting are as follows: Individuals in the population are divided into different dominance levels; for any two individuals and If satisfied Then it is called Dominate , recorded as ; Form the first layer of individuals in the population that are not dominated by any other individual. Remove the individuals in the first layer from the population. Repeat this process to find the remaining individuals that are not dominated by any other individual and form the second layer. Repeat this process until all individuals are classified into a certain layer.

10. The virtual simulation design system for mold flow behavior integrating multi-field characteristics according to claim 9, characterized in that: The calculation of congestion degree is specifically as follows: ;in, Indicates the first The first layer The degree of crowding of individuals; Indicates the first The normalized range of each objective function. Indicates the number of objective functions; and Indicates the first In the layer Two adjacent individuals.

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