CN108388736B - Soft metamaterial incision tip shape design method - Google Patents
Soft metamaterial incision tip shape design method Download PDFInfo
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Abstract
The invention discloses a design method of a soft metamaterial notch tip shape, which comprises the steps of establishing a simulation model, establishing the simulation model, and carrying out cubic spline curve simulation; generating an initial population, randomly generating N binary values based on a simulation model, and forming the initial population by individuals represented by the binary values; calculating individual fitness, calculating the maximum stress value of the soft metamaterial primitive cell corresponding to each individual, and measuring the individual fitness according to the principle that the maximum stress value is minimum; updating the population, sequentially executing selection, crossing and mutation genetic operations to generate a next generation population, enabling the population to evolve forwards, and updating the population; outputting a result, setting a stopping condition, and outputting the result if the stopping condition is met; the invention provides a soft metamaterial notch optimization method and an idea based on finite element calculation software and a genetic algorithm, and reduces notch tip stress through the optimization algorithm to improve the tensile property of the soft metamaterial.
Description
Technical Field
The invention relates to the field of soft metamaterial design, in particular to a soft metamaterial notch tip shape design method.
Background
The soft metamaterial with periodically arranged notches distributed in an elastomer such as a rubber material has extraordinary mechanical properties such as a negative Poisson ratio effect, large tensile property and programmable force-deformation relation. Due to the designability, easy production and huge design space of the incision, the cut soft metamaterial has recently attracted extensive attention and has wide application prospect in the fields of electronic equipment, phononic crystals, medical instruments and the like.
At present, in order to improve the mechanical properties of the soft metamaterial, the shape and arrangement of the cuts of the soft metamaterial are generally designed, but the geometric shape of the cut tip has a great influence on the mechanical properties, especially the tensile properties, of the soft metamaterial. Under tension, the soft metamaterial slit tip will be subjected to very large stresses due to stress concentration and create large deformations, which limit further stretching of the material and may lead to fractures at the slit tip. The performance of the soft metamaterial can be improved through structural optimization, but due to the strong nonlinearity of materials, large deformation and the like, the existing notch tip optimization method is still rarely researched. Therefore, a special optimization method is needed to be provided for the shape of the soft metamaterial notch tip to guide the design and processing of the soft metamaterial, and the method has very important engineering application value.
Disclosure of Invention
The invention aims to solve the problems and provide a soft metamaterial incision tip shape design method.
The invention realizes the purpose through the following technical scheme:
a soft metamaterial incision tip shape design method comprises the following steps:
s1, establishing a simulation model, establishing a parameterized numerical simulation model of the soft metamaterial primitive cell, and simulating 1/2 symmetrical to the incision tip through a cubic spline curve;
s2, generating an initial population, randomly generating N binary values based on a parameterized numerical simulation model of the metamaterials, forming the initial population by individuals represented by the binary values, and representing the geometric shape of a cut tip by each individual;
s3, calculating individual fitness, applying periodic boundary conditions to the soft copying material primitive cells by utilizing nonlinear finite element software, calculating the maximum stress value of the soft metamaterial primitive cells corresponding to each individual under the action of a certain tensile displacement load, and measuring the individual fitness according to the principle that the maximum stress value is minimum;
s4, updating the population, sequentially executing selection, crossing and mutation genetic operations to generate a next generation population, and enabling the population to evolve forwards to update the population;
and S5, outputting the result, setting a stopping condition, outputting the result if the stopping condition is met, and repeating the step S4 if the stopping condition is not met.
Specifically, the cubic spline curves in step S1 are determined by coordinates of four points, the abscissa and the ordinate of the first point are fixed, the abscissa and the ordinate of the second point and the third point are free to move in the constraint space, the fourth point is located on the symmetry plane of the incision tip, and the abscissa and the ordinate are fixed and free to move in the constraint space.
Specifically, the geometrical shape of the incision tip is arranged to be symmetrical about the central axis of the incision, the constraint space is arranged at the incision tip and has a rectangular structure, and one side of the constraint space coincides with the central line of the incision.
Specifically, the step S3 further includes a method for processing the abnormal individual, where, for the abnormal individual, the maximum stress value is artificially assigned, and a method of a penalty function is used to reduce the fitness of the abnormal individual.
Specifically, step S4 includes dividing all individuals into M islands for inheritance by using a multi-island genetic algorithm, and obtaining the next generation population through natural selection and genetic evolution.
Specifically, the stop condition in step S5 is that a predetermined number of evolutionary generations have been reached.
The invention has the beneficial effects that:
the design method of the soft metamaterial notch tip shape is based on finite element calculation software and a genetic algorithm, provides a method and an idea for optimizing the notch of the soft metamaterial, and reduces the stress of the notch tip through the optimization algorithm to improve the tensile property of the soft metamaterial.
Drawings
FIG. 1 is a schematic flow chart of a soft metamaterial notch tip shape design method according to the invention;
FIG. 2 is a schematic diagram of a 5L × 5L finite structure of a soft metamaterial according to an embodiment of the present invention;
FIG. 3 is a schematic structural diagram of an L × L primitive cell of a soft metamaterial according to an embodiment of the present invention;
FIG. 4 is a schematic structural diagram of a soft metamaterial incision tip according to an embodiment of the invention;
FIG. 5 is a graph of individual fitness changes during evolution of a genetic algorithm according to an embodiment of the present invention;
FIG. 6 is the geometry of the optimal soft metamaterial individual incision tip in the genetic algorithm evolution engineering of the embodiment of the invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings in which:
taking a Neo-Hooken rubber material model as an example, the parameters of the Neo-Hooken rubber material are as follows: the initial shear modulus is 1.1MPa, the initial elastic modulus E is 3.25MPa, the rubber model is an approximately incompressible material, and the ratio of the bulk modulus to the shear modulus K/μ is 50.
As shown in FIG. 1, the method for designing the shape of the soft metamaterial incision tip comprises the following steps:
step one, establishing a simulation model;
establishing a parameterized numerical simulation model of the metamaterials primitive cell, and simulating 1/2 symmetrical to the incision tip through a cubic spline curve;
the cubic spline curves are determined by coordinates of four points, the abscissa and the ordinate of a first point are fixed and unchanged, the abscissa and the ordinate of a second point and a third point move freely in a constraint space, a fourth point is located on a symmetrical plane of a notch tip, the abscissa of the fourth point is fixed and unchanged, the ordinate moves freely in the constraint space, the geometric shape of the notch tip is set to be symmetrical with the central axis of the notch, the constraint space is arranged at the notch tip and is of a rectangular structure, and one edge of the constraint space is overlapped with the central line of the notch.
As shown in fig. 2, 3 and 4, the coordinate system is shown in the figure, and the abscissa and the ordinate of the first point are fixed, such as the point (x) in fig. 41,y1) Shown, in this embodiment, x1＝0.025L，y10.08L; second and third points (x)2,y2) And (x)3,y3) Can move freely in a constrained space shown by a line box in the figure, wherein x2∈[0,0.05L]，x3∈[0,0.05L]，y2∈[0.03L,0.08L]，y3∈[0.03L,0.08L](ii) a The fourth point is located on the plane of symmetry of the incision tip, abscissa x4Fixed at 0, ordinate y4∈[0.03L,0.04L]。
Step two, generating an initial population;
randomly generating N binary values based on a parameterized numerical simulation model of the metamaterials primitive cells, forming an initial population by individuals represented by the binary values, and representing the geometric shape of a cut tip by each individual;
based on a parameterized numerical simulation model of the metamaterials primitive cells, chromosomes (individuals) represented by 100 binary numbers are randomly generated to form an initial population, each individual represents the geometrical shape of a cut tip, and each bit in the binary numbers is randomly set to be 0 or 1. Generally, the geometry of the cut-off tip corresponding to a randomly generated binary number is not necessarily regular, and thus, the diversity of the population can be ensured, thereby avoiding searching for a locally optimal solution.
Step three, calculating individual fitness;
applying periodic boundary conditions to the cells of the soft metamaterial by using nonlinear finite element software, calculating the maximum stress value of the cells of the soft metamaterial corresponding to each individual under the action of a certain tensile displacement load, and measuring the individual fitness according to the principle that the maximum stress value is minimum;
and applying periodic boundary conditions to the soft metamaterial primitive cells by using finite element software with strong nonlinear computing capability, calculating the maximum stress value in the soft metamaterial primitive cells corresponding to each genetic individual under the action of a certain 0.6L tensile displacement load, and measuring the fitness of the genetic individuals according to the principle of minimizing the maximum stress value. For abnormal individuals, punishment is performed by artificially assigning the maximum stress value to 1000MPa in this embodiment, and the fitness of the genetic individuals is reduced by using a method of a penalty function, where the individual fitness changes as shown in fig. 5.
Step four, updating the population;
sequentially executing selection, crossing and mutation genetic operations to generate a next generation population, so that the population evolves forwards and is updated;
in order to enhance the global search capability of the algorithm, a multi-island genetic algorithm is adopted, and 100 individuals are averagely distributed to 5 islands for inheritance in the embodiment. Due to the natural selection and genetic evolution mechanism of 'excellence and disadvantage, survival of the fittest' the incision tip geometry of the best individual is more and more close to the target requirement.
Step five, outputting a result;
a stop condition is set, and if the stop condition is satisfied, the result is output, and if the stop condition is not satisfied, step S4 is repeated.
The stop condition in this example was 30 generations of evolution. When the evolution condition of 30 generations is met, outputting an optimal result and exiting; otherwise, generating a next generation population and continuing to calculate.
The final result outputs the geometry of the incision tip as shown in fig. 6, with the optimization results: x is the number of2＝0.04627L，x3＝0.004957L，y2＝0.07661L，y3＝0.03016L，y40.03011L under tensile loadUnder load, the maximum stress at the tip of the incision is reduced by approximately 60%.
The technical solution of the present invention is not limited to the limitations of the above specific embodiments, and all technical modifications made according to the technical solution of the present invention fall within the protection scope of the present invention.
Claims (5)
1. A soft metamaterial incision tip shape design method is characterized in that: the method comprises the following steps:
s1, establishing a simulation model, establishing a parameterized numerical simulation model of the soft metamaterial primitive cell, and simulating 1/2 symmetrical to the incision tip through a cubic spline curve; the geometric shape of the incision tip is set to be symmetrical with the central axis of the incision, the constraint space is arranged at the incision tip and is of a rectangular structure, and one side of the constraint space is superposed with the central line of the incision;
s2, generating an initial population, randomly generating N binary values based on a parameterized numerical simulation model of the metamaterials, forming the initial population by individuals represented by the binary values, and representing the geometric shape of a cut tip by each individual;
s3, calculating individual fitness, applying periodic boundary conditions to the soft metamaterial primitive cells by utilizing nonlinear finite element software, calculating the maximum stress value of the soft metamaterial primitive cell corresponding to each individual under the action of a certain tensile displacement load, and measuring the individual fitness according to the principle that the maximum stress value is minimum;
s4, updating the population, sequentially executing selection, crossing and mutation genetic operations to generate a next generation population, and enabling the population to evolve forwards to update the population;
and S5, outputting the result, setting a stopping condition, outputting the result if the stopping condition is met, and repeating the step S4 if the stopping condition is not met.
2. The soft metamaterial notch tip shape design method as claimed in claim 1, wherein: the cubic spline curves in step S1 are determined by coordinates of four points, the abscissa and ordinate of the first point are fixed and unchanged, the abscissa and ordinate of the second point and the third point move freely in the constraint space, the fourth point is located on the symmetry plane of the incision tip, and the abscissa of the fourth point is fixed and unchanged, and the ordinate moves freely in the constraint space.
3. The soft metamaterial notch tip shape design method as claimed in claim 1, wherein: the step S3 further includes a method for processing the abnormal individual, in which, for the abnormal individual, the maximum stress value is manually assigned, and a penalty function method is used to reduce the fitness of the abnormal individual.
4. The soft metamaterial notch tip shape design method as claimed in claim 1, wherein: the step S4 specifically includes dividing all individuals into M islands for inheritance by using a multi-island genetic algorithm, and obtaining the next generation population through natural selection and genetic evolution.
5. The soft metamaterial notch tip shape design method as claimed in claim 1, wherein: the stop condition in step S5 is that a predetermined number of evolutionary generations have been reached.
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| CN115795967B (en) * | 2022-12-06 | 2023-07-21 | 海南师范大学 | Customized sole design method based on bionic metamaterial and data driving |
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