A method and device for analyzing the buckling behavior of a light-driven thin film substrate structure

Abstract

The application discloses a light-driven thin film substrate structure buckling behavior analysis method and device, and relates to the technical field of materials. An optical strain expression perpendicular to a liquid crystal material director direction and an optical strain expression of an arbitrary position in a thin film are obtained, and an equivalent optical strain expression is obtained by simplification; according to a von Karman nonlinear plate theory, an approximate expression of elastic strain is obtained based on a superposition relationship and the equivalent optical strain expression, and system average elastic performance is obtained based on the approximate expression of elastic strain; according to an energy minimum value principle, buckling wave numbers and buckling amplitudes of the thin film in an equilibrium state are determined based on the system average elastic performance; illumination conditions are changed, a thin film buckling morphology phase diagram is drawn, and influences of different material parameters on a critical illumination intensity and the thin film buckling morphology phase diagram are compared, so that the light-driven thin film substrate structure buckling behavior analysis is performed. The problem how to realize accurate analysis and effective control of the light-driven thin film substrate structure buckling behavior is solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of materials, in particular to a method and device for analyzing buckling behavior of a light-driven thin film substrate structure. BACKGROUND

[0002] Surface wrinkle morphology of thin film substrate structure widely exists in nature. When sufficient compressive stress is generated in the thin film, surface buckling of the thin film forms wrinkles to make the system have lower energy, thereby spontaneously generating out-of-plane displacement to release internal stress. Such surface wrinkle phenomenon is applied to fields of flexible electronic devices and optical devices.

[0003] With the development of smart materials, thin film substrate structures based on piezoelectric, flexoelectric and light-driven materials have appeared in succession. Among them, light-driven materials are concerned due to their flexible control, non-contact, fast response and other characteristics. The driving mechanism of the light-driven materials is that the photoactive component undergoes photoisomerization under ultraviolet light irradiation, disturbs the liquid crystal structure, and produces macroscopic spontaneous deformation. By reasonably setting conditions, internal stress can be accurately controlled.

[0004] However, object deformation of the light-driven materials is closely related to light conditions, which may produce light-deformation coupling phenomenon, and even cause continuous spontaneous motion, which increases the difficulty of accurate analysis and control of buckling behavior, and also limits its application in some fields with high accuracy requirements.

[0005] Therefore, how to realize accurate analysis and effective control of buckling behavior of the light-driven thin film substrate structure, so that it can stably and accurately produce the required morphology under specific light conditions and different material parameters as expected, and avoid uncontrollable spontaneous motion caused by light-deformation coupling phenomenon, becomes a problem to be solved. SUMMARY

[0006] In the embodiments of the present application, by providing a method for analyzing buckling behavior of a light-driven thin film substrate structure, the problem of how to realize accurate analysis and effective control of buckling behavior of the light-driven thin film substrate structure, so that it can stably and accurately produce the required morphology under specific light conditions and different material parameters as expected, and avoid uncontrollable spontaneous motion caused by light-deformation coupling phenomenon, is solved.

[0007] In a first aspect, the embodiments of the present application provide a method for analyzing buckling behavior of a photo-driven thin film substrate structure, comprising: establishing a photo-induced strain model considering local light conditions based on material parameters, describing the propagation and absorption process of light in the thin film of liquid crystal elastomer containing azobenzene, obtaining an expression of photo-induced strain perpendicular to the director direction of the liquid crystal material and an expression of photo-induced strain at any position in the thin film, and simplifying to obtain an equivalent photo-induced strain expression; wherein the material parameters include the equivalent elastic modulus of the thin film, the equivalent elastic modulus of the substrate, the thickness of the thin film, and the distance of light propagation when the light intensity decays by a unit under a unit azobenzene molecule content; obtaining an approximate expression of elastic strain based on the superposition relationship and the equivalent photo-induced strain expression according to the von Karman nonlinear plate theory, and obtaining the average elastic energy of the system based on the approximate expression of the elastic strain; determining the buckling wave number and the buckling amplitude of the thin film in the equilibrium state based on the average elastic energy of the system according to the energy minimum principle; changing the light conditions, drawing the buckling morphology phase diagram of the thin film based on the buckling wave number and the buckling amplitude of the thin film in the equilibrium state, and comparing the effects of different material parameters on the critical light intensity and the buckling morphology phase diagram of the thin film to determine the effects of the light conditions and the material parameters on the buckling behavior of the thin film.

[0008] In a possible implementation, the photo-induced strain model considering local light conditions is established based on the material parameters, the propagation and absorption process of light in the thin film of liquid crystal elastomer containing azobenzene is described, and the expression of photo-induced strain perpendicular to the director direction of the liquid crystal material and the expression of photo-induced strain at any position in the thin film are obtained, comprising: the expression of photo-induced strain perpendicular to the director direction of the liquid crystal material is: ; wherein, is the photo-induced strain perpendicular to the director direction of the liquid crystal material, is the light compliance perpendicular to the director direction of the liquid crystal material, is the initial light intensity, is the content of azobenzene molecules, is the thickness of the thin film, is the coordinate perpendicular to the substrate interface, is the distance of light propagation when the light intensity decays by a unit under a unit azobenzene molecule content, is the angle of parallel light incident on the surface of the thin film, is a natural constant; and the expression of photo-induced strain at any position in the thin film perpendicular to the director direction of the liquid crystal material is: ; wherein, is the photo-induced strain at any position in the thin film perpendicular to the director direction of the liquid crystal material, is the light incidence angle, is the coordinate perpendicular to the substrate interface, is the buckling amplitude, is the buckling wave number, is the coordinate parallel to the substrate interface.

[0009] In a possible implementation, the simplification obtains an equivalent photo-induced strain expression, comprising:

[0010] The equivalent photo-induced strain expression is: ; wherein, is the equivalent photo-induced strain, does not change with the change of the part, , is a cosine function term part related to the thin film displacement, , .

[0011] In a possible implementation, an approximate expression of the elastic strain is obtained based on the superposition relation and the equivalent photo-induced strain expression according to the von Karman nonlinear plate theory, comprising: the superposition relation is: ; wherein, is the total strain, is the elastic strain, is the photo-induced strain at any position in the thin film; and the expression of the elastic strain is: ; wherein, is the film strain on the surface of the thin film, is the bending strain introduced by bending; and the approximate expression of the elastic strain is: .

[0012] In a possible implementation, the system average elastic energy is obtained based on the approximate expression of the elastic strain, comprising: the expression of the system average elastic energy is: ; wherein, is the system average elastic energy, is the average elastic strain energy density of the thin film, is the equivalent elastic modulus of the thin film, is the elastic energy in the substrate, is the equivalent elastic modulus of the substrate, , , .

[0013] In a possible implementation, the buckling wave number and the buckling amplitude of the thin film in the equilibrium state are determined based on the system average elastic energy according to the energy minimum principle, comprising: the buckling wave number of the thin film in the equilibrium state is : ; and the buckling amplitude of the thin film in the equilibrium state is : .

[0014] In one possible implementation, the step of changing the illumination conditions and plotting a phase diagram of the film buckling morphology based on the buckling wavenumber and buckling amplitude of the film in equilibrium includes: changing the illumination conditions by setting different illumination intensities and light incidence angles; when the dimensionless illumination intensity... The film buckles when the preset illumination conditions are met; the preset illumination conditions are: By plotting the curve of the system's average elastic energy versus geometric parameters under certain illumination conditions, the actual buckling amplitude and buckling wavenumber at this point are determined based on its minimum value; where the geometric parameter is the buckling wavenumber. and buckling amplitude The buckling morphology phase diagram reflects the buckling of the film under different illumination conditions.

[0015] Secondly, embodiments of this application provide a device for analyzing the buckling behavior of a light-driven thin-film substrate structure, comprising: a modeling module, used to establish a photo-induced strain model considering local illumination conditions based on material parameters, describing the propagation and absorption process of light in a thin film containing azobenzene liquid crystal elastomer, obtaining a photo-induced strain expression perpendicular to the direction of the liquid crystal material and a photo-induced strain expression at any position within the thin film, and simplifying it to obtain an equivalent photo-induced strain expression; wherein, the material parameters include the equivalent elastic modulus of the thin film, the equivalent elastic modulus of the substrate, the thin film thickness, and the distance propagated by light per unit decay of light intensity under unit azobenzene molecule content; The module adds an approximate expression for elastic strain based on the von Kármán nonlinear plate theory, superposition relationship, and equivalent photoinduced strain expression, and obtains the average elastic energy of the system based on the approximate expression for elastic strain. The module determines the buckling wavenumber and buckling amplitude of the film in equilibrium state based on the energy minimization principle and the average elastic energy of the system. The module analyzes the film buckling morphology phase diagram by changing the illumination conditions and based on the buckling wavenumber and buckling amplitude of the film in equilibrium state. It compares the effects of different material parameters on the critical illumination intensity and the film buckling morphology phase diagram to determine the influence of illumination conditions and material parameters on the buckling behavior of the film.

[0016] Thirdly, embodiments of this application provide a light-driven thin-film substrate structure buckling behavior analysis server, including a memory and a processor; the memory is used to store computer-executable instructions; the processor is used to execute the computer-executable instructions to implement the method described in the first aspect or any possible implementation of the first aspect.

[0017] Fourthly, embodiments of this application provide a computer-readable storage medium storing executable instructions, which, when executed by a computer, enable the method described in the first aspect or any possible implementation thereof.

[0018] The one or more technical solutions provided in the embodiments of the present application have at least the following technical effects: the embodiments of the present application provide a light-driven thin film substrate structure buckling behavior analysis method, a photo-induced strain model considering local light conditions is established based on material parameters, the propagation and absorption process of light in the thin film of the liquid crystal elastomer containing azobenzene is described, and an expression of photo-induced strain perpendicular to the director direction of the liquid crystal material is obtained. An accurate theoretical basis is provided for in-depth understanding of the light-illumination-deformation coupling mechanism of the light-driven material, the internal relationship between the photo-induced strain and the illumination condition can be accurately described, which helps to reveal the deformation mechanism of the light-driven thin film from the microscopic level. The photo-induced strain expression at any position in the thin film fully considers the influence of the inclination angle and the illumination angle of the thin film at each position, so that the model is more in line with the actual situation. The equivalent photo-induced strain expression obtained by simplification simplifies the calculation process under the premise of ensuring a certain accuracy, provides convenience for subsequent mechanical analysis, and ignores the spontaneous bending caused by the non-uniform distribution of photo-induced strain in the thickness, so that the model is more targeted and practical. According to the von Karman nonlinear plate theory, the approximate expression of the elastic strain is obtained based on the superposition relationship and the equivalent photo-induced strain expression, and the average elastic energy of the system is obtained based on the approximate expression of the elastic strain. This step completely builds the energy analysis framework of the system, and lays a solid foundation for studying the buckling behavior of the thin film from the energy angle. According to the energy minimum principle, the buckling wave number and the buckling amplitude of the thin film in the equilibrium state are determined based on the average elastic energy of the system, which can accurately predict the buckling shape characteristics of the thin film under the light driving. The key parameters are provided for the structure design and performance optimization of the light-driven thin film. By changing the illumination condition, the buckling morphology phase diagram of the thin film is drawn based on the buckling wave number and the buckling amplitude of the thin film in the equilibrium state, the influence of different material parameters on the critical illumination intensity and the buckling morphology phase diagram of the thin film is compared, so as to determine the influence of the illumination condition and the material parameter on the buckling behavior of the thin film. Theoretical guidance is provided for the selection and optimization of the material. The problem of how to realize the accurate analysis and effective control of the buckling behavior of the light-driven thin film substrate structure is solved, so that the thin film can stably and accurately produce the required morphology under the specific illumination condition and different material parameters, and the uncontrollable spontaneous movement caused by the light-illumination-deformation coupling phenomenon is avoided. BRIEF DESCRIPTION OF DRAWINGS

[0019] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the description of the embodiments of the present application or the prior art will be briefly introduced. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creating any inventive labor.

[0020] Figure 1 A flowchart of a light-driven thin film substrate structure buckling behavior analysis method provided in the embodiments of the present application;

[0021] Figure 2 A schematic diagram of a photo-induced strain model provided by an embodiment of the present application;

[0022] Figure 3 A schematic diagram of the average elastic energy of a system varying with geometric parameters in a thin film buckling morphology phase diagram provided by an embodiment of the present application;

[0023] Figure 4 A schematic diagram of the difference between the photo-induced strain before and after simplification and the difference between the energy of the system before and after simplification provided by an embodiment of the present application;

[0024] Figure 5 A schematic diagram of the finite element analysis result provided by an embodiment of the present application;

[0025] Figure 6 A schematic diagram of the influence of the coupling effect and the influence of the buckling behavior of a thin film without considering the coupling effect provided by an embodiment of the present application;

[0026] Figure 7 A schematic diagram of the buckling behavior of a thin film substrate structure under different illumination states provided by an embodiment of the present application;

[0027] Figure 8 A schematic diagram of the influence of the modulus ratio on the buckling behavior provided by an embodiment of the present application;

[0028] Figure 9 A schematic diagram of the influence of the change of the content of a photosensitive substance provided by an embodiment of the present application;

[0029] Figure 10 A schematic diagram of the influence of the change of the characteristic length ratio on the buckling behavior provided by an embodiment of the present application;

[0030] Figure 11 A schematic diagram of a device for analyzing the buckling behavior of a photo-driven thin film substrate structure provided by an embodiment of the present application;

[0031] Figure 12 A schematic diagram of a server for analyzing the buckling behavior of a photo-driven thin film substrate structure provided by an embodiment of the present application. DETAILED DESCRIPTION

[0032] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative labor fall within the protection scope of the present application.

[0033] The following description of the technology relates to the embodiments of the present application and is intended to assist in understanding the same. It should be understood that these are merely exemplary. Therefore, those of ordinary skill in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the present application. Also, for the sake of clarity and conciseness, the following description omits the description of some well-known functions and structures.

[0034] The embodiments of the present application provide a buckling behavior analysis method for a light-driven thin film substrate structure, as shown in the following. Figure 1 The embodiments of the present application provide a buckling behavior analysis method for a light-driven thin film substrate structure, as shown in the following. Figure 1 The embodiments of the present application provide a buckling behavior analysis method for a light-driven thin film substrate structure, as shown in the following. Figure 1 The embodiments of the present application provide a buckling behavior analysis method for a light-driven thin film substrate structure, as shown in the following.

[0035] S101: A photo-induced strain model considering local light conditions is established based on material parameters, the propagation and absorption process of light in the thin film containing azobenzene liquid crystal elastomer is described, and the photo-induced strain expression perpendicular to the director direction of the liquid crystal material and the photo-induced strain expression at any position in the thin film are obtained, and the equivalent photo-induced strain expression is simplified. The material parameters include the equivalent elastic modulus of the thin film, the equivalent elastic modulus of the substrate, the thickness of the thin film, and the distance of light propagation when the light intensity decays by one unit under the unit azobenzene molecule content.

[0036] Figure 2 A schematic diagram of the photo-induced strain model provided by the embodiments of the present application. The structure is composed of a light-responsive liquid crystal thin film, i.e. a thin film containing azobenzene liquid crystal elastomer and a substrate. When ultraviolet light irradiates the surface of the light-responsive liquid crystal thin film, the chromophore in the liquid crystal material will absorb ultraviolet light energy and undergo photo-induced cis-trans isomerization. Specifically, the chromophore changes from the original trans structure to the curved cis structure. This structural change significantly changes the order of the liquid crystal system, which in turn causes the thin film to spontaneously expand in the direction perpendicular to the director direction of the liquid crystal material. Due to the restraining effect of the substrate on the thin film, the thin film will be restricted when it spontaneously expands, thereby generating in-plane stress in the thin film. When the stress in the film accumulates to a certain level, the thin film surface will release the stress through a destabilization process to maintain the stability of the structure. As the surface topography of the thin film changes due to the destabilization, the light incident angle of the light received by each part of the thin film surface will also change. Due to the difference in light incident angle, the propagation and absorption of light in the thin film will also be different, ultimately resulting in a non-uniform distribution of photo-induced strain in the length direction of the thin film. The present application uses a specific coordinate system to describe the thin film substrate structure, with the origin of the coordinate system set at the interface between the thin film and the substrate. Among them, the thin film in the coordinate system parallel to the substrate interface is denoted as x, the thin film in the coordinate system perpendicular to the substrate interface is denoted as y, and the substrate in the coordinate system perpendicular to the substrate interface is denoted as z. direction perpendicular to the director of the liquid crystal material, the film is in the coordinate parallel to the director of the liquid crystal material direction parallel to the director of the liquid crystal material, the film is in the coordinate perpendicular to the interface of the substrate direction perpendicular to the interface and pointing to the film. Let the thickness of the film be , the substrate is an elastic substrate with infinite thickness. It is assumed that both the film and the substrate are isotropic linear elastic materials, and the equivalent elastic modulus of the film is set as , the equivalent elastic modulus of the substrate is , the Poisson's ratio of the film is , the Poisson's ratio of the substrate is In this application, the substrate conforms to the Winkler substrate model, and perfect bonding is achieved between the substrate and the film, while the shear force on the bonding surface of the two is ignored. Figure 2 UV-light is ultraviolet light, Visible Light is visible light. Cis is cis structure, the chromophore presents a bent shape, Trans is trans structure, the chromophore presents a rod shape. Liquid-crystal Film is a liquid crystal elastomer film, Substrate is a substrate. k is the bending wave number, is the bending amplitude.

[0037] Based on the material parameters, a photo-induced strain model considering local illumination conditions is established to describe the propagation and absorption process of light in the liquid crystal elastomer film containing azobenzene, and the photo-induced strain expression perpendicular to the director direction of the liquid crystal material is obtained, including the following contents.

[0038] According to the energy absorption law of light propagation in the liquid crystal elastomer film containing azobenzene, the light absorption equation is established, and the light intensity expression is obtained. Wherein, is the light intensity, is the content of azobenzene molecules, is the distance of light propagation when the light intensity decays by one unit per unit content of azobenzene molecules, is the distance of light traveling in the film, is the initial light intensity, is the light intensity after traveling a distance of in the liquid crystal elastomer film containing azobenzene, is a natural constant.

[0039] Specifically, in the actual illumination condition, the parallel light will be incident at a certain angle with the surface of the film.

[0040] Considering the parallel light incident at an angle of with the surface of the film, geometric analysis is carried out according to the propagation path of the incident light and the geometric structure of the film, and the distance of light traveling in the film is obtained with the film thickness and the coordinate perpendicular to the substrate interface The expression of the relationship is: .

[0041] Substitute the expression of the relationship into the light intensity expression to obtain the photo-induced strain expression perpendicular to the director direction of the liquid crystal material: . Wherein, is the photo-induced strain perpendicular to the director direction of the liquid crystal material, is the optical compliance perpendicular to the director direction of the liquid crystal material.

[0042] Based on the film displacement field assumption, by obtaining the tilt angle of each part of the film and the illumination angle, the photo-induced strain expression perpendicular to the director direction of the liquid crystal material is extended to obtain the photo-induced strain expression at any position in the film, including the following contents.

[0043] The film displacement field assumption is: , . Wherein, is the displacement of the film in the coordinate direction perpendicular to the substrate interface, is the displacement of the film in the coordinate direction parallel to the substrate interface, is the amplitude of buckling, is the wave number of buckling.

[0044] The photo-induced strain expression at any position in the film perpendicular to the director direction of the liquid crystal material is: . Wherein, is the photo-induced strain at any position in the film perpendicular to the director direction of the liquid crystal material, is the light incidence angle. The light incidence angle is the angle between the ultraviolet light and the horizontal plane.

[0045] Based on the case of perpendicular incidence of ultraviolet light, the photo-induced strain expression at any position in the film is simplified, and the spontaneous bending caused by the uneven distribution of photo-induced strain in the thickness is ignored, to obtain the equivalent photo-induced strain expression, including the following contents.

[0046] Based on the case of perpendicular incidence of ultraviolet light, let , the expression obtained by simplifying the photo-induced strain expression at any position in the film is: . Wherein, , is the dimensionless thickness direction coordinate, and the coordinate origin is on the interface between the film and the substrate. is a simple symbol proposed for the sake of concise formula, and has no actual meaning.

[0047] The specific solving process of the expression obtained by simplifying the photo-induced strain expression at any position in the film perpendicular to the director direction of the liquid crystal material is as follows.

[0048] .

[0049] . wherein, is the dimensionless light intensity.

[0050] Specifically, indicates that the ultraviolet light is incident on the film surface perpendicular to the horizontal plane.

[0051] Further, since the film thickness is small, it is assumed that the photo-induced strain does not change much in the film thickness direction, and therefore the spontaneous bending caused by the non-uniform distribution of the photo-induced strain in the thickness direction can be ignored. Based on this assumption, the equivalent photo-induced strain expression is obtained by integrating the expression obtained by simplifying the photo-induced strain expression at any position in the film.

[0052] The equivalent photo-induced strain expression is: . wherein, is the equivalent photo-induced strain, is the film thickness, is the part that does not change with , , is the cosine function term part related to the displacement of the film, , . has no specific physical meaning.

[0053] S102: According to the von Karman nonlinear plate theory, an approximate expression of the elastic strain is obtained based on the superposition relationship and the equivalent photo-induced strain expression, and the system average elastic energy is obtained based on the approximate expression of the elastic strain.

[0054] Specifically, in the film mechanics analysis, the stress state of any point in the film can be obtained by superimposing the stress state on the film surface and the bending stress caused by the bending of each point on the cross section of the film.

[0055] According to the von Karman nonlinear plate theory, the membrane strain expression on the film surface and the bending strain expression introduced by bending are obtained, the total strain is obtained by superimposing the elastic strain and the photo-induced strain, the superposition relationship is formed, the expression of the elastic strain is obtained based on the superposition relationship, the membrane strain, the bending strain and the equivalent photo-induced strain are substituted into the expression of the elastic strain to obtain the approximate expression of the elastic strain, which includes the following contents.

[0056] The membrane strain expression on the film surface is: . wherein, is the membrane strain, is the initial strain, is the partial derivative.

[0057] The expression of the bending strain induced by bending is: where, is the bending strain. Where, , is a simple notation introduced for the sake of simplicity of the formulas, and has no physical meaning.

[0058] The superposition relation is: where, is the total strain, is the elastic strain, is the photo-induced strain at any position in the film.

[0059] The expression of the elastic strain is: .

[0060] Specifically, the expression of the elastic strain is derived from the superposition relation.

[0061] The approximate expression of the elastic strain is: .

[0062] The average elastic strain energy density is calculated by integrating the elastic strain energy density over the film area corresponding to one wavelength and then averaging. The elastic energy in the substrate is also calculated. The average elastic energy in the system is obtained by adding the average elastic strain energy density and the elastic energy in the substrate, including the following content.

[0063] The expression of the elastic strain energy density at any point in the film is: .

[0064] The expression of the elastic strain energy density is: where, is the elastic strain energy density, is the equivalent elastic modulus of the film.

[0065] Specifically, the expression of the elastic strain energy density is obtained by substituting the approximate expression of the elastic strain into the expression of the elastic strain energy density at any point in the film.

[0066] The expression of the average elastic strain energy density of the film is: where, is the average elastic strain energy density of the film, is the buckling wavelength of the film.

[0067] The expression of the elastic energy in the substrate is: where, is the elastic energy in the substrate, is the equivalent elastic modulus of the substrate.

[0068] The expression of the system average elastic energy is: wherein, is the system average elastic energy, is the average elastic strain energy density of the film, is the equivalent elastic modulus of the film, is the elastic energy in the substrate, is the equivalent elastic modulus of the substrate, , , , is the equivalent elastic modulus of the film. , , all have no specific physical meaning.

[0069] S103: According to the energy minimum principle, the buckling wave number and the buckling amplitude of the film in the equilibrium state are determined based on the system average elastic energy.

[0070] According to the energy minimum principle, the buckling amplitude and the buckling wave number are derived based on the system average elastic energy, and the partial derivatives are set to zero to obtain a system of equations, and by solving the system of equations, the buckling wave number and the buckling amplitude of the film in the equilibrium state are determined, including the following contents.

[0071] The expression of the system average elastic energy derivative with respect to the buckling amplitude is: .

[0072] The expression of the system average elastic energy derivative with respect to the buckling wave number is: .

[0073] Let and , the system of equations is obtained: , .

[0074] Given , according to the properties of cubic polynomials, when the preset condition is met, the system of equations has a non-zero real solution, and there is an equilibrium position .

[0075] Solving the system of equations, the buckling wave number of the film in the equilibrium state is determined as: .

[0076] Specifically, the buckling wave number of the film is related to the thickness of the film and the equivalent elastic modulus of the film and the equivalent elastic modulus of the substrate.

[0077] Determination of buckling amplitude of thin film in equilibrium state For: .

[0078] Specifically, the buckling amplitude of thin film There are two non-zero real number solutions of 0 and positive and negative.

[0079] Substitute the buckling wave number into the preset condition to obtain The condition for non-zero real number solution is: Wherein, , .

[0080] Specifically, only when , , The condition for non-zero real number solution is established, thereby ensuring that the thin film has a non-zero amplitude equilibrium state.

[0081] S104: Change the light condition, draw the buckling morphology phase diagram of the thin film based on the buckling wave number and buckling amplitude of the thin film in the equilibrium state, and compare the influence of different material parameters on the critical light intensity and the buckling morphology phase diagram of the thin film to determine the influence of light conditions and material parameters on the buckling behavior of the thin film.

[0082] By changing the light condition, the buckling morphology phase diagram of the thin film is drawn based on the buckling wave number and buckling amplitude of the thin film in the equilibrium state, including the following contents.

[0083] By setting different light intensities and light incident angles, the light condition is changed.

[0084] When the dimensionless light intensity satisfies the preset light condition, the thin film buckles.

[0085] The preset light condition is: .

[0086] Specifically, the satisfaction of the dimensionless light intensity by the preset light condition ensures that the light intensity is within the range that can effectively induce the buckling of the thin film.

[0087] By drawing the curve of the average elastic energy of the system with the change of the geometric parameters under certain light conditions, the actual buckling amplitude and buckling wave number at this time are determined according to the minimum value. Wherein, the geometric parameters are buckling wave number and buckling amplitude .

[0088] The buckling morphology phase diagram reflects the buckling of the thin film under different light conditions.

[0089] Specifically, the average elastic energy of the system is the key factor to determine the surface morphology of the thin film substrate structure. In order to study the influence of the light condition, the modulus ratio is set to 1500, the mass fraction of the photosensitive component of the thin film is set to 8%, and the ratio of the thickness of the thin film to the characteristic length is set to 0.5.

[0090] Figure 3 The schematic diagram of the variation of the average elastic energy of the system with the geometric parameters in the buckling morphology phase diagram of the thin film provided in the embodiments of the present application is shown. The geometric parameters are the buckling wave number and the buckling amplitude . According to the energy minimum principle, the buckling amplitude and the buckling wave number corresponding to the minimum value of the curve in the buckling morphology phase diagram of the thin film are the actual buckling amplitude and the buckling wave number. Figure 3 The buckling amplitude in (a) of Figure 3 and (c) of is the dimensionless buckling amplitude . Figure 3 (a) of (a) of FIG. 6 shows the variation of the average elastic energy of the system with the buckling amplitude when the ultraviolet light of different intensities is vertically incident. When the dimensionless light intensity is 0.05, the energy minimum point of the system is located at 0, and the thin film does not buckle. With the increase of the dimensionless light intensity, the minimum point moves to the right, indicating that the buckling amplitude increases with the increase of the dimensionless light intensity. Figure 3 (b) of FIG. 6 shows the variation of the average elastic energy of the system with the buckling wave number when the ultraviolet light of different intensities is vertically incident. The energy curves under different light intensities have obvious numerical differences. The greater the dimensionless light intensity, the higher the total energy of the system under the same buckling wave number, but the buckling wave number corresponding to the energy minimum value does not change significantly, indicating that changing the light intensity has no significant effect on the buckling wave number. Figure 3 (c) of FIG. 6 shows the influence of the change of the light incidence angle on the buckling amplitude. Figure 3 (d) of FIG. 6 shows the influence of the change of the light incidence angle on the buckling wave number. Within a certain range, changing the light incidence angle does not change the energy of the system significantly, so it will not cause significant changes in the buckling amplitude and the wave number. The energy of the system in the present application is the average elastic energy of the system. It should be noted that Figure 3 in (a) of FIG. 6 is the dimensionless buckling wave number , is the dimensionless buckling amplitude.

[0091] Figure 4 The schematic diagram of the difference between the photo-induced strain before and after the simplification and the difference between the energy of the system before and after the simplification provided in the embodiments of the present application is shown. Figure 4 The contour line drawn by the thick dashed line in (a) of FIG. 7 is before the simplification, and the colored area and the thin contour line are after the simplification. Figure 4 in (b) of FIG. 7 For dimensionless buckling wavenumber , . Figure 4 (a) shows the equivalent photostrain calculated over one fold period using the simplified photostrain model and the unsimplified photostrain model. Distribution. In Figure 4 (b) shows the average elastic properties of the system before and after the simplification of photo-induced strain. The situation varies with the geometric parameters of the morphology. According to... Figure 4 It can be seen that the minimum average elastic energy of the simplified system and its corresponding morphological geometric parameters are not significantly different from those before simplification. This indicates that the simplified equivalent photo-induced strain in this application has high accuracy, meaning that this simplification will not have a significant impact on the analysis results of the film buckling morphology.

[0092] Figure 5 This is a schematic diagram of the finite element analysis results provided in an embodiment of this application. The research object of this application conforms to the plane strain assumption, and a two-dimensional analysis model is established using the commercial finite element analysis software ABAQUS, as shown below. Figure 5 (a) shows the established two-dimensional analysis model. The film thickness was set to 1 mm, and the substrate thickness to 60 mm; the Young's moduli of the film and the substrate were 1365 MPa and 0.8 MPa, respectively, and their Poisson's ratios were 0.3 and 0.45, respectively. After mesh convergence analysis, 200 B21 beam elements were used to simulate the film, and 3597 CPS4R planar shell elements were used to simulate the substrate. The film and the substrate were connected by Tie constraints. The finite element analysis model served as the representative element of the actual research object. Symmetrical boundary conditions were applied on both sides to simulate the influence of the unmodeled parts, and longitudinal displacement constraints were applied to the lower surface of the substrate to eliminate the rigid body free motion in this direction. Since ABAQUS does not have a preset photo-induced strain loading method, thermal expansion loading was used instead. To realize that the load changes with the morphology, the thermal expansion of each incremental step was handled independently in the simulation using an ABAQUS user subroutine. The specific process is as follows: At the end of the previous iteration step, the URDFIL subroutine is called to extract the displacement of each node of the thin film and output it to an external file; before the start of the next iteration step, the USDFLD subroutine is called to read the external file storing displacement information, calculate the incident angle of illumination and the corresponding photoinduced strain of each element, and transfer the strain increment value to the UEXPAN subroutine through the independent variable SDV to update the thermal expansion load. To induce thin film buckling in the finite element analysis, geometric defects need to be introduced. Using the Buckling analysis step, the first few buckling modes of the structure are calculated while retaining the boundary conditions and without applying temperature loads, and these modes are appropriately scaled down and introduced into the calculation model as initial geometric defects. Based on the above method, finite element analysis is carried out on the thin film substrate structure considering the illumination-morphology coupling effect using the static general analysis step. Figure 5(b) in FIG. 4 shows When the model converges to a steady state, the distribution of photo-induced strain in the film is shown in (b) in FIG. 4. The results show that when the UV light is not perpendicular to the horizontal plane, the distribution of photo-induced strain in the film is related to the local tilt angle, and the intensity of photo-induced strain increases as the angle between the local normal and the incident light decreases, which is consistent with the theoretical model established. Figure 5 (c) in FIG. 4 shows When the model converges to a steady state, the distribution of photo-induced strain in the film is shown in (b) in FIG. 4. The results show that when the UV light is not perpendicular to the horizontal plane, the distribution of photo-induced strain in the film is related to the local tilt angle, and the intensity of photo-induced strain increases as the angle between the local normal and the incident light decreases, which is consistent with the theoretical model established.

[0093] Without considering the light-morphology coupling effect, the photo-induced strain can be treated as a uniaxial compression load: wherein is the equivalent uniaxial compression load generated by the photo-induced strain, is the Poisson's ratio of the film. At the same time, there is a relationship between the dimensionless buckling amplitude and the load size: wherein is the critical load, , is the dimensionless buckling amplitude.

[0094] Figure 6 is the schematic diagram provided by the embodiment of the present application considering the influence of the coupling effect and the influence of the film buckling behavior without considering the coupling effect. Compared with considering the coupling, when the coupling is not considered, the film buckling amplitude increases faster with the increase of the light intensity. This is because when the film buckles, the local light angle of the film surface except for individual points is less than 90 degrees, and the average photo-induced strain generated is small, so the amplitude grows slowly. The simulation results of the finite element also prove this point. In addition, when the coupling is considered, the critical buckling light intensity of the light-driven film substrate structure is slightly lower than when the coupling is not considered. This may be because the non-uniform photo-induced strain causes the film to produce uneven spontaneous bending in the length direction, which makes the film produce out-of-plane displacement earlier, and then triggers surface instability. Figure 6Uncoupled means the case without considering the coupling effect. Coupled means the case considering the coupling effect. FEA means the result of Finite Element Analysis. Flat is the flat state of the thin film without buckling. At this time, the light irradiates uniformly on the surface of the thin film, and the distribution of the photo-induced strain is relatively regular. Wrinkled is the wrinkled state of the thin film after buckling. Due to the change of the surface morphology of the thin film, the local light irradiation angle changes, resulting in the uneven distribution of the photo-induced strain.

[0095] According to the theoretical analysis, the buckling behavior of the thin film is closely related to the photo-induced strain, and there is a critical photo-induced strain value. When the photo-induced strain is less than the critical value by adjusting the light intensity or the light irradiation angle, the surface of the thin film remains flat; once the photo-induced strain exceeds the critical value, the thin film will buckle. When the light incidence angle is too large or too small, the buckling morphology may cause local light shielding, causing the light irradiation state of some areas to change suddenly, thereby triggering spontaneous sustained motion. However, the present application can predict the critical light irradiation condition, i.e. the critical light irradiation angle, for triggering spontaneous sustained motion based on the static buckling morphology. The condition for spontaneous motion to occur is that the buckled thin film shields the local light irradiation, i.e. the light incidence angle is less than the maximum value of the local inclination angle θ of the thin film, and according to the displacement expression of the thin film, the maximum value of the local inclination angle θ of the thin film can be obtained as . , When , the right end of the inequality has a maximum value of . Wherein, n is an integer, is an integer set, that is n takes an integer multiple of . If the effect of the light irradiation angle on the buckling amplitude is ignored, the buckling amplitude under the condition of vertical incidence is used instead of the real buckling amplitude, and substituted into , , the critical light irradiation condition formula for generating spontaneous motion is obtained as .

[0096] Figure 7 ​A schematic diagram of buckling behavior of the film-substrate structure under different illumination conditions is provided in the embodiments of the present application. Each point in the diagram corresponds to an illumination condition, wherein the blue region represents a state in which the film does not wrinkle, and the orange region represents a state in which the film wrinkles. The green curve is a demarcation line between the two states, i.e., the critical illumination condition, and each point on the curve corresponds to a film photo-induced strain equal to the critical photo-induced strain. As can be seen from the diagram, when the global illumination angle changes near the vertical direction, the illumination intensity corresponding to the critical condition does not change significantly, which is consistent with the energy curve analysis result. When the illumination angle exceeds a certain range and local light blocking occurs, the film enters a spontaneous motion state, i.e., the oblique line region in the diagram. In addition, the demarcation line between the wrinkled state and the spontaneous motion state in the diagram gradually extends with the increase of the light intensity, because with the increase of the illumination intensity, the buckling amplitude increases, while the buckling wavelength changes little, resulting in the increase of the maximum inclination angle of the film with the increase of the illumination intensity, and further resulting in the increase of the critical illumination angle entering the spontaneous motion. Figure 7 Spontaneous Motion in the diagram refers to spontaneous motion.

[0097] Since the response of the light-driven film-substrate structure to illumination is closely related to material parameters, the present application focuses on discussing the influence of different material parameters on the buckling behavior. For convenience of discussion, some material parameters are dimensionless processed, and the modulus ratio and the characteristic length ratio are defined.

[0098] Figure 8 A schematic diagram of the influence of the modulus ratio on the buckling behavior is provided in the embodiments of the present application. Under the condition of vertical incidence, Figure 8 (a) in the diagram presents the trend of the dimensionless critical buckling light intensity and the dimensionless buckling wavelength with the change of the film-substrate elastic modulus ratio. Figure 8 in (a) in the diagram is the dimensionless illumination intensity of the critical buckling state. With the increase of the modulus ratio, the dimensionless buckling critical light intensity gradually decreases. From the buckling mechanism, when the modulus ratio increases, the stiffness of the film increases. Compared with bending deformation, in-plane deformation makes the structure in a higher elastic potential state, so the structure is more likely to buckle, i.e., the critical buckling stress decreases with the increase of the modulus ratio. Since the photo-induced deformation can be equivalent to applying a pre-strain to the film, and the size of the photo-induced strain is linearly related to the light intensity, the light intensity corresponding to the critical buckling, i.e., the dimensionless illumination intensity, is negatively related to the modulus ratio. The dimensionless buckling wavelength significantly increases with the increase of the modulus ratio, which is consistent with the general characteristics of the buckling behavior of the film-substrate structure. Figure 8(b) in FIG. 6 shows the phase diagram of buckling state of the film-substrate structure as a function of illumination state at different modulus ratio of the film-substrate. As mentioned before, the dimensionless illumination intensity state of the film-substrate structure will change significantly when the modulus ratio increases. The boundary between the spontaneous motion and the static buckling will move with the change of the modulus ratio. This phenomenon has two reasons: one is that the buckling amplitude increases, leading to the increase of the local inclination angle maximum at the same illumination state; the other is that the buckling wavelength increases with the increase of the modulus ratio, which makes the local inclination angle decrease. These two factors have opposite effects on the local inclination angle of the buckling morphology. Considering the effects of the two aspects, according to the critical illumination condition formula of the spontaneous motion, the local inclination angle maximum will increase with the increase of the modulus ratio, and then the boundary between the two buckling states will move upwards.

[0099] In the background of the influence of material parameters on the buckling behavior of the light-driven film-substrate structure, the present application further analyzes the influence of the change of the content of the photosensitive substance. Figure 9 The schematic diagram of the influence of the change of the content of the photosensitive substance provided for the embodiments of the present application. Figure 9 (a) in FIG. 6 presents the dimensionless illumination intensity as a function of the modulus ratio of the film-substrate under the condition of normal incidence. With the increase of the azobenzene mass fraction, the dimensionless illumination intensity shows a downward trend. This is because when the film is irradiated by ultraviolet light, the number of azobenzene molecules undergoing cis-trans isomerization in the film increases, and the disturbance to the order degree of the original liquid crystal system is more intense, which macroscopically shows that a larger photo-induced strain is generated. Therefore, under the condition of smaller light intensity, the film can reach the critical strain condition to cause buckling. Figure 9 (b) in FIG. 6 shows the phase diagram of buckling state of the film-substrate structure as a function of illumination state at different modulus ratio of the film-substrate. As mentioned before, the dimensionless illumination intensity state of the film-substrate structure will change significantly when the modulus ratio increases. The boundary between the spontaneous motion and the static buckling will move with the change of the modulus ratio. This phenomenon has two reasons: one is that the buckling amplitude increases, leading to the increase of the local inclination angle maximum at the same illumination state; the other is that the buckling wavelength increases with the increase of the modulus ratio, which makes the local inclination angle decrease. These two factors have opposite effects on the local inclination angle of the buckling morphology. Considering the effects of the two aspects, according to the critical illumination condition formula of the spontaneous motion, the local inclination angle maximum will increase with the increase of the modulus ratio, and then the boundary between the two buckling states will move upwards.

[0100] Figure 10 The schematic diagram of the influence of the change of the characteristic length ratio on the buckling behavior provided for the embodiments of the present application. Figure 10(a) in FIG. 6 shows the variation of the dimensionless critical buckling light intensity with the characteristic length ratio under normal incidence. It can be found that the dimensionless critical buckling light intensity increases with the increase of the characteristic length ratio. This is because when the characteristic length ratio increases, the thickness of the film increases significantly compared with the light attenuation distance, and the UV light quickly attenuates at the surface layer of the film, and the bottom does not receive sufficient light. The overall generated photo-induced strain is small, so the critical light intensity value is correspondingly increased, and under the same light condition, the buckling peak is lower. Figure 10 (b) in FIG. 6 shows the phase diagram of the buckling state of the film-based structure under different characteristic length ratios. It can be seen that after increasing the characteristic length ratio, the dividing line between the buckling and non-buckling states of the film is more obviously curved, indicating that the light angle has an increasingly significant effect on the buckling behavior of the film. In addition, the dividing line between the buckling state and the spontaneous motion state also significantly moves down with the increase of the characteristic length ratio. It can be found that when the characteristic length ratio of the film is larger, the light-induced strain changes more greatly when the light angle changes by the same size. This is because when the light is obliquely incident, the light travels a longer distance in the film, and its attenuation process is more significantly affected by the material parameters. This also leads to the fact that when the film with a larger characteristic length ratio is irradiated at a small angle, the buckling amplitude under the same light condition is significantly reduced, and the local inclination angle of the film is also reduced. Therefore, a smaller light angle or an increased light intensity is required to meet the conditions for causing spontaneous motion. At the same time, since the buckling behavior of the film is greatly affected by the light angle, the critical light conditions for generating spontaneous motion no longer meet the assumptions of the formula derivation, and exceed the applicable range of the simplified model.

[0101] The embodiment of the present application further provides a device 1100 for analyzing the buckling behavior of a light-driven film-based structure, as shown in FIG. 11, the device comprises: a establishing module 1101, a superposition module 1102, a determining module 1103 and an analyzing module 1104. Figure 11

[0102] The establishing module 1101 is configured to establish a photo-induced strain model considering local light conditions based on material parameters, describe the propagation and absorption process of light in the thin film containing azobenzene liquid crystal elastomer, obtain the photo-induced strain expression perpendicular to the director direction of the liquid crystal material and the photo-induced strain expression at any position in the thin film, and simplify to obtain an equivalent photo-induced strain expression. The material parameters include the equivalent elastic modulus of the film, the equivalent elastic modulus of the substrate, the thickness of the film and the distance of light propagation when the light intensity decays by one unit under the unit azobenzene molecule content.

[0103] The superposition module 1102 is configured to obtain an approximate expression of the elastic strain based on the superposition relationship and the equivalent photo-induced strain expression according to the von Karman nonlinear plate theory, and obtain the average elastic energy of the system based on the approximate expression of the elastic strain.

[0104] ​The determining module 1103 is configured to determine the buckling wave number and the buckling amplitude of the film in the equilibrium state based on the average elastic energy of the system according to the energy minimum principle.

[0105] The analyzing module 1104 is configured to change the illumination condition, draw a buckling morphology phase diagram of the film based on the buckling wave number and the buckling amplitude of the film in the equilibrium state, and compare the influence of different material parameters on the critical illumination intensity and the buckling morphology phase diagram of the film, so as to determine the influence of the illumination condition and the material parameters on the buckling behavior of the film.

[0106] Some of the modules in the apparatus described in the present application can be described in the general context of computer-executable instructions, such as program modules, which are executed by computers. Generally, program modules include routines, programs, objects, components, data structures, classes, and the like, which perform particular tasks or implement particular abstract data types. The present application can also be practiced in distributed computing environments where tasks are performed by remote processing devices that are connected through a communication network. In a distributed computing environment, program modules can be located in both local and remote computer storage media including memory storage devices.

[0107] The apparatus or modules described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions. For the convenience of description, the above apparatus is described as various modules with functions. In the implementation of the embodiments of the present application, the functions of the modules can be implemented in the same or multiple software and / or hardware. Of course, the modules implementing certain functions can also be implemented by multiple sub-modules or sub-units.

[0108] The method, device or module described in the present application can be implemented in a computer readable program code. The controller can be implemented in any appropriate manner, for example, the controller can take the form of a microprocessor or processor and a computer readable medium storing computer readable program code (for example, software or firmware) executable by the (micro)processor, logic gates, switches, application specific integrated circuits (ASIC), programmable logic controllers and embedded microcontrollers. Examples of the controller include, but are not limited to, the following microcontrollers: ARC 625D, Atmel AT91SAM, Microchip PIC18F26K20 and Silicone Labs C8051F320. The memory controller can also be implemented as part of the control logic of the memory. Those skilled in the art also know that, in addition to implementing the controller in a pure computer readable program code manner, the same function can also be achieved by logically programming the method steps in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers and embedded microcontrollers. Therefore, such a controller can be considered as a hardware component, and the means included therein for implementing various functions can also be considered as structures within the hardware component. Alternatively, the means for implementing various functions can even be considered as both a software module implementing the method and a structure within the hardware component.

[0109] As shown in Figure 12 The embodiment of the present application also provides a light-driven thin film substrate structure buckling behavior analysis server, including a memory 1201 and a processor 1202; the memory 1201 is used for storing computer executable instructions; the processor 1202 is used for executing the computer executable instructions to realize the light-driven thin film substrate structure buckling behavior analysis method provided in the above embodiment of the present application.

[0110] The embodiment of the present application also provides a computer readable storage medium, the computer readable storage medium stores executable instructions, and the computer executes the executable instructions to realize the light-driven thin film substrate structure buckling behavior analysis method provided in the above embodiment of the present application.

[0111] From the description of the above embodiments, those skilled in the art can clearly understand that the present application can be implemented by means of software plus necessary hardware. Based on such an understanding, the technical solutions of the present application can be embodied in the form of a software product or can be embodied in the implementation process of data migration. The computer software product can be stored in a storage medium, such as a ROM / RAM, a magnetic disk, an optical disk, and the like, and includes a plurality of instructions for causing a computer device (which can be a personal computer, a mobile terminal, a server, or a network device, etc.) to execute the methods described in the embodiments of the present application.

[0112] The various embodiments in the specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on the difference from other embodiments. The whole or part of the present application can be used in a plurality of general or special computer system environments or configurations.

[0113] The above embodiments are only used to illustrate the technical solutions of the present application, and not to limit the present application; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacements for some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the present application.

Claims

1. A method for analyzing the buckling behavior of a light-driven thin film substrate structure, characterized by, The method comprises the following steps: A photo-induced strain model considering local light conditions is established based on material parameters, a propagation and absorption process of light in a thin film of liquid crystal elastomer containing azobenzene is described, an expression of photo-induced strain perpendicular to a director direction of the liquid crystal material and an expression of photo-induced strain at any position in the thin film are obtained, and an equivalent photo-induced strain expression is obtained by simplification; wherein the material parameters include an equivalent elastic modulus of the thin film, an equivalent elastic modulus of the substrate, a thickness of the thin film, and a distance of light propagation when a unit attenuation of light intensity occurs under a unit azobenzene molecule content; According to the von Karman nonlinear plate theory, an approximate expression of elastic strain is obtained based on the superposition relationship and the equivalent photo-induced strain expression, and the average elastic performance of the system is obtained based on the approximate expression of the elastic strain; According to the energy minimum principle, the buckling wave number and the buckling amplitude of the thin film in the equilibrium state are determined based on the average elastic performance of the system; The light conditions are changed, and the buckling morphology phase diagram of the thin film is drawn based on the buckling wave number and the buckling amplitude of the thin film in the equilibrium state, and the effects of the light conditions and the material parameters on the buckling behavior of the thin film are determined by comparing the effects of different material parameters on the critical light intensity and the buckling morphology phase diagram of the thin film; The photo-induced strain model considering local illumination conditions is established based on material parameters, describes the propagation and absorption process of light in the thin film of liquid crystal elastomer containing azobenzene, and obtains the photo-induced strain expression perpendicular to the director direction of the liquid crystal material and the photo-induced strain expression at any position in the thin film, including: the photo-induced strain expression perpendicular to the director direction of the liquid crystal material is: ; wherein, is the photo-induced strain perpendicular to the director direction of the liquid crystal material, is the light compliance perpendicular to the director direction of the liquid crystal material, is the initial light intensity, is the content of azobenzene molecules, is the thickness of the thin film, is the coordinate perpendicular to the substrate interface, is the distance of light propagation when the unit attenuation of light intensity occurs under the unit content of azobenzene molecules, is the angle of parallel light incident on the surface of the thin film, is a natural constant; the photo-induced strain expression at any position in the thin film perpendicular to the director direction of the liquid crystal material is: ; wherein, is the photo-induced strain at any position in the thin film perpendicular to the director direction of the liquid crystal material, is the light incidence angle, is the coordinate perpendicular to the substrate interface, is the amplitude of buckling, is the buckling wave number, is the coordinate parallel to the substrate interface.

2. The method of claim 1, wherein the method further comprises: The equivalent photo-induced strain expression obtained by simplification comprises: The equivalent photo-induced strain expression is: ; wherein, is the equivalent photo-induced strain, is a part that does not change with the change of , , is a cosine function term part related to the displacement of the thin film, , .

3. The method of claim 2, wherein the method further comprises: According to the von Karman nonlinear plate theory, an approximate expression of elastic strain is obtained based on the superposition relationship and the equivalent photo-induced strain expression, and the average elastic performance of the system is obtained based on the approximate expression of the elastic strain; The superposition relation is: ; wherein, is the total strain, is the elastic strain, is the photo-induced strain at any position within the thin film; The expression for the elastic strain is: ; where, is the film strain in the plane of the film, is the bending strain introduced by the bending; An approximate expression for the elastic strain is: .

4. The method of claim 3, wherein the method further comprises: The average elastic performance of the system is obtained based on the approximate expression of the elastic strain, and the average elastic performance of the system is obtained based on the approximate expression of the elastic strain. The expression for the average elastic energy of the system is: ; where is the average elastic energy of the system, is the average elastic strain energy density of the film, is the equivalent elastic modulus of the film, is the elastic energy in the substrate, is the equivalent elastic modulus of the substrate, , , .

5. The method of claim 4, wherein the method further comprises: The buckling wave number and the buckling amplitude of the thin film in the equilibrium state are determined based on the energy minimum principle, and the buckling wave number and the buckling amplitude of the thin film in the equilibrium state are determined based on the energy minimum principle. Buckling wave number of thin film in equilibrium state To: ; Determining buckling amplitude of a thin film in equilibrium To: .

6. The method of claim 5, wherein the method further comprises: The light conditions are changed, and the buckling morphology phase diagram of the thin film is drawn based on the buckling wave number and the buckling amplitude of the thin film in the equilibrium state, and the effects of the light conditions and the material parameters on the buckling behavior of the thin film are determined by comparing the effects of different material parameters on the critical light intensity and the buckling morphology phase diagram of the thin film. The light conditions are changed, and the buckling morphology phase diagram of the thin film is drawn based on the buckling wave number and the buckling amplitude of the thin film in the equilibrium state, and the effects of the light conditions and the material parameters on the buckling behavior of the thin film are determined by comparing the effects of different material parameters on the critical light intensity and the buckling morphology phase diagram of the thin film. when the dimensionless light intensity The film buckles when the preset light condition is met. The preset light condition is: ; By drawing the curve of the average elastic energy of the system under certain light conditions and the change of geometric parameters, the actual buckling amplitude and buckling wave number at this time are determined according to the minimum value; wherein the geometric parameters are buckling wave number and buckling amplitude ; The buckling morphology phase diagram reflects the buckling of the thin film under different light conditions.

7. A device for analyzing the buckling behavior of a light-driven thin-film substrate structure, characterized in that, The method comprises the following steps: The establishing module is used to establish a photo-induced strain model considering local light conditions based on material parameters, describe a propagation and absorption process of light in a thin film of liquid crystal elastomer containing azobenzene, obtain an expression of photo-induced strain perpendicular to a director direction of the liquid crystal material and an expression of photo-induced strain at any position in the thin film, and obtain an equivalent photo-induced strain expression by simplification; wherein the material parameters include an equivalent elastic modulus of the thin film, an equivalent elastic modulus of the substrate, a thickness of the thin film, and a distance of light propagation when a unit attenuation of light intensity occurs under a unit azobenzene molecule content; The superposition module is used to obtain an approximate expression of elastic strain based on the superposition relationship and the equivalent photo-induced strain expression according to the von Karman nonlinear plate theory, and obtain the average elastic performance of the system based on the approximate expression of the elastic strain; The determining module is used to determine the buckling wave number and the buckling amplitude of the thin film in the equilibrium state based on the energy minimum principle and the average elastic performance of the system; The analyzing module is used to change the light conditions, draw the buckling morphology phase diagram of the thin film based on the buckling wave number and the buckling amplitude of the thin film in the equilibrium state, and determine the effects of the light conditions and the material parameters on the buckling behavior of the thin film by comparing the effects of different material parameters on the critical light intensity and the buckling morphology phase diagram of the thin film. The photo-induced strain model considering local illumination conditions is established based on material parameters, describes the propagation and absorption process of light in the thin film of liquid crystal elastomer containing azobenzene, and obtains the photo-induced strain expression perpendicular to the director direction of the liquid crystal material and the photo-induced strain expression at any position in the thin film, including: the photo-induced strain expression perpendicular to the director direction of the liquid crystal material is: ; wherein, is the photo-induced strain perpendicular to the director direction of the liquid crystal material, is the light compliance perpendicular to the director direction of the liquid crystal material, is the initial light intensity, is the content of azobenzene molecules, is the thickness of the thin film, is the coordinate perpendicular to the substrate interface, is the distance of light propagation when the unit attenuation of light intensity occurs under the unit content of azobenzene molecules, is the angle of parallel light incident on the surface of the thin film, is a natural constant; the photo-induced strain expression at any position in the thin film perpendicular to the director direction of the liquid crystal material is: ; wherein, is the photo-induced strain at any position in the thin film perpendicular to the director direction of the liquid crystal material, is the light incidence angle, is the coordinate perpendicular to the substrate interface, is the bending amplitude, is the bending wave number, is the coordinate parallel to the substrate interface.

8. An optical drive thin film substrate structure buckling behavior analysis server, characterized by, The computer device comprises a memory and a processor; The memory is used to store computer executable instructions; The processor is configured to execute the computer-executable instructions to implement the method of any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores executable instructions, and the computer executes the executable instructions to implement the method of any one of claims 1-6.

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