A soft material bubble dynamics finite element analysis method, electronic equipment and medium

Abstract

The application discloses a soft material bubble dynamics finite element analysis method, electronic equipment and medium, and the method comprises the steps of constructing a soft material bubble model; the method comprises the steps of establishing a hollow sphere model, dividing the hollow sphere model into blocks and dividing the grid, so that the grid forms a uniformly distributed wedge-shaped grid in space; defining the physical parameters of the soft material bubble model; defining the gas pressure on the inner surface of the bubble and setting the contact condition; applying a dynamic load and superimposing an initial defect including displacement and / or pressure; based on the orthogonality of spherical harmonics, identifying the relationship between the amplitude of the asymmetric deformation of the bubble and time.

Description

Technical Field

[0001] This invention belongs to the field of soft matter mechanics, and particularly relates to a finite element analysis method for bubble dynamics in soft materials, electronic devices, and media. Background Technology

[0002] Since the 1950s, ultrasound technology has made significant strides in the medical field and has become a core technology for diagnostic and therapeutic procedures such as imaging, puncture-guided procedures, extracorporeal shock wave lithotripsy, targeted drug delivery, and tissue ablation. Taking tissue ablation and targeted drug delivery as examples, both heavily rely on the cavitation effect of bubbles under high / low intensity ultrasound excitation (e.g., using mechanical effects to shatter cells, or releasing drugs by triggering microjets through bubble collapse). However, bubbles are highly susceptible to dynamic instability under cyclic ultrasound loads. Accurate prediction of bubble dynamics directly determines the control precision of ultrasound medical equipment and is crucial for ensuring the safety and effectiveness of clinical treatment.

[0003] Early research in bubble dynamics primarily focused on fluid cavitation behavior. Although the governing equations for spherical bubbles in ideal fluids (such as the RP, KM, and GA equations) are quite well-developed, existing theories face the following significant challenges in practical medical applications:

[0004] 1. It is difficult to accurately describe the mechanical properties of complex soft materials.

[0005] Soft materials, such as human biological tissues, exhibit highly complex hyperelasticity and viscoelasticity, and undergo large nonlinear deformations under ultrasonic excitation. Although existing studies have attempted to incorporate stress integrals into models and employ Kelvin models (describing creep), Maxwell models (describing relaxation), or Zener models to correct viscoelastic behavior, the accurate quantification of bubble behavior in soft materials still faces significant challenges.

[0006] 2. Research on asymmetric oscillations in soft media is severely lacking.

[0007] Experiments and numerical simulations confirm that, due to the macroscopic discontinuities, microscopic anisotropy, or intrinsic dynamic instabilities of materials, bubbles in soft media are extremely difficult to maintain ideal spherically symmetric oscillations. Although Plesset, Prosperetti, and others pioneered the use of spherical harmonic functions to characterize the surface of non-spherical bubbles, splitting the governing equations into spherically symmetric and asymmetric oscillations, and Versluis et al. also verified the parametric instability of asymmetric oscillations, most of these classic studies are limited to bubbles in aquatic environments. Currently, research extending stability analysis to viscoelastic or hyperelastic media (i.e., soft materials) remains extremely limited.

[0008] In summary, traditional computational methods cannot accurately reflect the physical reality of soft materials such as biological tissues, nor can they effectively quantify the asymmetric instability evolution of bubbles in complex media. Therefore, there is an urgent need to establish a bubble dynamics simulation method specifically for soft materials to fill the gaps in existing models and provide accurate technical support for the stability theory analysis of bubble dynamics and the safety control of ultrasound medical equipment. Summary of the Invention

[0009] To address the shortcomings of existing technologies, embodiments of the present invention provide a finite element analysis method for bubble dynamics in soft materials, an electronic device, and a medium.

[0010] In a first aspect, embodiments of the present invention provide a finite element analysis method for bubble dynamics in soft materials, the method comprising the following steps:

[0011] Constructing a bubble model of soft materials includes: establishing a hollow sphere model, dividing the hollow sphere model into blocks and meshing them, so that the mesh forms a uniformly distributed wedge-shaped mesh in space;

[0012] Define the physical parameters of the soft material bubble model;

[0013] Define the gas pressure on the inner surface of the bubble and set the contact conditions; apply dynamic loads and superimpose initial defects including displacement and / or pressure;

[0014] Based on the orthogonality of spherical harmonic functions, the relationship between the amplitude of asymmetric deformation of bubbles and time is identified.

[0015] Secondly, embodiments of the present invention provide an electronic device, characterized in that it includes:

[0016] At least one processor; and

[0017] A memory communicatively connected to the at least one processor; wherein,

[0018] The memory stores one or more computer programs that can be executed by the at least one processor, and the one or more computer programs are executed by the at least one processor to enable the at least one processor to perform the above-described finite element analysis method for soft material bubble dynamics.

[0019] Thirdly, embodiments of the present invention provide a computer-readable storage medium having a computer program stored thereon, characterized in that the computer program, when executed by a processor, implements the above-described finite element analysis method for soft material bubble dynamics.

[0020] Fourthly, embodiments of the present invention provide a computer program product, including a computer program / instruction, characterized in that the computer program / instruction, when executed by a processor, implements the aforementioned finite element analysis method for soft material bubble dynamics.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0022] (1) This invention establishes a three-dimensional hollow sphere model and, based on Euler's convex polyhedron theorem (i.e., the geometric characteristics of a regular icosahedron), divides the solid into blocks and performs structured meshing (i.e., dividing the angular direction into triangles and the radial direction into quadrilaterals), thus solving for the optimal three-dimensional meshing scheme. This makes the meshing of the model more uniform in space, minimizing the numerical interference and errors caused by mesh inhomogeneity in explicit dynamic calculations. This not only improves the accuracy of asymmetric modal calculations in the field of bubble dynamics but also more effectively realizes high-precision three-dimensional bubble model dynamic calculations.

[0023] (2) This invention defines the physical parameters of the soft material bubble model, defines the gas pressure on the inner surface of the bubble, sets the contact conditions, and applies dynamic loads, providing a multi-dimensional function setting to restore physical properties, which greatly improves the realism of the simulation. At the same time, the parameters can be flexibly modified according to actual working conditions (such as ultrasound, impact loads, and different soft tissue properties), which greatly restores the dynamic behavior of complex bubble systems, improves the similarity between numerical simulation conditions and real physical conditions, and effectively realizes the accurate correspondence between the virtual bubble model and the real physical world.

[0024] (3) In the post-processing stage of the present invention, the calculation results are converted to a spherical coordinate system. Utilizing the orthogonality of spherical harmonic functions and the geometric meaning of spherical surface integrals, a single grid area approximates the integral element, cleverly transforming the complex continuous integral expression into a discrete grid summation expression. This invention not only achieves a breakthrough in the quantitative identification of asymmetric modal oscillation amplitudes in the calculation results, but also significantly improves the accuracy of quantitative analysis of bubble dynamics calculation results, providing accurate and efficient technical support for the identification and evaluation of the dynamic stability of three-dimensional bubble models. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 A flowchart of a finite element analysis method for bubble dynamics in soft materials provided in an embodiment of the present invention;

[0027] Figure 2 A schematic diagram of mesh generation for a soft material bubble model provided in an embodiment of the present invention;

[0028] Figure 3 This is a schematic diagram of the modality recognition results provided in an embodiment of the present invention;

[0029] Figure 4 A schematic diagram illustrating the relationship between the amplitude of asymmetric deformation of a bubble and time, provided in an embodiment of the present invention;

[0030] Figure 5 This is a schematic diagram of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0031] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] It should be noted that, unless otherwise specified, the features in the following embodiments and implementation methods can be combined with each other.

[0033] like Figure 1 As shown, this invention provides a finite element analysis method for bubble dynamics in soft materials, which can effectively compare the time evolution of asymmetric deformation of the bubble surface under instability parameters and instability parameter loading. The method includes the following steps:

[0034] Step S1, constructing a soft material bubble model; including: establishing a hollow sphere model, dividing the hollow sphere model into blocks and dividing it into meshes, so that the meshes form uniformly distributed wedge-shaped meshes in space.

[0035] Specifically, in this example, the inner boundary of the hollow sphere model is set to 0.5 mm, and the outer boundary is set to 100 times or more than the inner boundary. At this time, the size of the material around the bubble is much larger than the size of the bubble, and from the perspective of calculation effect, it can be approximated as an infinite boundary.

[0036] The process of dividing the hollow sphere model into blocks and meshing them to form a uniformly distributed wedge-shaped mesh in space includes:

[0037] The hollow sphere model is divided into 20 identical regions based on the angle between the vertices and the center of the icosahedron.

[0038] Each region is divided into a structured mesh, with triangles in the angular direction and quadrilaterals in the radial direction, thus forming a uniformly distributed wedge-shaped mesh in space. For example, in this instance, the arc is divided into 20 or more equal parts in the angular direction, and these auxiliary lines are connected to form a planar sectional entity, forming a triangular mesh on the sphere. In the radial direction, the radius is divided into 50 or more parts proportionally, and a gradient size of 100 is set to form a quadrilateral gradient mesh in the radial direction, finally obtaining a wedge-shaped three-dimensional mesh.

[0039] It should be noted that, for the inner surface of the bubble, the meshing of the sphere is essentially an approximation of a convex polyhedron, using a combination of vertices, edges, and planes to approximate the sphere. A convex polyhedron satisfies Euler's theorem V + F – E = 2, where V is the number of vertices, F is the number of faces, and E is the number of edges. The most suitable meshing for the sphere can be found from this. Assuming the sphere is divided by n fine triangles, with adjacent triangles approximately on the same plane, a total of 3n / 6 vertices, n surfaces, and 3n / 2 edges are generated. The left side of the equation is zero, with no positive integer solutions. Therefore, we can only consider relaxing the shared vertex condition. Suppose that the characteristics of x triangles are changed, and each of these triangles has one vertex that is associated with only 5 triangles. Then the number of vertices becomes (3n - x) / 6 + x / 5, thus obtaining the integer solution x = 60, and the value of n can be arbitrarily chosen. Therefore, the sphere has 12 special vertices, these vertices are associated with only 5 triangles, while the other vertices are associated with 6 triangles each. Inspired by the above conclusions, by refining the mesh of each face using a regular icosahedron as a reference, a relatively optimal mesh can be obtained.

[0040] Figure 2 A schematic diagram of the mesh generation for a bubble model of soft materials is shown, as follows: Figure 2 As shown in (a), the hollow sphere model is divided into blocks based on the angle between the vertices and the center of the icosahedron. Connecting the center of the sphere to the corresponding vertices on the surface, two adjacent lines form a plane that cuts the hollow sphere solid. Figure 2 As shown in (b), the above method divides the hollow sphere model into 20 identical regions. The yellow solid represents the resulting region, with an angle φ of 72° and an angle θ of approximately 63.435°. Figure 2 (c) Figure 2 (d) Figure 2 As shown in (e), each region is divided into structured meshes. The arc is divided into 20 equal parts along the angular direction, and these auxiliary lines are connected to cut the solid, forming a triangular mesh on the sphere. In this example, the radius is divided into 50 parts radially, with the mesh size being smaller on the inside and larger on the outside, at a ratio of 100, forming a gradient quadrilateral mesh in the radial direction, ultimately resulting in a wedge-shaped 3D mesh. After combining the individual modular models, they are restored to a hollow sphere solid model, with the mesh effect as shown... Figure 2 As shown in (f) in the figure.

[0041] Step S2: Define the physical parameters of the soft material bubble model.

[0042] Specifically, the physical parameters of the soft material bubble model include: the density of the material, the hyperelastic parameter describing the elastic behavior of the soft material, and the viscoelastic parameter describing the viscous behavior of the soft material.

[0043] For example, in this instance, the density of the soft material surrounding the bubble is taken as ρ = 1060 kg / m³. 3 For simplicity, a dissipationless hyperelastic material was chosen for the soft material bubble model. The constitutive equation adopted the parametric neo-Hookean model, with the shear modulus taken as G = 10 kPa and the wave velocity as c = 1500 m / s. The bulk modulus was calculated to be K = 2385 MPa. The material parameters C in the neo-Hookean model were... 10 = 5 kPa, the compressibility parameter D1 in the neo-Hookean model is 0.000838574 MPa. -1 If the material exhibits strain rate effects, the viscoelastic equations and constitutive equations can be superimposed, typically using a Prony series in the time domain. If there are no strain rate effects, superposition is not necessary.

[0044] Step S3: Define the gas pressure on the inner surface of the bubble and set the contact conditions; apply a dynamic load and superimpose an initial defect including displacement and / or pressure.

[0045] Furthermore, defining the gas pressure at the inner surface of the bubble includes: if it is necessary to calculate the response under adiabatic conditions, ensuring that the gas behavior conforms to the adiabatic equation pV. κ = C. Where p is the pressure of the gas inside the bubble, V is the volume of the bubble, κ is the adiabatic index of the ideal gas, and C represents a constant, meaning that the value on the left side of the equation remains unchanged. The value of this constant is determined by the parameters of the bubble in its initial state.

[0046] Furthermore, the process of setting contact conditions on the inner surface of the bubble includes: setting a tangential first contact condition and a normal second contact condition on the inner surface of the bubble; wherein, the first contact condition is frictionless; and the second contact condition is hard contact, and allows separation after contact.

[0047] Furthermore, the dynamic load applied to the inner surface of the bubble needs to conform to the spherical symmetry assumption. It can be a dynamic load such as ultrasonic excitation or impact load, applied to the inner surface of the bubble in a tabular form that correlates time and amplitude.

[0048] Furthermore, the non-spherical symmetric defects pre-placed on the bubble surface are added through field functions. Specifically, a new spherical coordinate system is created under the original coordinate system, the spherical harmonic function is defined in the form of a field function, and then a short-term pressure load is applied to the bubble surface, the distribution of which is the above field function, thereby forming the initial defect, thus realizing the application of deformation or pressure in the form of spherical harmonic function as the initial defect.

[0049] For example, in this instance, the load applied to the bubble surface is a spherically symmetric ultrasonic excitation, expressed as y = A × sin(2πft), where A = 0.3 × [1 – exp(– f / 5×t)] MPa, simulating the process of the ultrasonic load gradually increasing to a steady state. This embodiment calculates two operating conditions: ultrasonic excitations of f1 = 22000 Hz and f2 = 28000 Hz, with identical load intensities. The parameters of f1 are in the unstable region, while those of f2 are in the non-instable region. The pre-defined defect on the bubble surface is a non-spherically symmetric function. A spherical coordinate system is established at the bubble center, and the spherical harmonic function Y6 is... 0 ≈ – 0.318 + 6.67 cos 2 θ – 20.0 cos 4 θ + 14.7 cos 6 θ is defined in the software as a field function. A brief pressure load is set on the bubble surface in the form of this function to form an initial defect on the surface.

[0050] Step S4: Based on the orthogonality of spherical harmonic functions, identify the relationship between the amplitude of asymmetric deformation of the bubble and time.

[0051] Specifically, the calculation results of bubble dynamics are transformed into a spherical coordinate system to obtain the radial displacement values ​​of all nodes on the bubble surface. The orthogonality of the normalized spherical harmonic function is used to calculate the amplitude of the asymmetric modal oscillation, as shown in the following expression:

[0052]

[0053] Where R(t) is the change of the average bubble radius with time, and a(t) is the change of the bubble's asymmetric displacement amplitude with time; these two physical quantities describe the evolution of the bubble's motion over time; while Y l m (θ,φ) and Y k n (θ, φ) represent the (l, m)-th order spherical harmonic functions and the (k, n)-th order spherical harmonic functions, respectively, where θ and φ represent their azimuth angles. The spherical harmonic functions describe the spatial distribution of the bubble's asymmetric motion. δ on the right-hand side of the formula... kl and δ mnAll are Kronecker symbols, δ if and only if k = l, m = n. kl δ mn = 1, under other conditions δ kl δ mn = 0, and based on this property, the modes of asymmetric deformation and their amplitudes can be identified.

[0054] Because the displacement values ​​in the simulation results of the bubble dynamics model include both spherically symmetric and asymmetric displacements, which cannot be effectively separated, i.e., u(θ,φ) = R(t) + a(t) Y l m (θ,φ), therefore, the above expression is needed for identification and analysis. To calculate the above expression, the geometric meaning of the spherical surface integral needs to be considered. The integral expression can be reduced to a summation expression, and the area of ​​a single triangular mesh can be used to approximate the infinitesimal element of the spherical surface integral, as shown in the following expression.

[0055]

[0056] Where u(θ,φ) is the radial displacement of the nodes on the bubble surface, and θ and φ represent the azimuth angles; while Y l m (θ,φ) denotes a (l,m)-order spherical harmonic function, where θ and φ represent the azimuth angles. The n on the right-hand side of the formula represents the total number of triangular grids on the sphere. The integral expression is approximately transformed into a summation expression, summing the values ​​corresponding to each grid, where u... i (θ i ,φ i ) represents the radial displacement of the i-th grid, (θ) i ,φ i ) represents the azimuth angle of the grid; Y l m (θ i ,φ i Then ) represents the azimuth angle (θ) of the i-th grid. i ,φ i The spherical harmonic function value at point S. ΔNi1Ni2Ni3 Let ΔN be the area of ​​the i-th mesh after deformation, approximated as an integral infinitesimal element. i1 N i2 N i3 These represent the three nodes of the i-th mesh. The area of ​​the mesh after deformation is corrected by the area before deformation and the current equivalent radius. The area before deformation is calculated from the initial coordinates of the mesh, and the correction factor is the square of the ratio of the initial bubble radius to the current bubble radius.

[0057] Specifically, all nodes on the sphere are associated with corresponding triangular meshes, each mesh consisting of three nodes. First, based on the spatial coordinates of the three nodes, the area of ​​the mesh before deformation can be directly calculated. Then, based on the correction relationship between the initial radius and the current radius of the bubble, the area S of the i-th mesh after deformation can be calculated. ΔNi1Ni2Ni3 Secondly, the grid center is defined as the average of the initial coordinates of the three nodes. Based on this information, the azimuth angle (θ) of the i-th grid at the initial moment is calculated. i ,φ i Based on this data, the spherical harmonic function value Y corresponding to the i-th grid is obtained. l m (θ i ,φ i Finally, when the bubble surface undergoes non-spherical deformation, the meshes at different azimuth angles produce unequal radial displacements. The mesh displacement is defined as the average of the radial displacements of the three nodes, thus obtaining the radial displacement u of the i-th mesh on the bubble surface. i (θ i ,φ i Having obtained all the information needed for the summation expression, the result is the asymmetric mode Y. l m The corresponding amplitude.

[0058] To verify the above identification scheme, the following verification case was conducted. Figure 3 This is a schematic diagram of the modality recognition results. Figure 3 (a) illustrates the geometric meaning of the transformation from integration to summation of infinitesimal elements. For example... Figure 3 As shown in (b), a displacement boundary condition is given to the bubble surface to cause the bubble to generate Y2. 0 Y3 0 Y4 0 Y5 0 Y6 0 Five asymmetric deformation modes were identified, and the results were plotted as a bar chart. The conclusions are clear and accurate, verifying the function of this scheme in accurately identifying mode types; for example... Figure 3 As shown in (c), displacement boundary conditions are given to the bubble surface to cause the bubble to generate Y3 with different amplitudes. 0 The asymmetric deformation mode was identified as the red dot on the right, which basically matches the theoretical value represented by the blue line, verifying the function of this scheme in accurately identifying the modal amplitude.

[0059] In this embodiment, the time evolution of bubble surface deformation under both loading parameters is consistent with the instability prediction theory. The deformation results under non-instability parameter conditions are as follows: Figure 4 As shown in (a) above, the deformation results under the instability parameter conditions are as follows: Figure 3As shown in (b) of the figure, asymmetric deformation under instability conditions can be clearly observed, while the bubble remains essentially spherical under non-instability conditions. The bubble volume change curves over time for the two conditions are shown in the figure. Figure 3 As shown in (c), both processes undergo a gradual intensification process and eventually stabilize as simple harmonic motion after several cycles. The curves showing the asymmetric deformation of the bubble over time in both conditions are as follows: Figure 3 As shown in (d), the unstable condition is represented by the blue line, and the non-instability condition by the yellow line. Both exhibit a large wave in the initial stage of loading, which is caused by a pre-existing defect in pressure excitation. After a certain period of loading, the asymmetric deformation in the unstable condition increases exponentially and eventually reaches a steady state, with the amplitude of the asymmetric deformation being approximately 15% of the bubble radius. In contrast, the asymmetric deformation in the non-instability condition gradually decreases and eventually becomes limited to small oscillations, with the amplitude of the asymmetric deformation being less than 0.1% of the bubble radius, which can be approximated as spherical.

[0060] In summary, this invention provides a finite element method for analyzing bubble dynamics in soft materials. Based on the geometry of an icosahedron, this invention optimizes the 3D mesh division scheme; by restoring the physical properties of the material inside and around the bubble, it improves the realism of the dynamic system; and by utilizing the orthogonality of spherical harmonic functions and the geometric transformation of spherical surface integrals, it achieves the identification of asymmetric modes of the bubble. Compared to traditional calculation methods, this method realizes the calculation of bubble dynamics behavior based on a 3D model that closely reflects physical reality, and achieves quantitative analysis of asymmetric modes of the bubble, providing a more accurate technical means for bubble dynamic stability analysis.

[0061] According to embodiments of the present invention, the present invention also provides an electronic device and a readable storage medium.

[0062] Figure 5 A schematic block diagram of an electronic device that can be used to implement embodiments of the present invention is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the invention described and / or claimed herein.

[0063] The electronic device includes a computing unit 101, which can perform various appropriate actions and processes according to a computer program stored in ROM 102 or a computer program loaded into RAM 103 from storage unit 108. RAM 103 may also store various programs and data required for the operation of the electronic device. The computing unit 101, ROM 102, and RAM 103 are interconnected via bus 104. I / O interface 105 is also connected to bus 104.

[0064] Multiple components in the electronic device are connected to the I / O interface 105, including: an input unit 106, such as a keyboard, mouse, etc.; an output unit 107, such as various types of displays, speakers, etc.; a storage unit 108, such as a disk, optical disk, etc.; and a communication unit 109, such as a network card, modem, wireless transceiver, etc. The communication unit 109 allows the electronic device to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0065] The computing unit 101 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of the computing unit 101 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. The computing unit 101 performs the various methods and processes described above. For example, in some embodiments, the methods in the multidimensional early warning system for pressure injuries can be implemented as a computer software program tangibly contained in a machine-readable medium, such as storage unit 108. In some embodiments, part or all of the computer program can be loaded and / or installed on an electronic device via ROM 102 and / or communication unit 109. When the computer program is loaded into RAM 103 and executed by the computing unit 101, one or more steps of the methods in the multidimensional early warning system for pressure injuries described above can be performed. Alternatively, in other embodiments, the computing unit 101 can be configured to perform the methods in the multidimensional early warning system for pressure injuries by any other suitable means (e.g., by means of firmware).

[0066] Various embodiments of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SoCs), payload-programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0067] The program code used to implement the methods of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code can be executed entirely on the machine, partially on the machine, as a standalone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0068] In the context of this invention, a readable storage medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A readable storage medium can be a machine-readable signal medium or a machine-readable storage medium. A readable storage medium can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0069] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the computer. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including voice input, speech input, or tactile input).

[0070] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as a data server), or computing systems that include middleware components (e.g., an application server), or computing systems that include frontend components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., a communication network). Examples of communication networks include local area networks (LANs), wide area networks (WANs), and the Internet.

[0071] Computer systems can include clients and servers. Clients and servers are generally located far apart and typically interact via communication networks. Client-server relationships are created by computer programs running on the respective computers and having a client-server relationship with each other. Servers can be cloud servers, servers in distributed systems, or servers incorporating blockchain technology.

[0072] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only.

[0073] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope.

Claims

1. A finite element method for analyzing bubble dynamics in soft materials, characterized in that, The method includes: Constructing a bubble model of soft materials includes: establishing a hollow sphere model, dividing the hollow sphere model into blocks and meshing them according to the angle between the vertices and the center of the icosahedron, so that the mesh forms a uniformly distributed wedge-shaped mesh in space; Define the physical parameters of the soft material bubble model; Define the gas pressure on the inner surface of the bubble and set the contact conditions; apply dynamic loads and superimpose initial defects including displacement and / or pressure; Based on the orthogonality of spherical harmonic functions, the relationship between the amplitude of asymmetric deformation of bubbles and time is identified; including: Associate all nodes on the spherical surface of the soft material bubble model with the corresponding triangular mesh, each triangular mesh consisting of three nodes; According to the i Calculate the spatial coordinates of three nodes in the triangular mesh. i The area of ​​the first triangular mesh before deformation; based on the correction relationship between the initial radius and the current radius of the bubble, the area of ​​the first triangular mesh before deformation is obtained. i The area of ​​a deformed triangular grid; The first i The average of the initial coordinates of the three nodes in the first triangular mesh is used as the mesh center of that triangular mesh. The first triangular mesh is then calculated based on this mesh center. i The azimuth angle of the first triangular mesh at the initial moment is obtained to obtain the first... i The spherical harmonic function values ​​corresponding to each triangular grid; When the surface of the bubble undergoes non-spherical symmetric deformation, the first... i The average radial displacement of three nodes in a triangular mesh is taken as the radial displacement. Traverse each triangular mesh and use the sum of the product of the deformed area, the spherical harmonic function value, and the radial displacement of each triangular mesh as the amplitude corresponding to the asymmetric mode.

2. The finite element analysis method for bubble dynamics in soft materials according to claim 1, characterized in that, The process of dividing the hollow sphere model into blocks and meshing them to form a uniformly distributed wedge-shaped mesh in space includes: The hollow sphere model is divided into 20 identical regions based on the angle between the vertices and the center of the icosahedron. Each region is divided into a structured grid, with triangles at the corners and quadrilaterals at the radial direction, thus forming a uniformly distributed wedge-shaped grid in space.

3. The finite element analysis method for bubble dynamics in soft materials according to claim 1, characterized in that, The process of dividing each region into a structured grid includes: For each region, the arc is divided into at least 20 equal parts in the angular direction and the radius is divided into at least 50 proportional parts in the radial direction.

4. The finite element analysis method for bubble dynamics in soft materials according to claim 1, characterized in that, The physical parameters of the soft material bubble model include: the density of the material, the hyperelastic parameter describing the elastic behavior of the soft material, and the viscoelastic parameter describing the viscous behavior of the soft material.

5. The finite element analysis method for bubble dynamics in soft materials according to claim 1, characterized in that, The process of setting contact conditions on the inner surface of a bubble includes: A tangential first contact condition and a normal second contact condition are provided on the inner surface of the bubble; wherein, the first contact condition is frictionless; and the second contact condition is hard contact, and separation is allowed after contact.

6. The finite element analysis method for bubble dynamics in soft materials according to claim 1, characterized in that, The process of applying a dynamic load to the inner surface of a bubble includes: The dynamic load conforms to the spherical symmetry assumption and is applied to the inner surface of the bubble in a time-amplitude correlated manner; wherein, the dynamic load includes ultrasonic excitation or impact load.

7. An electronic device, characterized in that, include: At least one processor; as well as A memory communicatively connected to the at least one processor; wherein, The memory stores one or more computer programs that can be executed by the at least one processor, the one or more of the computer programs being executed by the at least one processor to enable the at least one processor to perform the finite element analysis method for soft material bubble dynamics as described in any one of claims 1-5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the finite element analysis method for bubble dynamics of soft materials as described in any one of claims 1-5.

9. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the finite element analysis method for bubble dynamics of soft materials as described in any one of claims 1-5.

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