Flexible physical simulation method and system based on dynamic topology cutting

Abstract

The invention provides a flexible physical simulation method and system based on dynamic topology cutting, and the method comprises the steps: carrying out the dynamic topology mapping and aggregation processing of the geometric vertex data of a flexible body, and generating a surface particle topological structure; constructing an elastic response model based on the relative displacement between the mass points, and combining implicit Euler correction and toughness gradient extraction to generate an elastic potential energy parameter set; constructing a fracture sensitive energy field in combination with the rigid body motion trail and an energy permeation threshold value, and performing multi-domain response screening; and further carrying out region identification, structure redirection and phase reconstruction to generate a continuous deformation harmonic map, and realizing dynamic stable repair of the flexible body topology through repair domain construction and rebound fusion. Dynamic response, self-adaptive energy path identification, regional continuous deformation recovery and efficient and stable local topological repair of a flexible topological structure are realized, and physical precision and evolution robustness of flexible simulation are remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of computer graphics and computer-aided simulation, in particular to a method and system for soft body physics simulation based on dynamic topology cutting. BACKGROUND

[0002] In the fields of computer graphics, virtual reality and intelligent manufacturing, soft body physics simulation is an important supporting method for realizing high-fidelity physical interaction, deformation simulation and fracture reconstruction, and is attracting increasing attention. Soft body systems often exhibit complex nonlinear responses when subjected to external disturbances or internal stress changes due to their continuous structure and high degree of freedom characteristics. Therefore, a simulation method with high dynamic adaptability and structure evolution control capability is needed to meet the multiple requirements of real-time interaction, physical consistency and visual precision.

[0003] Existing soft body simulation methods usually construct soft body structures based on mass points and elastic systems, finite element models or graph structure grids, simulate local mechanical responses by introducing elastic potential energy, damping factors and other parameters, and introduce topology reconstruction mechanisms under certain conditions to support deformation and fracture behavior. Some improved methods attempt to use energy-driven fracture judgment, phase field modeling or regional remapping to improve the flexibility and realism of the simulation, but still rely on static adjacency structures and fixed deformation path mappings in most applications.

[0004] However, in practical applications, existing soft body simulation techniques still have significant limitations. On the one hand, the topology structure response has a delay or update lag, making it difficult to respond to complex dynamic disturbances. On the other hand, the energy propagation path modeling accuracy is insufficient, and the sensitivity identification and energy control capability of the fracture region are limited. In addition, the deformation recovery between regions lacks a continuous transition mechanism, resulting in discontinuous jumps in the simulation results after structure reconstruction. At the same time, the current methods lack efficient local repair scheduling strategies for disturbance characteristics, affecting the overall stability and response speed of the soft body simulation. SUMMARY

[0005] In view of the above actual situation, the present application proposes a method and system for soft body physics simulation based on dynamic topology cutting to solve the problems of topology response delay, inaccurate energy propagation path, poor regional recovery continuity and lack of efficient local repair scheduling in existing soft body simulation.

[0006] A method for soft body physics simulation based on dynamic topology cutting, the method comprising the following steps:

[0007] S1, performing vertex aggregation processing on the flexible geometry vertex data based on dynamic topology mapping to generate surface particle topology structure data, wherein the vertex aggregation processing based on dynamic topology mapping is performed by merging adjacent vertices to generate an aggregated particle set and synchronously constructing a compressed adjacency matrix through a Euclidean distance clustering algorithm, and the compressed adjacency matrix inherits the original adjacency relationship and is mapped to the aggregated particle space dimension;

[0008] S2, performing elastic potential energy constraint modeling processing on the surface particle topology structure data, wherein the elastic potential energy constraint modeling processing is performed by constructing an initial elastic response model based on a relative displacement vector between particles, and combining an implicit Euler correction and a toughness gradient field extraction mechanism to generate an elastic potential energy constraint parameter set;

[0009] S3, performing fracture-sensitive energy field construction and multi-domain response screening fusion processing on the elastic potential energy constraint parameter set combined with external input interaction data, wherein the fracture-sensitive energy field construction and multi-domain response screening fusion processing is performed by generating dynamic topology response screening atlas data through kinetic energy transmission direction modeling and flux tensor network screening in cooperation, and the interaction data includes rigid body motion trajectory data and energy penetration threshold data;

[0010] S4, performing domain-specific deformation recovery constraint processing on the dynamic topology response screening atlas data to generate deformation harmonic recovery atlas data, wherein the domain-specific deformation recovery constraint processing is performed by combining partition labels for region identification, local structure redirection, and deformation phase reconstruction to form a continuous controllable recovery constraint model;

[0011] S5, performing repair processing on the deformation harmonic recovery atlas data to generate flexible topology continuity repair data, wherein the repair processing is performed by constructing a target repair domain and performing structure topology reconstruction and dynamic stable rebound processing.

[0012] Further, the S2 step includes the following sub-steps:

[0013] S201, generating initial elastic potential energy parameters based on the surface particle topology structure data through a relative displacement vector calculation model between particles, wherein the initial elastic potential energy parameters include elastic stiffness coefficients and damping attenuation factors between particles;

[0014] S202, performing implicit Euler error correction and toughness gradient field extraction processing on the initial elastic potential energy parameters to generate an elastic potential energy constraint parameter set, wherein the implicit Euler error correction and toughness gradient field extraction processing is performed by iteratively solving particle displacement deviation, dynamically adjusting elastic stiffness coefficients and damping attenuation factors to balance constraint forces and motion inertia in cooperation, and synchronously generating toughness gradient field data based on plastic deformation accumulation rate and energy dissipation sensitivity in the correction process.

[0015] Further, the S3 step includes the following sub-steps:

[0016] S301, fracture-sensitive energy field modeling processing is performed on the elastic potential energy constraint parameter set and the rigid body motion trajectory data to generate fracture-sensitive energy chain data. The fracture-sensitive energy field modeling processing is performed by calculating kinetic energy transmission direction through rigid body motion trajectory integral, combining elastic stiffness coefficient, damping attenuation factor and toughness gradient field data in the elastic potential energy constraint parameter set, constructing a dynamic energy coupling model based on fracture sensitivity index, generating energy propagation main path and branch fracture path, and recording path energy density, toughness attenuation factor and fracture sensitivity index;

[0017] S302, multi-energy energy retention and attenuation rate collaborative screening processing is performed on the fracture-sensitive energy chain data combined with energy penetration threshold data to generate dynamic topological response screening map data. The multi-energy energy retention and attenuation rate collaborative screening processing is performed by constructing a nonlinear flux tensor network based on the difference between path energy density and penetration threshold, constructing an energy residual domain mapping graph by comprehensively considering the toughness attenuation factor and fracture sensitivity index of each node in the main path and branch path, and inhibiting false energy diffusion path through a dynamic penetration redundancy filtering mechanism to realize multi-level labeling partitioning of structure cutting zone, buffer zone and reconstruction zone.

[0018] Further, the S4 step includes the following sub-steps:

[0019] S401, label-guided domain identification processing is performed on the dynamic topological response screening map data to generate partition correlation graph data. The label-guided domain identification processing is performed by constructing an adjacency label tensor field based on the label information of the cutting zone, buffer zone and reconstruction zone, and normalizing clustering the topological difference degree of the boundary of each region through a continuity enhancement factor to output a region boundary relationship graph and a structure classification matrix;

[0020] S402, inter-regional deformation vector field redirection processing is performed on the partition correlation graph data to generate multi-domain structure pointing graph data. The inter-regional deformation vector field redirection processing is performed by constructing a three-state deformation response template based on the structure classification matrix, and driving an inter-regional pointing boundary update mechanism through a minimum deformation tensor overlap rate to output a multi-domain boundary deformation consistent structure vector graph. The three-state deformation response template includes cutting cleavage response, buffer elastic transfer response, and reconstruction fusion response.

[0021] S403, deformation phase reconstruction processing is performed on the multi-domain structure pointing graph data to generate deformation harmonic recovery map data. The deformation phase reconstruction processing is performed by constructing a multi-scale deformation phase graph convolution template, locally embedding a fracture gap completion term in the cutting zone, introducing a deformation release factor in the buffer zone, introducing a continuity inflation function in the reconstruction zone, and uniformly constructing a phase splicing index map to realize inter-regional continuity connection and output deformation harmonic recovery map data.

[0022] Further, the S5 step includes the following sub-steps:

[0023] S501, target repair domain construction processing is performed on the deformation harmonic restoration map data to generate target repair scheduling map data, the target repair domain construction processing is based on phase splicing index map screening topology discontinuous node set, and local repair priority queue is constructed in combination with historical displacement disturbance information of each node, and global flexible continuity scheduling map is established, local repair scheduling sorting is realized;

[0024] S502, topology reconstruction and dynamic rebound fusion processing is performed on the target repair scheduling map data to generate flexible topology continuity repair data, the topology reconstruction and dynamic rebound fusion processing is based on scheduling priority driven topology connection prediction mechanism, local edge reconstruction is performed on the discontinuous node set, and node-by-node elastic rebound harmonic is performed based on elastic potential curvature balance principle, so as to output flexible topology continuity repair data.

[0025] Further, the S201 includes that the initial elastic potential energy parameter is generated by a relative displacement vector calculation model between surface particles based on the surface particle topology structure data, which includes topology connection displacement analysis processing and material constitutive parameter mapping processing.

[0026] Further, the fracture sensitive energy field modeling processing in the S301 is to calculate kinetic energy transmission direction by rigid body motion trajectory integral, to construct a dynamic energy coupling model based on fracture sensitive index by combining elastic stiffness coefficient, damping attenuation factor and toughness gradient field data in the elastic potential energy constraint parameter set, to generate energy propagation main path and branch fracture path, and to record path energy density, toughness attenuation factor and fracture sensitive index, including kinetic energy flux field construction processing and fracture path evolution processing; the multi-energy energy retention and attenuation rate collaborative screening processing in the S302 is to construct a nonlinear flux tensor network based on the difference between path energy density and permeation threshold value, to construct an energy residual domain mapping graph by combining the toughness attenuation factor and the fracture sensitive index of each node in the main path and the branch path, and to inhibit false energy diffusion path by a dynamic permeation redundancy filtering mechanism, including flux tensor field construction processing and multi-level energy domain segmentation processing.

[0027] Further, the label-guided domain recognition processing in S401 is to construct an adjacency label tensor field based on label information of the cutting zone, the buffer zone and the reconstruction zone, and to regularize clustering of topological differences of boundaries of each zone by a continuity enhancement factor, including an adjacency topological field construction processing and a boundary regularized clustering processing; the inter-zone deformation vector field redirection processing in S402 is to construct a three-state deformation response template based on a structure classification matrix, and to drive an inter-zone pointing boundary update mechanism by a minimum deformation tensor overlap rate, including a response template construction processing and a boundary pointing optimization processing; the deformation phase reconstruction processing in S403 is to locally embed a fracture gap completion term in the cutting zone by constructing a multi-scale deformation phase map convolution template, introduce a deformation release factor in the buffer zone, introduce a continuity expansion function in the reconstruction zone, and uniformly construct a phase stitching index atlas, including a partition deformation field convolution processing and a cross-domain phase harmonization processing.

[0028] Further, the target repair domain construction processing in S501 is to screen a set of topologically discontinuous nodes based on the phase stitching index atlas, construct a local repair priority queue in combination with historical displacement disturbance information of each node, and establish a flexible continuity scheduling graph globally, to realize local repair scheduling sorting, including a topological fracture point identification processing and a repair scheduling graph generation processing; the topological reconstruction and dynamic rebound fusion processing in S502 is to perform local edge reconstruction on the set of discontinuous nodes based on a topological connection prediction mechanism driven by scheduling priority, and execute node-by-node elastic rebound harmonization based on an elastic potential curvature equalization principle, including a priority-driven topological reconstruction processing and a curvature equalization rebound processing.

[0029] In addition, the present application also discloses a flexible physical simulation system based on dynamic topological cutting, which comprises:

[0030] A topological aggregation construction unit is configured to perform vertex aggregation processing based on dynamic topological mapping on the flexible geometric vertex data, to generate surface particle topological structure data, wherein the vertex aggregation processing based on dynamic topological mapping is to generate an aggregated particle set by merging adjacent vertices through a Euclidean distance clustering algorithm and to synchronously construct a compressed adjacency matrix, and the compressed adjacency matrix inherits original adjacency relationships and is mapped to an aggregated particle spatial dimension;

[0031] An elastic response modeling unit is configured to perform elastic potential energy constraint modeling processing on the surface particle topological structure data, wherein the elastic potential energy constraint modeling processing is to construct an initial elastic response model based on relative displacement vectors between particles, and to generate an elastic potential energy constraint parameter set in combination with an implicit Euler correction and a ductility gradient field extraction mechanism;

[0032] An energy field analysis screening unit is used to perform fracture sensitivity energy field construction and multi-domain response screening fusion processing on a set of elastic potential energy constraint parameters combined with external input interaction data, the fracture sensitivity energy field construction and multi-domain response screening fusion processing is to generate dynamic topological response screening atlas data through kinetic energy transmission direction modeling and flux tensor network screening, and the interaction data includes rigid body motion trajectory data and energy penetration threshold data;

[0033] A domain deformation recovery unit is used to perform domain deformation recovery constraint processing on the dynamic topological response screening atlas data to generate deformation harmonic recovery atlas data, and the domain deformation recovery constraint processing is to perform region identification, local structure redirection and deformation phase reconstruction in combination with partition labels to form a continuous controllable recovery constraint model.

[0034] A topological repair harmonic unit is used to perform repair processing on the deformation harmonic recovery atlas data to generate soft topological continuity repair data, and the repair processing is to construct a target repair domain and perform structure topological reconstruction and dynamic stable rebound processing.

[0035] The soft physical simulation method and system based on dynamic topological cutting proposed in the present application realize dynamic response of soft topological structure, adaptive energy path identification, regional continuity deformation recovery and efficient and stable local topological repair, which significantly improves the physical precision and evolution robustness of soft simulation. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 A method flowchart of the soft physical simulation method based on dynamic topological cutting proposed in the present application is shown in the figure.

[0037] Figure 2 A deformation harmonic recovery atlas data generation flowchart of the soft physical simulation method based on dynamic topological cutting proposed in the present application is shown in the figure.

[0038] Figure 3 A system structure diagram of the system for inversely predicting production parameters based on tar quantity provided in the embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0039] The simulation technical route in the embodiment of the present application will be described clearly and completely in combination with the figures of the present application. Obviously, the described embodiment is only a part of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0040] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail in combination with the figures and specific embodiments.

[0041] The features and properties of the present application are further described in detail below in conjunction with the embodiments. Please refer to the accompanying drawings Figure 1 As shown in the drawings, a soft body physics simulation method based on dynamic topology cutting, the method comprising the following steps:

[0042] S1, the vertex aggregation processing based on dynamic topology mapping is performed on the soft body geometry vertex data, and surface particle topology structure data is generated, the vertex aggregation processing based on dynamic topology mapping is to merge adjacent vertices to generate an aggregated particle set by using a Euclidean distance clustering algorithm and to construct a compressed adjacency matrix synchronously, the compressed adjacency matrix inherits the original adjacency relationship and is mapped to the aggregated particle space dimension;

[0043] In some embodiments, the vertex aggregation processing based on dynamic topology mapping is to merge adjacent vertices to generate an aggregated particle set by using a Euclidean distance clustering algorithm and to construct a compressed adjacency matrix synchronously, which includes vertex space clustering processing and adjacency relationship migration processing. Specifically, the vertex space clustering processing performs an iterative merging operation on the vertices in the soft body mesh model that meet the spatial proximity condition according to a preset dynamic aggregation radius threshold, the dynamic aggregation radius threshold is related to the local curvature feature of the soft body and a preset material strain energy density parameter; the adjacency relationship migration processing projects the original vertex adjacency relationship to the aggregated particle space dimension by constructing a compressed mapping operator to generate a compressed adjacency matrix that inherits the original topological connectivity. It should be noted that the two processes are coupled through a vertex-particle mapping function, and the original vertex attribution relationship is recorded synchronously during the clustering process to provide a topological mapping basis for the adjacency migration.

[0044] In this embodiment, the vertex space clustering processing performs the following mathematical process: define the original vertex set V = {v i |i = 1, 2,..., n} and its three-dimensional coordinate vector set X = {x i ∈ R 3}. The dynamic calculation model of the clustering radius threshold δ is: δ = δ0·(1+α|κ i |), where δ0 is the reference clustering radius, α is the curvature sensitivity coefficient, κ i is the Gaussian curvature value at the vertex v i . Preferably, δ0 is determined by the material physical properties: where E is the Young's modulus, ρ is the material density, is the maximum allowable strain rate, and β is the scale adjustment factor. Specifically, the algorithm traverses the unaggregated vertex v k , constructs a neighborhood vertex set C k that satisfies ||x j -x k ||2≤δ, calculates the aggregated particle coordinate and mass Output aggregated particle set P = {p k = (c k , m k )|k = 1,..., K}. Further, a mapping function φ: V→ P is generated to record the aggregated particle number to which each original vertex belongs.

[0045] In some embodiments, the adjacency relationship migration processing constructs a compressed adjacency matrix A c ∈R K×K based on the mapping function φ. Specifically, the matrix element assignment rule is defined as: wherein A ij = 1 indicates that the vertex v i is topologically connected with v j . Preferably, the weight coefficient N mn is the number of edges whose starting point belongs to the particle p m and whose ending point belongs to the particle p n . This design makes the compressed adjacency matrix element value reflect the cross-particle connection strength and retain the topological characteristics of the original mesh. It should be noted that the inverse mapping φ -1 generated by the mapping function φ is used to quickly locate the original vertex set contained in each particle during the matrix construction process.

[0046] In this embodiment, the surface particle topological structure data is represented by a triple mathematical model as T = <P, A c , Φ >, wherein P = {p c} is the aggregated particle coordinate and mass set, A n is a K × K compressed adjacency matrix, and Φ = [φ(v T )] c is the mapping vector of the original vertex to the particle. Further, the data structure functions in physical simulation as follows: the particle set P reduces the calculation dimension as the solving unit of the dynamic differential equation, the compressed adjacency matrix A m provides a topological connection basis for subsequent elastic potential energy constraints, and the mapping vector Φ supports the reverse mapping of the original geometric details and the aggregated model. Specifically, this topological structure makes the soft body tearing simulation reduce the calculation complexity from the original vertex number n to the aggregated particle number K (satisfying K << n) while maintaining physical accuracy. S2, perform an elastic potential energy constraint modeling processing on the surface particle topological structure data, wherein the elastic potential energy constraint modeling processing is based on the relative displacement vector between particles to construct an initial elastic response model, and combines an implicit Euler correction and a ductility gradient field extraction mechanism to generate an elastic potential energy constraint parameter set;

[0047] Specifically, this step includes the following sub-steps:

[0049] S201, Based on the surface particle topology data, an initial elastic potential energy parameter is generated through a particle relative displacement vector calculation model. The initial elastic potential energy parameter includes the particle elastic stiffness coefficient and damping attenuation factor.

[0050] In some implementations, the generation of initial elastic potential energy parameters based on the surface particle topology data through a particle relative displacement vector calculation model includes topological connection displacement analysis and material constitutive parameter mapping. Specifically, the topological connection displacement analysis uses a compressed adjacency matrix to select effectively connected particle pairs and calculates their relative displacement vectors; the material constitutive parameter mapping transforms material physical parameters into elastic constraint parameters based on the rate of change of distance between particles and the original geometric properties. It should be noted that the two processes achieve data coordination through a particle spatial topological connection graph, where the compressed adjacency matrix defines the connection relationships, and the relative displacement vector provides the basis for deformation measurement.

[0051] In this embodiment, the topological connection displacement analytical processing performs the following procedure: Let the aggregate mass set P = {p m The current coordinate position of |m=1,...,K} is {x m The initial configuration coordinates are Define the set of valid pairs of connected particles. Where A c This is the compressed adjacency matrix generated in step S1. For any pair of connections (p... m ,p n Calculate the relative displacement vector ∈ ε: Preferably, the current connection distance l is calculated simultaneously. mn =||x m -x n ||2 and initial distance Generate deformation measurement factor Furthermore, output the topological displacement dataset.

[0052] In some implementations, the material constitutive parameter mapping process calculates the elastic stiffness coefficient and damping attenuation factor based on the topological displacement dataset. Specifically, for each connection pair (p m ,p n ), elastic stiffness coefficient k mn The generative model is: In the formula, E is the Young's modulus of the material (a preset physical parameter), and A... mn The equivalent cross-sectional area is calculated using the following formula: Where s m For point mass p mThe corresponding original surface area is calculated reversely from the mapping vector Φ of S1 step ω mn The element value of the compressed adjacency matrix A c characterizes the topological connection strength.

[0053] The damping attenuation factor c mn The calculation model is: wherein is the reduced mass, m m is the mass of the particle, is the preset damping ratio coefficient. It should be noted that the model maps the material physical properties E, geometric properties A mn and dynamic properties μ mn to the constraint parameter space uniformly.

[0054] In the embodiment, the initial elastic potential energy parameter is represented by a binary group mathematical model as: Preferably, a sparse tensor storage structure is used, and the non-zero element positions are determined by the non-zero mode of the compressed adjacency matrix A c . Specifically, the role of the parameter set in the soft body physics simulation is embodied as follows: the elastic stiffness coefficient k mn directly participates in the calculation of the potential energy function , and the damping attenuation factor c mn acts on the velocity-related dissipation force calculation Further, the parameter set provides a basic physical constraint framework for the subsequent implicit Euler correction of S202 step.

[0055] S202, implicit Euler error correction and toughness gradient field extraction processing are performed on the initial elastic potential energy parameter to generate an elastic potential energy constraint parameter set. The implicit Euler error correction and toughness gradient field extraction processing is achieved by iteratively solving the particle displacement deviation, dynamically adjusting the elastic stiffness coefficient and the damping attenuation factor to balance the constraint force and the motion inertia, and simultaneously generating the toughness gradient field data based on the plastic deformation accumulation rate and the energy dissipation sensitivity in the correction process.

[0056] In some embodiments, the implicit Euler error correction and toughness gradient field extraction processing of the initial elastic potential energy parameter realizes dynamic optimization of the elastic parameter and extraction of the toughness feature through a cooperative iteration mechanism. Specifically, the processing establishes an adaptive adjustment model of the elastic stiffness coefficient and the damping attenuation factor based on displacement deviation feedback, and simultaneously constructs the toughness gradient field data based on the plastic deformation accumulation rate and the energy dissipation sensitivity. It should be noted that the input of this process is the initial elastic potential energy parameter set K={(k mn ,c mn )} generated by S201 step and the current particle motion state data.

[0057] In the present embodiment, the implicit Euler error correction performs the following process: let the motion equation of the particle system at the t-th simulation step be: where M ∈ R 3K×3K is a mass diagonal matrix whose elements are constructed from the particle masses m k Each particle mass m k occupies a 3x3 diagonal sub-block. K ∈ R 3K×3K is a stiffness matrix whose elements are constructed from the elastic stiffness coefficients k mn : where I3 is a 3x3 identity matrix, N(m) represents the set of neighboring particles connected to particle p m , C ∈ R 3K×3K is a damping matrix whose structure is isomorphic to K, whose elements are replaced by the damping decay factors c mn : mn , Δx t = x t - x t-1 is the displacement increment. are the acceleration vector and the velocity vector, respectively, arranged by particle index, f ext ∈ R 3K is the external force vector, containing external loads such as gravity, collision forces, etc. It should be noted that the motion equation is discretized using the implicit Euler integration format: where Δt is the simulation time step. Preferably, the predicted value is extrapolated from the previous step state: The implicit Euler discretization produces a numerical deviation: where is the predicted acceleration and velocity. Preferably, the parameter is dynamically adjusted by iteratively solving the displacement deviation ||e′||2: where i is the iteration number, and γ, η are convergence control coefficients. This adjustment makes the constraint force and the motion inertia reach a dynamic balance, suppressing numerical oscillation. The deviation-driven elastic parameter iterative correction makes the system satisfy the dynamic balance condition ||e t ||2 < ε (ε is the tolerance threshold).

[0058] Further, the parameter correction process and the ductility gradient field generation form a two-way coupling: the adjustment of the elastic stiffness coefficient k mn affects the plastic deformation accumulation rate The update of the damping decay factor c mn changes the energy dissipation sensitivity and together determine the spatial distribution of the ductility gradient field G tough .

[0059] In some embodiments, the ductility gradient field extraction process is performed synchronously, defining the plastic deformation accumulation rate wherein is the elastic strain threshold. The energy dissipation sensitivity is calculated as: Preferably, the ductility gradient field data generation model is: wherein the topological space gradient operator (based on the compressed adjacency matrix A c , α, β are the material ductility weight coefficients. It should be noted that the gradient field represents the spatial distribution characteristics of the material's anti-fracture ability.

[0060] In this embodiment, the elastic potential energy constraint parameter set is represented by a triple mathematical model: P = <K adj , C adj , G tough >, wherein is the corrected elastic stiffness coefficient set, is the corrected damping attenuation factor set, G tougt is the KxK-dimensional ductility gradient field tensor

[0061] Further, the role of the parameter set in the flexible body fracture simulation is: the corrected k mn , c mn ensures the numerical stability of the dynamics integration, and the ductility gradient field provides a material failure criterion for the subsequent S301 step of the fracture sensitive energy field modeling. In particular, the high ductility gradient region corresponds to the fracture path inhibition zone, and the low gradient region identifies the potential fracture propagation path.

[0062] S3, the elastic potential energy constraint parameter set is combined with external input interaction data to perform fracture sensitive energy field construction and multi-domain response screening fusion processing. The fracture sensitive energy field construction and multi-domain response screening fusion processing is to generate dynamic topological response screening atlas data through the kinetic energy transmission direction modeling and the flux tensor network screening. The interaction data includes rigid body motion trajectory data and energy penetration threshold data.

[0063] Specifically, this step includes the following sub-steps:

[0064] S301, the elastic potential energy constraint parameter set and the rigid body motion trajectory data are subjected to fracture sensitive energy field modeling processing to generate fracture sensitive energy chain data. The fracture sensitive energy field modeling processing is to calculate the kinetic energy transmission direction through rigid body motion trajectory integration, combine the elastic stiffness coefficient, the damping attenuation factor and the ductility gradient field data in the elastic potential energy constraint parameter set, construct a dynamic energy coupling model based on the fracture sensitive index, generate the energy propagation main path and the branch fracture path, and record the path energy density, the ductility attenuation factor and the fracture sensitive index.

[0065] In some embodiments, the fracture-sensitive energy field modeling process is to calculate kinetic energy transmission direction by rigid body motion trajectory integration, combine elastic stiffness coefficient, damping attenuation factor and toughness gradient field data in the parameter set of elastic constraint, construct dynamic energy coupling model based on fracture-sensitive index, generate main path of energy propagation and branch fracture path, and record path energy density, toughness attenuation factor and fracture-sensitive index, including kinetic energy flux field construction process and fracture path evolution process. Specifically, the kinetic energy flux field construction process calculates kinetic energy input distribution and transmission direction by time integration of rigid body motion trajectory; the fracture path evolution process solves energy propagation path and quantifies path fracture characteristics based on dynamic energy coupling model. It should be noted that the two processes are coupled through the fracture-sensitive index, which integrates kinetic energy flux, elastic constraint parameters and toughness gradient field data to drive fracture path prediction together.

[0066] In the present embodiment, the kinetic energy flux field construction process performs the following mathematical process: let the rigid body motion trajectory function be R(t), the contact point position set be {p c} The kinetic energy flux vector field is defined as: In the formula, p is the material density, v c = dR / dt is the contact point velocity, d is the Dirac function, v c (τ) represents the velocity vector of the rigid body at contact point c at time τ, ||v c (τ)|| is the Euclidean norm of the velocity vector, d(x-p c (τ)) is a three-dimensional Dirac function, which takes the limit value when the spatial position x coincides with the contact point position p c (τ), dτ is the time integration infinitesimal, t0 to t is the time integration interval of kinetic energy transmission. Preferably, the Gaussian kernel diffusion model is used for discrete calculation: Where s is the energy diffusion radius parameter, At is the time discretization step, t k is the discrete time point index, x m is the spatial coordinate of the mth aggregation particle, is the Gaussian kernel normalization coefficient, and the flux field represents the spatial distribution and direction characteristics of kinetic energy input.

[0067] In some embodiments, the fracture path evolution process constructs a dynamic energy coupling model: define the differential form of the fracture-sensitive index F s : Where k mn , c mn are taken from the S202 modified parameter set, G tough is the toughness gradient field. Specifically, the main path of energy propagation is obtained by solving the following path integral: where γ denotes an arbitrary continuous path curve (a curve in topological space) connecting the collision point to the boundary point, dx is the differential displacement vector of the path curve (an infinitesimal displacement in three-dimensional space), and γ F s dx is the fracture-sensitive index line integral along the path γ, representing the cumulative fracture tendency of the path, and argmax is the optimal path that maximizes the integral value. The branch fracture path is generated by local extremum search: where is the path variation operator, representing the functional derivative of the path curve γ, λ is a curvature penalty weight coefficient that balances the path bending cost, κ(γ) is the curvature function of the path γ, defined as κ = ||d 2 x / ds 2 || (s is the arc length parameter), and γ F s dx-λκ(γ) is the path evaluation functional, including the fracture-sensitive integral and the curvature penalty term, and the equation represents that the branch path needs to satisfy the extremum condition of the functional. Preferably, each path record three groups of characteristic parameters: the energy density the toughness attenuation factor and the fracture-sensitive index ψ = max s∈γ F s (s).

[0068] In this embodiment, the fracture-sensitive energy chain data is represented by a graph structure mathematical model: L =, where V = {v i |v i ∈ P} is the path key point (aggregated particle), the edge set ε = {e j |e j ∈ Γ main ∪ Γ branch}, and the data field D = {(ξ j , η j , ψ j )} is associated with each edge e j .

[0069] Further, the application of the data in the flexible body fracture simulation is embodied as: the energy propagation main path Γ main identifies the high-probability fracture channel, and the branch path Γ branch predicts the secondary crack propagation direction. Specifically, the path energy density ξ and the fracture-sensitive index ψ are positively correlated with the crack initiation probability, and the toughness attenuation factor η is negatively correlated with the crack propagation resistance. It should be noted that the energy chain data provides a topological segmentation basis for the multi-domain screening of the subsequent S302 step.

[0070] In this embodiment, the physical basis of the dynamic energy coupling model is verified by the energy conservation equation:

[0071] where Ω is the flexible spatial domain, representing the three-dimensional flexible geometric region to be simulated, p is the material density, taken from the mass distribution of the particles in S1 step, v is the particle velocity vector field, v = dx / dt (x is the particle position coordinate), is the flexible boundary surface, Φ k is the kinetic energy flux vector field, calculated by integrating the rigid body motion trajectory in S301 step, ds is the boundary surface micro-element normal vector, ε is the strain scalar field, (relative displacement strain), strain rate field, strain gradient field, The equation ensures that the fracture sensitive index F s satisfies the physical constraints of energy input, storage and dissipation. Preferably, the model solution is discretized along the kinetic energy flux direction using the method of characteristics.

[0072] S302, the multi-energy energy retention and attenuation rate collaborative screening processing of the fracture sensitive energy chain data combined with the energy penetration threshold data is performed to generate dynamic topological response screening map data. The multi-energy energy retention and attenuation rate collaborative screening processing is performed by constructing a nonlinear flux tensor network based on the difference between the path energy density and the penetration threshold, constructing an energy residual domain mapping graph by comprehensively considering the toughness attenuation factor and the fracture sensitive index of each node in the main path and the branch path, and inhibiting false energy diffusion paths through a dynamic penetration redundancy filtering mechanism to realize multi-level labeling partitioning of the structure cutting zone, the buffer zone and the reconstruction zone. The buffer zone not only covers the fracture path boundary region, but also includes a region that is caused by external collision and has high elastic deformation but does not form an actual cut.

[0073] In some embodiments, the multi-energy energy retention and attenuation rate collaborative screening processing, which is performed by constructing a nonlinear flux tensor network based on the difference between the path energy density and the penetration threshold, constructing an energy residual domain mapping graph by comprehensively considering the toughness attenuation factor and the fracture sensitive index of each node in the main path and the branch path, and inhibiting false energy diffusion paths through a dynamic penetration redundancy filtering mechanism, includes flux tensor field construction processing and multi-level energy domain segmentation processing. Specifically, the flux tensor field construction processing establishes a tensor network model according to the nonlinear relationship between the path energy density and the preset energy penetration threshold; and the multi-level energy domain segmentation processing performs dynamic penetration filtering based on the energy residual domain mapping graph and generates a multi-label partitioning result. It should be noted that the two processes are coupled through an energy retention rate index, which calculates the local energy retention strength by comprehensively considering the path energy density, the toughness attenuation factor and the fracture sensitive index.

[0074] In this embodiment, the flux tensor field construction processing performs the following process: assuming that the edge ej The energy density is ξ j Energy permeability threshold data provides the spatial variable threshold τ(x). Define the flux tensor components: In the formula σ τ η is the threshold sensitivity coefficient. j ψ is the toughness attenuation factor (taken from D). j n is the fracture sensitivity index (taken from D). j For path e j The unit direction vector. Preferably, at point p. m The composite tensor field at point is: Where N(m) is the correlation p m The set of paths, weights ω mj This represents the spatial association weight between particle pm and path ej, reflecting the strength of the influence of their geometric proximity on energy transfer. Its value range is (0,1], x m particle p m The spatial coordinate vector (taken from the aggregated particle set P in step S1), c j These are the coordinates of the geometric center point of path ej, calculated from the average coordinates of the path endpoints. Where x js ,x je Path e j The starting and ending coordinates (from the fracture-sensitive energy chain of step S301), σ g It is the width parameter of the Gaussian kernel function, controlling the rate at which the weights decay with distance; its physical meaning is the radius of influence of path energy, ||x m -c j || 2 Represents point mass p m With path center c j The Euclidean distance is given. It should be noted that the weighting function is designed to give higher weights to particles closer to the energy propagation path, satisfying ω. mj →1 when ||x m -c j ||→0;ω mj →0 when ||x m -c j ||>σ g The principal eigenvector of this tensor field identifies the direction of residual energy.

[0075] In some implementations, the multi-level energy domain segmentation process includes energy residual domain mapping and dynamic permeation filtering: defining the energy retention rate: In the formula ρ m particle p mThe energy retention rate (a dimensionless scalar) represents the proportion of kinetic energy in a local area that is not dissipated or transferred per unit time; the number of elements in the set |N(m)| represents the total number of associated paths. Path e j The gradient magnitude of the toughness attenuation factor is calculated as follows: It reflects the varying strength of resilience along the path; This represents the lower bound cutoff function for the gradient magnitude, when... Output 1 to avoid overflow caused by a small denominator. It should be noted that the denominator term... This constitutes the energy dissipation resistance term; the larger the value, the more difficult it is for energy to remain. Construct the energy residue domain mapping diagram M: The dynamic permeation redundancy filtering mechanism performs iterative operations: in[·] + This indicates a positive value operation; κ is a preset permeation attenuation rate constant (dimensionless) used to control the intensity of energy permeation in the neighborhood. particle p m The set of adjacent particles is given by the compressed adjacency matrix A. c The non-zero elements are determined, T m The flux tensor (second-order tensor) at particle pm is generated by constructing and processing the flux tensor field. Adjacent mass p n The scalar value of energy retention rate at iteration step t. This operation suppresses the satisfaction of |T m ·(x n -x m The spurious diffusion path is )|<ε.

[0076] In this embodiment, the multi-level tagging partitioning rule is defined as follows: Where τ l ,τ h Energy retention rate threshold (τ) l <τ h ), ψ crit η is the fracture sensitivity threshold, θ is the threshold value of the energy-sensitivity product, and η is the sensitivity threshold. crit This is the critical value for toughness degradation. It should be noted that the buffer zone definition covers two types of regions: the fracture path boundary region with a moderate energy retention rate (τ). l ≤ρ m ≤τ h ), and satisfying ρ m ·ψ m >θ and η m <η crit The highly elastic deformation uncut region expands the physical meaning of the buffer zone.

[0077] In this embodiment, the dynamic topological response screening map data is represented by a labeled graph structure: wherein P is the set of polymeric particles of step S1, A c is the compressed adjacency matrix, L is the set of fracture sensitive energy chain data of step S301, Λ = {l m | i m ∈ {cutting zone, buffer zone, reconstitution zone} is the set of particle labels.

[0078] Further, the application of the atlas data in the soft fracture simulation is embodied as: the cutting zone label indicates a high-risk domain where topological splitting is about to occur, the buffer zone transmits and absorbs elastic deformation, and the reconstitution zone maintains structural integrity. In particular, the atlas provides a partition basis for subsequent label-guided domain identification of step S401. Preferably, the atlas storage adopts a four-tuple sparse tensor format:

[0079] S4, performing domain deformation recovery constraint processing on the atlas data responding to the dynamic topology to generate deformation harmonics recovery atlas data, wherein the domain deformation recovery constraint processing is a combination of regional identification, local structure redirection, and deformation phase reconstruction based on the partition labels, to form a continuous and controllable recovery constraint model;

[0080] Specifically, please refer to the accompanying Figure 2 illustrated, this step includes the following sub-steps:

[0081] S401, performing label-guided domain identification processing on the atlas data responding to the dynamic topology to generate partition correlation graph data, wherein the label-guided domain identification processing is to construct an adjacency label tensor field based on the label information of the cutting zone, the buffer zone, and the reconstitution zone, and to regularize and cluster the topological difference degree of the boundaries of each region through a continuity enhancement factor, to output a region boundary relationship graph and a structure classification matrix;

[0082] In some embodiments, the label-guided domain identification processing based on the label information of the cutting zone, the buffer zone, and the reconstitution zone to construct an adjacency label tensor field and to regularize and cluster the topological difference degree of the boundaries of each region through a continuity enhancement factor includes adjacency topology field construction processing and boundary regularized clustering processing. In particular, the adjacency topology field construction processing constructs a label tensor field describing the adjacency relationship of the regions according to the particle label distribution; and the boundary regularized clustering processing optimizes the topological consistency of the boundary regions through a continuity enhancement factor. It should be noted that the two processes are coupled through a label compatibility matrix, which quantifies the topological connection strength between different label regions.

[0083] In this embodiment, the adjacency topology field construction processing performs the following mathematical process: let the dynamic topology response screening atlas data be P = {pi}i∈Λ, where the set of particle labels is Λ = {l m}. Define the adjacency label tensor field: Preferably, the label compatibility matrix is increased: where B is the adjacency label tensor field with dimension K x K, m, n are the index of aggregated particles (1≤m,n≤K), the element value of the compressed adjacency matrix at position (m, n), l m , n is the label value of particle p m and p n (taking value set {cut region, buffer region, reconstruction region}), x m , x n is the spatial coordinate vector of particle p m and p n , ||·|| is the Euclidean distance calculation operator, C is the label compatibility matrix with dimension 3 x 3, a, b are the region label type index (for example, a = 1 represents the cut region, a = 2 represents the buffer region, and a = 3 represents the reconstruction region), and it needs to be explained that the physical meaning of the element value C ab of the label compatibility matrix is the topological connection strength between the unit particle pair in the label a and the label b. When a = b, C aa reflects the internal connection density of the same label region; when a ≠ b, C ab characterizes the boundary connection strength between different label regions. That is, the positive elements of the tensor field identify the internal connection of the same label region, and the negative elements record the cross-label boundary distance.

[0084] In some embodiments, the boundary regularization clustering process introduces a continuity enhancement factor γ to optimize the topological difference degree. Specifically, the boundary particle set V b is defined as: V mn = {m | there exists an adjacent particle n such that B mn < 0}, where m is the current particle index, n is the adjacent particle index that has topological connection with the particle m (satisfying ), B m is the adjacency label tensor field element (taking a negative value when l n ≠ l b ). The topological difference degree calculation model is: where N b (m) represents the adjacent particle set of particle m in the boundary region (satisfying n ∈ V m and ), ||x n -x -6 ||2 is the Euclidean distance between particles m and n, is the compressed adjacency matrix element (characterizing the original connection strength), ε is a very small positive number (to prevent division by zero error, taking 10 -6 ), and Label compatibility matrix element (value range [-1, 1]), |·| is an absolute value operator. Its regularized clustering iteration formula is: In the formula , the region label of the particle m at the kth iteration (value in the cutting zone / buffer zone / reconstruction zone) is represented, a represents the candidate label variable (traverse all region types), γ represents the continuity enhancement factor (defined as γ = λexp(-βk), where λ is the initial enhancement intensity and β is the decay rate), , represents the topological difference of particle m at the kth iteration, is an indicator function: when the current label of the particle is not equal to the candidate label a, the function value is 1, otherwise it is 0; is an indicator function: when the label of the adjacent particle n is equal to the candidate label a, the function value is 1, otherwise it is 0. This process gradually merges the fragmented boundary region to the label domain with higher physical consistency.

[0085] In this embodiment, the output data contains two types of core structures: region boundary relationship graph R = <V r ,ε r >, where V r = {r i} is the vertex set, where r i represents the same label connected region (i.e. the aggregated particle subset satisfying ). ε r = {(r i , r j )} is the edge set, where the edge (r i , r j ) exists if there exists a particle m ∈ r i and a particle n ∈ r j satisfying B mn <0 (i.e. there is a physical adjacent boundary between the two regions); the structure classification matrix , the row index i corresponds to the region r i ∈ V r , and the column index k takes a specific value k = 1 is the cutting zone label, k = 2 is the buffer zone label, and k = 3 is the reconstruction zone label. Then the element assignment rule is: , where V b is the boundary particle set, |r i ∩ V b | represents the number of particles in the region r i located on the boundary, and |r i | is the total number of particles in the region. Preferably, the third column of the matrix stores the buffer sub-class identifier: Further, the partition association graph data is represented by a binary tuple mathematical model: D part= <R, S>, in particular, the data plays a role in the simulation of soft fracture as follows: the region adjacency graph R describes the spatial adjacency topology among the cut zone, buffer zone, and reconstruction zone, and the structure classification matrix S records the physical property weights of each region and the buffer zone subclasses.

[0086] S402, the inter-regional deformation vector field redirection processing is performed on the region association graph data to generate multi-domain structure pointing graph data, the inter-regional deformation vector field redirection processing is based on the structure classification matrix to construct a three-state deformation response template, and an inter-regional pointing boundary update mechanism is driven by a minimum deformation tensor overlap rate to output a multi-domain boundary deformation consistent structure vector graph, the three-state deformation response template includes a cut splitting response, a buffer elastic transfer response, and a reconstruction fusion response.

[0087] In some embodiments, the inter-regional deformation vector field redirection processing is based on the structure classification matrix to construct a three-state deformation response template, and an inter-regional pointing boundary update mechanism is driven by a minimum deformation tensor overlap rate, which includes response template construction processing and boundary pointing optimization processing. In particular, the response template construction processing generates region deformation constraint rules according to the label type of the structure classification matrix and the buffer zone subclass identifier; the boundary pointing optimization processing iteratively updates the boundary deformation direction by the minimum criterion of the deformation tensor overlap rate. It should be noted that the two processes are coordinated by a deformation consistency operator, which quantifies the physical compatibility of the deformation vectors of adjacent regions.

[0088] In this embodiment, the response template construction processing defines a three-state deformation response function:

[0089] Cut splitting response: acting on the cut zone label region (S i1 = 1) where u is the particle displacement vector, n b is the boundary normal vector. This function decomposes the displacement along the tangential direction of the boundary to achieve material separation.

[0090] Buffer elastic transfer response: acting on the buffer zone label region (S i2 > 0) where λ1, λ2 are elastic attenuation coefficients.

[0091] Reconstruction fusion response: acting on the reconstruction zone label region (S i3 = 1)f rec (u) = u + βΔu avg where is the neighborhood average displacement, and β is the fusion gain.

[0092] In some embodiments, the boundary pointing optimization processing performs the following process: let the adjacent regions r i , r jthe set of boundary vertex pairs of r ij is defined as i j mn where is the boundary tangent vector of r i j is the response function of r ij is the set of boundary vertex pairs of r i and r j , |P ij | is the number of boundary vertex pairs, m is the vertex index in r i , n is the vertex index in r j , u m is the displacement vector of vertex m, u n is the displacement vector of vertex n, and ||·|| is the vector norm. The objective function is minimized as where (r i , r j ) is the adjacent region pair, μ is the displacement variation regularization coefficient, u (k) is the vertex displacement vector set of the kth iteration, and ||·||2 is the Euclidean norm. The boundary vertex displacement is iteratively updated by the gradient descent method as where u is the displacement vector of vertex m in the kth iteration, γ is the gradient descent learning rate, is the partial derivative of the objective function L with respect to the displacement vector of vertex m.

[0093] In this embodiment, the multi-domain structure directed graph data is represented by a graph structure with deformation vectors as where V d = {v i |v i ∈ V r} is the region vertex set (inherited from the region boundary relationship graph R), ε d = {e ij |(r i , r j ) ∈ ε r} is the region connection edge, F = {(f i , D i )} is the region deformation attribute set, including the response function type identifier f i ∈ {cut, buf, rec} and the boundary deformation tensor where V is the boundary vertex set of r i , is the cardinality (number of vertices) of the boundary vertex set, and m is the boundary vertex index,​​​​ u m displacement vector of the particle m, n m is the unit normal vector at the particle m, Tensor product (outer product) operator. Specifically, the role of this data in the simulation of flexible fracture is embodied in: the multi-domain boundary deformation consistent structure vector diagram is constrained and optimized by the response function, so that the cutting zone produces directional separation displacement, the buffer zone absorbs deformation energy, and the reconstruction zone maintains topological continuity.

[0094] S403, the deformation phase reconstruction processing is performed on the multi-domain structure pointing graph data to generate deformation harmonic recovery graph data, the deformation phase reconstruction processing is performed by constructing a multi-scale deformation phase graph convolution template, locally embedding a fracture gap completion term in the cutting zone, introducing a deformation release factor in the buffer zone, introducing a continuity expansion function in the reconstruction zone, and uniformly constructing a phase splicing index graph, realizing the continuity connection between regions and outputting the deformation harmonic recovery graph data;

[0095] In some embodiments, the deformation phase reconstruction processing is performed by constructing a multi-scale deformation phase graph convolution template, locally embedding a fracture gap completion term in the cutting zone, introducing a deformation release factor in the buffer zone, introducing a continuity expansion function in the reconstruction zone, and uniformly constructing a phase splicing index graph includes partition deformation field convolution processing and cross-domain phase harmonic processing. Specifically, the partition deformation field convolution processing performs multi-scale graph convolution operation based on the deformation attribute set of the multi-domain structure pointing graph data; the cross-domain phase harmonic processing realizes the continuity connection of regional deformation field through partition function embedding and index graph construction. It should be noted that the two processes are coordinated through a phase gradient alignment operator, which uses boundary deformation tensor data to ensure cross-regional deformation coordination. Specifically, this step is to realize the geometric continuity recovery in the fracture scene through partition customized deformation modification and cross-domain coordination mechanism. The processing first uses the multi-domain structure pointing graph data Drive the whole process: where the regional vertex set V d Function: each regional vertex v i corresponds to a homogeneous label region (cutting zone / buffer zone / reconstruction zone), which is the basic unit for deformation field calculation. Its spatial position information is used to determine the neighborhood range of multi-scale convolution, and the regional centroid coordinates are used as the distance calculation reference of the Gaussian kernel function; wherein the regional connection edge ε dFunctions: Defines the adjacency topology between regions, used to filter the set of adjacent regions (i.e., the receptive field of the convolution operation) in multi-scale graph convolution, and directly generates the boundary harmonic field in the phase stitching stage to ensure that the cross-region deformation transmission path is consistent with the physical connection structure; The function of the deformation attribute set F: contains the response function type identifier and the boundary deformation tensor. The response type identifier (cut / buffer / reconstruction) directly determines the specific harmonic function used for the region: the cut region activates the fracture gap compensation mechanism, the buffer applies deformation slow-release attenuation, and the reconstruction region performs continuous expansion enhancement. The boundary deformation tensor serves as the core input feature of multi-scale convolution, and extracts the main pattern of the region deformation phase through three layers of weighted aggregation (near / middle / far neighborhood). The processing flow is divided into two stages:

[0096] First-stage partitioned deformation field convolution: based on V d The regional division is based on ε. d The adjacency relationship is used as the convolution path, and the boundary deformation tensor in F is input into the multi-scale convolution template. This template outputs a multi-scale phase field that integrates macroscopic and microscopic deformation features through spatial weighted aggregation at three scales (local close neighborhood, mid-range correlation domain, and global weakly connected domain), forming the initial restored morphology of the region.

[0097] The second stage involves cross-domain phase harmonics: based on the response type identifier in F, partition correction is performed on the convolution results: a fracture gap compensation term is embedded in the cutting region (supplementing the separation amount along the fracture surface normal when the displacement exceeds the threshold), a deformation mitigation factor is introduced in the buffer (attenuating the displacement proportional to the energy density), and a continuity expansion function is loaded in the reconstruction region (enhancing displacement continuity). Simultaneously, ε is utilized... d The adjacency relationship is used to construct a phase splicing index map, which quantifies the similarity and spatial proximity of the boundary deformation tensors of adjacent regions, drives the weighted fusion of the boundary displacement field, and enables the separation displacement of the cutting region to smoothly transition to the elastic deformation of the buffer zone, and naturally connects the continuous expansion of the reconstruction region.

[0098] The deformation harmonic reconstruction map data generated after the above processing is then... The synergy of the three components transforms the fracture physical response (cut zone separation, buffer zone energy absorption, and reconstruction zone shape preservation) into a computable geometric correction operation, and uses the index map to enforce cross-regional deformation compatibility, providing a geometric consistency basis for subsequent topology repair.

[0099] In this embodiment, the partitioned deformation field convolution processing performs the following procedure: Assume the multi-domain structure points to the graph data. Mid-region vertex set V d ={r i}Associated Boundary Deformation Tensor D i It is worth mentioning that V r Let r be the vertex set of the region boundary relationship graph. iV represents a connected region with the same label (i.e., a subset of aggregated particles). d Inheritance V r The structure will r i Abstracted as graph node v i That is, v i It is region r i Based on the equivalent representation in the graph structure, a multi-scale graph convolution template is constructed: Where s is the scale level, s∈{1,2,3} corresponds to three convolutional scales, and c i Region r i The coordinates of the centroid, g (s) (d) is the Gaussian kernel function. σ s For the scale-dependent radius, W (s) D is a learnable weight matrix. j It is the adjacent region r j The boundary deformation tensor is taken from The F attribute set, N(i) is the region r i The set of adjacent regions is ε d The edge relationships are determined, and σ is the output range constrained by the activation function σ(x)=tanh(x).

[0100] Preferably, the output multi-scale deformation phase field

[0101] In some implementations, the cross-domain phase harmonic processing introduces partitioning functions and indexing mechanisms: defining region-specific deformation harmonic functions:

[0102] Cutting area (f) i =cut): Where H is the Heaviside step function, δ is the gap compensation amount, and θ g n is the fracture threshold. g The normal vector of the fracture surface (from D) i (Main feature direction derivation);

[0103] Buffer (f) i =buf): in Deformation-controlled release factor (S i2 (Taken from the S401 structural classification matrix);

[0104] Reconstruction region (f) i =rec):H rec (u)=u·(1+αtanh(||u||)), where α is the continuous expansion coefficient.

[0105] Constructing a phase splicing index map: wherein: denotes the tensor double dot product. The inter-region harmonic phase field is fused by index weighting: In the present embodiment, the morphing harmonic restoration atlas data is represented by a four-tuple mathematical model: R rec = <Ψ, Θ, I, H>, wherein Ψ = {Ψ } is a set of regional phase fields, I = {I ij} is a set of boundary harmonic fields, I = {I cut , I buf , I rec} is a set of harmonic functions. Specifically, the role of the atlas in the simulation of flexible fracture is embodied as follows: regional morphing features are extracted by a multi-scale convolution template, the partition function embeds a fracture gap compensation (H(·) term) for the cutting zone, applies morphing attenuation (γ b control) for the buffer zone, and enhances continuity (tanh(·) expansion) for the reconstruction zone, and the index atlas I ij achieves smooth transition based on boundary tensor similarity (D i : D j term). Preferably, the atlas data storage adopts a block tensor structure. It should be noted that the atlas provides a geometric restoration benchmark for the construction of the target repair domain in the subsequent S501 step.

[0106] S5, the morphing harmonic restoration atlas data is repaired to generate flexible topological continuity repair data, and the repair processing is performed by constructing a target repair domain and performing structure topology reconstruction and dynamic stability rebound processing.

[0107] Specifically, the step includes the following sub-steps:

[0108] S501, the morphing harmonic restoration atlas data is processed to construct a target repair domain to generate target repair scheduling graph data, the target repair domain construction processing is based on the phase splicing index atlas to screen a set of topological discontinuous nodes, and combined with historical displacement disturbance information of each node, a local repair priority queue is constructed, and a flexible continuity scheduling graph is established globally to realize local repair scheduling sorting;

[0109] In some embodiments, the target repair domain construction process is based on a phase stitching index atlas to screen a set of topological discontinuity nodes, and a local repair priority queue is constructed in combination with historical displacement disturbance information of each node, and a global flexible continuity scheduling graph is established to realize local repair scheduling sorting, including topological fracture point identification processing and repair scheduling graph generation processing. Specifically, the topological fracture point identification processing detects inter-regional deformation discontinuity nodes using a phase stitching index atlas; the repair scheduling graph generation processing fuses historical displacement disturbance data to construct a priority queue and generate a global scheduling topology. It should be noted that the two processes are realized in cooperation through a discontinuity quantization operator, which defines repair urgency by integrating geometric discontinuity characteristics and dynamic disturbance history.

[0110] In the present embodiment, the topological fracture point identification processing performs the following process: set the deformation harmonic restoration atlas data R rec = <Ψ, Θ, I, H> in which the phase stitching index atlas is I = {I ij}. Define the discontinuity degree of the boundary particle b k where N e (k) is the set of inter-regional connection edges containing the particle b k (taken from ε d ). The selection rule of the set of topological discontinuity nodes V disc is specifically that, in the boundary particle set generated by the label-guided structure domain identification processing, the discontinuity degree value of each boundary particle is calculated, which is quantized by the average deviation degree of the index values of the associated region connection edges in the phase stitching index atlas; at the same time, the difference between the current simulation timestamp and the timestamp of the last repair operation accepted by the particle is obtained, the basic discontinuity threshold value is dynamically adjusted by an exponential decay function, and the decay strength is controlled by a time decay coefficient; thereby all boundary particles with a discontinuity degree value greater than the dynamically adjusted threshold value are screened out to form the set of topological discontinuity nodes.

[0111] In some embodiments, the repair scheduling graph generation processing includes a three-stage operation, the first stage performs historical displacement disturbance calculation, which is actually the displacement trajectory u m (τ) calculation of the input node m in the time window [t-T, t] calculates the deviation between the actual displacement and the restoration displacement and integrates the square norm of the deviation and superimposes time decay, thereby quantizing the recent motion instability of the node, and the greater the value, the higher the repair urgency, which directly participates in priority calculation. Specifically, the disturbance energy integral of the particle m ∈ V disc is calculated: where is the deviation between the actual displacement and the restoration displacement, λ is a decay factor for controlling the weight of historical disturbance, and p m is the disturbance energy value of the particle m, e -λ(t-τ) ​is an exponential decay kernel function. The second stage is to construct the local priority queue, specifically, define the repair priority: where Prio(m) is the repair priority value of particle m, d m is the discontinuity, p m is the disturbance energy, is the number of boundary particles directly adjacent to particle m, |Ω m is the total number of particles in the region where particle m is located, and a, b, and g are weight coefficients of geometric / dynamic / topological influences; the third stage is to establish a global scheduling graph, specifically, to construct a flexible continuity scheduling graph where the vertex set V disc is a topological discontinuity node, and the edge set e sch ={(m, n)|||x m -x n ||2<r sch} defines the repair correlation domain, where r sch represents the repair correlation radius, which is a pre-set spatial distance threshold. In the scheduling graph, if the spatial Euclidean distance between two topological discontinuity nodes m and n is less than r sch , a connection edge (m, n) is established, representing that the two nodes need to be repaired cooperatively, and its value is determined according to r sch =k·δ0, where d0 is the baseline clustering radius of step S1, and k is a proportionality coefficient (typical value k e [2, 3]). This design ensures that the correlation domain size matches the original grid resolution, and the vertex attribute Q={q m} stores the priority value and historical disturbance data.

[0112] In this embodiment, the target repair scheduling graph data is represented by a triple model: where is the scheduling graph structure, P=[Prio(m1),...,Prio(m N )] T is the priority vector, is the time series of node fracture generation. Specifically, the role of this data in flexible fracture simulation is as follows: the scheduling graph guides the repair order through the priority queue (P), the correlation domain edge set (e sch ) ensures that spatially adjacent nodes are repaired cooperatively, and the time series (T) records the fracture evolution history. Preferably, the priority queue is maintained in real time using a minimum heap data structure: H=Heapify(P), with an insertion / extraction operation complexity of O(logN), meeting the real-time scheduling requirements. It should be noted that this scheduling graph provides an execution sequence basis for the subsequent topological reconstruction of step S502, ensuring that high disturbance areas (p m terms) and high geometric discontinuity areas (d m terms) are repaired first.

[0113] S502, topology reconstruction and dynamic rebound fusion processing are performed on the target repair scheduling graph data to generate flexible body topology continuity repair data. The topology reconstruction and dynamic rebound fusion processing is based on the topology connection prediction mechanism driven by scheduling priority. Local edge reconstruction is performed on the discontinuous node set and node-by-node elastic rebound harmonization is performed based on the principle of elastic potential energy curvature balance, thereby outputting flexible body topology continuity repair data.

[0114] In some implementations, the fusion of topology reconstruction and dynamic rebound processing is based on a scheduling priority-driven topology connection prediction mechanism. This mechanism reconstructs local edges on discontinuous node sets and performs node-by-node elastic rebound harmonic processing based on the elastic potential energy curvature equilibrium principle. Specifically, the priority-driven topology reconstruction process predicts broken node edges according to the priority queue order of the target repair scheduling graph data; the curvature equilibrium rebound process optimizes node displacement distribution through elastic potential energy curvature constraints. It should be noted that the two processes achieve collaborative iteration through dual convergence conditions of topology and energy.

[0115] In this embodiment, the priority-driven topology reconstruction process performs the following mathematical procedure: Assume the priority queues in the target repair scheduling graph data are arranged in descending order of P. For the current repair node m∈V disc The topology connectivity prediction model is as follows: in θ is the initial distance (taken from the S1 surface particle topology data). g As the geometric similarity threshold, the edge reconstruction rule is defined as follows: Weight Preferably, this operation synchronously updates the compressed adjacency matrix A. c .

[0116] In some implementations, the curvature equalization bounce process performs iterative optimization: defining the elastic potential energy curvature of node m: in (Parameters are taken from the S202 modified parameter set) In other words, the relative displacement, N(m) is the set of adjacent particles of particle m. The potential energy function U is a Hessian matrix sub-block with respect to the coordinates of the particle m and n, which physically represents the local components of the stiffness matrix, ||·|| F The Frobenius norm is used to quantify the curvature intensity of a matrix. κ m The output is the average curvature of the elastic potential energy function at point m, reflecting the spatial rate of change of local deformation energy. The springback displacement update equation is: In the formula Let γ be the mean curvature, and μ be the iteration step size parameters. The convergence condition is: and where max m maximizes disc maximizes the Euclidean norm (L2 norm) of the displacement correction vector of node m at the kth iteration, ε is a preset displacement convergence threshold (scalar constant), and δ k is a preset curvature difference convergence threshold, which requires that the displacement adjustment amount of all nodes is small enough and the curvature distribution is uniform enough.

[0117] In the embodiment, the soft topology continuity repair data is represented by a four-tuple mathematical model: where P adj is a set of repaired particle coordinates is a reconstructed compressed adjacency matrix, X opt is an optimized displacement record matrix, F state = [f m ] T is a node repair state identifier (f m represents repaired).

[0118] Specifically, the data functions in the soft fracture simulation as follows: the adjacency relationship of the fracture area is restored through topology reconstruction, the geometric discontinuous feature is eliminated through elastic rebound reconciliation, and finally a soft model with physical continuity is output. The soft topology continuity repair data includes the reconstructed particle space coordinates, the updated topology connection matrix, the displacement optimization process record, and the node repair state marker, which together constitute a complete soft physical state recovery result.

[0119] Based on the description of the above-mentioned soft physical simulation method based on dynamic topology cutting, the embodiment of the application also discloses a soft physical simulation system based on dynamic topology cutting. The soft physical simulation system based on dynamic topology cutting can be a computer program (including program code) running the above-mentioned soft physical simulation method based on dynamic topology cutting. Please refer to FIG. 11. Figure 3 As shown in FIG. 11, the soft physical simulation system based on dynamic topology cutting can run the following units:

[0120] The topology aggregation construction unit 110 is configured to perform vertex aggregation processing based on dynamic topology mapping on the soft geometry vertex data to generate surface particle topology structure data. The vertex aggregation processing based on dynamic topology mapping is performed by merging adjacent vertices to generate an aggregated particle set and synchronously constructing a compressed adjacency matrix through a Euclidean distance clustering algorithm. The compressed adjacency matrix inherits the original adjacency relationship and is mapped to the aggregated particle space dimension.

[0121] The elastic response modeling unit 120 is configured to perform elastic potential energy constraint modeling processing on the surface particle topology data, the elastic potential energy constraint modeling processing being based on constructing an initial elastic response model according to relative displacement vectors between particles, and combining implicit Euler correction and ductile gradient field extraction mechanism to generate a set of elastic potential energy constraint parameters;

[0122] The energy field analysis and screening unit 130 is configured to perform fracture-sensitive energy field construction and multi-domain response screening fusion processing on the set of elastic potential energy constraint parameters in combination with external input interaction data, the fracture-sensitive energy field construction and multi-domain response screening fusion processing being based on dynamic topology response screening atlas data generated by kinetic energy transmission direction modeling and flux tensor network screening in cooperation, the interaction data including rigid body motion trajectory data and energy penetration threshold data;

[0123] The domain deformation recovery unit 140 is configured to perform domain deformation recovery constraint processing on the dynamic topology response screening atlas data to generate deformation harmonic recovery atlas data, the domain deformation recovery constraint processing being based on region identification, local structure redirection and deformation phase reconstruction in combination with partition labels to form a continuous controllable recovery constraint model.

[0124] The topology repair and harmonic unit 150 is configured to perform repair processing on the deformation harmonic recovery atlas data to generate soft topology continuity repair data, the repair processing being based on constructing a target repair domain and performing structure topology reconstruction and dynamic stability springback processing.

[0125] The above description is only preferred embodiments of the present application, and it should be understood that the present application is not limited to the forms disclosed herein, and should not be considered as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be modified within the scope of the concepts described herein, by the above teachings or related art or knowledge. Any modification and change made by those skilled in the art without departing from the spirit and scope of the present application shall fall within the scope of protection of the appended claims of the present application.

Claims

1. A method for soft body physics simulation based on dynamic topology cuts, characterized in that, The method comprises the following steps: S1, the vertex aggregation processing based on dynamic topological mapping is performed on the flexible geometry vertex data to generate surface particle topological structure data, the vertex aggregation processing based on dynamic topological mapping is to merge adjacent vertices to generate an aggregated particle set by using a Euclidean distance clustering algorithm and to construct a compressed adjacency matrix synchronously, and the compressed adjacency matrix inherits the original adjacency relationship and is mapped to the aggregated particle space dimension; S2, the elastic potential energy constraint modeling processing is performed on the surface particle topological structure data, the elastic potential energy constraint modeling processing is to construct an initial elastic response model based on a relative displacement vector between particles, and to generate an elastic potential energy constraint parameter set in combination with an implicit Euler correction and a toughness gradient field extraction mechanism; S3, the fracture-sensitive energy field construction and multi-domain response screening fusion processing are performed on the elastic potential energy constraint parameter set in combination with external input interaction data, the fracture-sensitive energy field construction and multi-domain response screening fusion processing is to generate dynamic topological response screening atlas data by means of kinetic energy transmission direction modeling and flux tensor network screening in cooperation, and the interaction data comprises rigid body motion trajectory data and energy penetration threshold data; S4, the domain deformation recovery constraint processing is performed on the dynamic topological response screening atlas data to generate deformation reconciliation recovery atlas data, the domain deformation recovery constraint processing is to perform regional identification, local structure redirection and deformation phase reconstruction in combination with a partition label to form a continuous controllable recovery constraint model; S5, the repair processing is performed on the deformation reconciliation recovery atlas data to generate flexible topological continuity repair data, the repair processing is to construct a target repair domain and to perform structure topological reconstruction and dynamic stable rebound processing.

2. The method of claim 1, wherein, The S2 step comprises the following sub-steps: S201, initial elastic potential energy parameters are generated based on a relative displacement vector between particles by means of a particle interconnection calculation model based on surface particle topological structure data, and the initial elastic potential energy parameters comprise particle interconnection elastic stiffness coefficients and damping attenuation factors; S202, the initial elastic potential energy parameters are subjected to implicit Euler error correction and toughness gradient field extraction processing to generate an elastic potential energy constraint parameter set, the implicit Euler error correction and toughness gradient field extraction processing is to dynamically adjust the elastic stiffness coefficients and the damping attenuation factors to balance the constraint force and the motion inertia by means of iterative solution of particle displacement deviation, and to generate toughness gradient field data based on the plastic deformation accumulation rate and the energy dissipation sensitivity in the correction process synchronously.

3. The method of claim 2, wherein, The S3 step comprises the following sub-steps: S301, the fracture-sensitive energy field modeling processing is performed on the elastic potential energy constraint parameter set and the rigid body motion trajectory data to generate fracture-sensitive energy chain data, the fracture-sensitive energy field modeling processing is to calculate kinetic energy transmission directions by means of rigid body motion trajectory integral, to construct a dynamic energy coupling model based on a fracture-sensitive index in combination with the elastic stiffness coefficients, the damping attenuation factors and the toughness gradient field data in the elastic potential energy constraint parameter set, to generate an energy propagation main path and a branch fracture path, and to record the path energy density, the toughness attenuation factor and the fracture-sensitive index; S302, the energy chain data of the fracture sensitivity is combined with the energy penetration threshold data for multi-energy energy retention and decay rate collaborative screening processing to generate dynamic topological response screening map data, the multi-energy energy retention and decay rate collaborative screening processing is through constructing a nonlinear flux tensor network based on the difference between path energy density and penetration threshold, constructing an energy residual domain mapping graph by comprehensively considering the toughness decay factor and fracture sensitivity index of each node in the main path and branch path, and inhibiting false energy diffusion paths through a dynamic penetration redundancy filtering mechanism to realize multi-level labeling partitioning of the structure cutting zone, buffer zone and reconstruction zone.

4. The method of claim 3, wherein, The S4 step includes the following sub-steps: S401, the dynamic topological response screening map data is subjected to label-guided domain identification processing to generate partition correlation graph data, the label-guided domain identification processing is based on the label information of the cutting zone, buffer zone and reconstruction zone to construct an adjacency label tensor field, and the topological difference degree of each region boundary is regularized clustering through a continuity enhancement factor, and a region boundary relationship graph and a structure classification matrix are outputted; S402, the partition correlation graph data is subjected to inter-regional deformation vector field redirection processing to generate multi-domain structure pointing graph data, the inter-regional deformation vector field redirection processing is based on the structure classification matrix to construct a three-state deformation response template, and a inter-regional pointing boundary update mechanism is driven by the minimum deformation tensor overlap rate to output a multi-domain boundary deformation consistent structure vector graph, the three-state deformation response template includes cutting cleavage response, buffer elastic transfer response and reconstruction fusion response; S403, the multi-domain structure pointing graph data is subjected to deformation phase reconstruction processing to generate deformation harmonic recovery map data, the deformation phase reconstruction processing is through constructing a multi-scale deformation phase graph convolution template, locally embedding a fracture gap completion term in the cutting zone, introducing a deformation release factor in the buffer zone, introducing a continuity inflation function in the reconstruction zone, and uniformly constructing a phase splicing index map to realize the continuity connection between regions and output the deformation harmonic recovery map data.

5. The method of claim 4, wherein, The S5 step includes the following sub-steps: S501, the deformation harmonic recovery map data is subjected to target repair domain construction processing to generate target repair scheduling graph data, the target repair domain construction processing is based on the phase splicing index map to screen a set of topologically discontinuous nodes, construct a local repair priority queue combined with historical displacement disturbance information of each node, and establish a flexible continuity scheduling graph globally to realize local repair scheduling sorting; S502, the target repair scheduling graph data is subjected to topological reconstruction and dynamic rebound fusion processing to generate flexible topological continuity repair data, the topological reconstruction and dynamic rebound fusion processing is based on a topological connection prediction mechanism driven by scheduling priority to locally reconstruct the discontinuous node set and perform node-by-node elastic rebound harmonization based on the elastic potential curvature equalization principle, thereby outputting the flexible topological continuity repair data.

6. The method of claim 2, wherein, In the S201, the initial elastic potential energy parameters are generated by a relative displacement vector calculation model based on the surface particle topological structure data, which includes topological connection displacement analysis processing and material constitutive parameter mapping processing.

7. The method of claim 3, wherein, The fracture-sensitive energy field modeling process in S301 is to calculate kinetic energy transmission direction by rigid body motion trajectory integral, combine elastic stiffness coefficient, damping attenuation factor and toughness gradient field data in parameter set of elastic potential energy constraint, construct dynamic energy coupling model based on fracture sensitivity index, generate main path and branch fracture path of energy propagation, and record path energy density, toughness attenuation factor and fracture sensitivity index, including energy flux field construction process and fracture path evolution process; the multi-energy energy retention and decay rate collaborative screening process in S302 is to construct nonlinear flux tensor network based on path energy density and permeation threshold difference, construct energy residual domain mapping graph by combining toughness attenuation factor and fracture sensitivity index of each node in main path and branch path, and inhibit false energy diffusion path by dynamic permeation redundancy filtering mechanism, including flux tensor field construction process and multi-level energy domain segmentation process.

8. The method of claim 4, wherein, The label-guided domain recognition process in S401 is to construct an adjacency label tensor field based on label information of the cutting zone, the buffer zone and the reconstruction zone, and to regularize and cluster the topological difference of the boundary of each zone by a continuity enhancement factor, including adjacency topological field construction process and boundary regularization clustering process. The inter-zone deformation vector field redirection process in S402 is to construct a three-state deformation response template based on a structure classification matrix, and to drive an inter-zone pointing boundary update mechanism by a minimum deformation tensor overlap rate, including response template construction process and boundary pointing optimization process; the deformation phase reconstruction process in S403 is to construct a multi-scale deformation phase map convolution template, locally embed a fracture gap completion term in the cutting zone, introduce a deformation release factor in the buffer zone, introduce a continuity inflation function in the reconstruction zone, and uniformly construct a phase stitching index atlas, including partition deformation field convolution processing and cross-domain phase reconciliation processing.

9. The method of claim 5, wherein, The target repair domain construction process in S501 is to screen a set of topologically discontinuous nodes based on the phase stitching index atlas, construct a local repair priority queue in combination with historical displacement disturbance information of each node, and establish a flexible continuity scheduling graph globally, to realize local repair scheduling sorting, including topological fracture point identification processing and repair scheduling graph generation processing; the topological reconstruction and dynamic rebound fusion processing in S502 is based on a topological connection prediction mechanism driven by scheduling priority, to locally reconstruct the edges of the discontinuous node set and execute node-by-node elastic rebound reconciliation based on the elastic potential energy curvature equalization principle, including priority-driven topological reconstruction processing and curvature equalization rebound processing.

10. A soft-body physics simulation system based on dynamic topology cuts, characterized in that, The system comprises: a topological aggregation construction unit configured to perform vertex aggregation processing on the flexible geometry vertex data based on dynamic topological mapping, to generate surface particle topological structure data, and the vertex aggregation processing based on dynamic topological mapping is to merge adjacent vertices by a Euclidean distance clustering algorithm to generate an aggregated particle set and synchronously construct a compressed adjacency matrix, and the compressed adjacency matrix inherits the original adjacency relationship and is mapped to the aggregated particle space dimension; The elastic response modeling unit is configured to perform elastic potential energy constraint modeling processing on the surface particle topology data, the elastic potential energy constraint modeling processing is based on the relative displacement vector between particles to construct an initial elastic response model, and combined with implicit Euler correction and toughness gradient field extraction mechanism, an elastic potential energy constraint parameter set is generated; The energy field analysis and screening unit is configured to perform fracture-sensitive energy field construction and multi-domain response screening fusion processing on the elastic potential energy constraint parameter set combined with external input interaction data, the fracture-sensitive energy field construction and multi-domain response screening fusion processing is to generate dynamic topology response screening atlas data through kinetic energy transmission direction modeling and flux tensor network screening, and the interaction data includes rigid body motion trajectory data and energy penetration threshold data; The domain deformation recovery unit is configured to perform domain deformation recovery constraint processing on the dynamic topology response screening atlas data to generate deformation harmonic recovery atlas data, the domain deformation recovery constraint processing is combined with partition label to perform region identification, local structure redirection and deformation phase reconstruction, and a continuous controllable recovery constraint model is formed; The topology repair and harmonic unit is configured to perform repair processing on the deformation harmonic recovery atlas data to generate soft topology continuity repair data, the repair processing is to construct a target repair domain and perform structure topology reconstruction and dynamic stability rebound processing.

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