86 results about "Constitutive equation" patented technology

The invention relates to the technical field of computer-aided engineering, in particular to a nonlinear efficient iterative solving method for thermal strain load, which is used for solving an obtained finite element equation by using a modified Newton-Raphson method and comprises the following steps of: firstly, establishing a geometric model to be analyzed and performing grid division; the method comprises the following steps: firstly, setting a model to be analyzed, then setting boundary conditions and temperature field change conditions of the model to be analyzed, finally, inputting the conditions into an algorithm solver, solving a nonlinear equation set, iteratively inputting a load continuously according to a modified Newton-Raphson method in the solving process, calculating node displacement until convergence, and solving stress-strain conditions in the welding process according to a material constitutive relation. In the solving process, by judging the size of the two norms of the displacement increment obtained in the adjacent increment step heuristic stage, the convergence of nonlinear solving of the structure is enhanced through the calculation mode, and the solving speed of the nonlinear problem in the thermal elastic-plastic constitutive structure is increased.

The invention provides a composite material damage type identification method based on multiple characteristic parameters of an acoustic emission signal, which comprises the following steps: designing and carrying out an acoustic emission signal acquisition test aiming at a composite material damage evolution behavior; key acoustic emission signal features are screened out based on a principal component analysis method, and the corresponding relation between a clustering result and a damage form is verified; a transient damage contribution index is proposed based on a clustering result to represent the contribution degree of each damage to the overall damage at a certain moment, and a damage function is proposed in combination with strain energy. The method effectively solves the bottleneck problems of high feature redundancy and serious mode confusion of the traditional acoustic emission signal, perfects the spatial correlation model of the energy release rate and the damage mode in the composite material progressive damage theory, provides an experimental basis for establishing an anisotropic damage constitutive equation considering the laying layer direction, and has a wide application prospect. And a new method is provided for online monitoring of a composite material structure under a complex working condition.

The invention provides a frequency dispersion curve calculation method based on a decoupling type Legendre-Gauss-Labatto spectral element method, and belongs to the technical field of discrete solution of guided wave propagation in a thin plate, and the method comprises the following steps: S1, constructing a wave equation which comprises a Cartesian space coordinate system based on an orthotropic plate, and combining a constitutive equation, a geometrical relationship under the coordinate system and guided wave displacement to obtain a wave dispersion curve; substituting into a control equation when the volume force is zero to obtain an improved three-dimensional elastic wave equation; s2, a differential matrix is constructed, wherein discretization and decoupling are carried out on a wave equation on the basis of a Lagrange interpolation basis function of a Legendre-Gauss-Labatto node; s3, explicitly embedding the stress free boundary condition into the solving process through matrix line transformation, and solving to obtain a frequency dispersion curve, the derivation process is simplified, the boundary and the interior of the material are decoupled, and the physical significance is clearer. And meanwhile, the high-precision advantage of the spectrum method is maintained, and the calculation rate is remarkably improved.

The invention relates to the technical field of industrial adaptive control, in particular to an automatic processing parameter optimization method and system for a five-axis numerical control machine tool. The specific implementation process comprises the following steps: carrying out discrete analysis on machine tool parameters containing a cutter shaft vector and a translation shaft position coordinate, and generating time-varying geometric features; constructing a numerical control machine tool simulation model according to the material constitutive equation and the frequency domain response function, calculating a regenerative flutter prediction sequence, and dividing a real-time parameter feasible region by combining global rigidity and local flexibility data; and performing global iteration optimization on the processing parameter function group by using a multi-target optimization algorithm in the feasible region, and locking a Pareto optimal solution set to perform automatic optimization on the processing process. According to the method, the simulation model containing the physical dynamic characteristics and the real-time parameter feasible region are constructed, flutter and errors caused by stiffness matching imbalance are avoided, collaborative optimization of multiple target variables is achieved, and the productivity efficiency of the numerical control machine tool is remarkably improved on the premise that the machining precision is guaranteed.

The invention relates to the technical field of coal mining and rock mechanics numerical simulation, and discloses a stress field reconstruction method of a plane strain numerical simulation model for coal mining, and the method comprises the following steps: firstly, obtaining an actually measured vertical stress increment and an actually measured bearing pressure peak value position of a stope face; then, an initial plane strain numerical simulation model is constructed, the space error between the peak position of the simulated bearing pressure and the actual measurement position meets a preset threshold value by adjusting the excavation step pitch, and therefore the numerical simulation calculation state is locked to eliminate space-time dislocation; a simulation strain increment is extracted in a locked state, a theoretical vertical stress difference equation is constructed based on an elastic mechanics plane strain constitutive relation, and a parameter inversion equation set is established in combination with multi-measurement-point data; and solving the corrected elastic modulus and Poisson's ratio by using a least square optimization algorithm. According to the method, through physical state locking and incremental theory inversion, system errors are effectively eliminated, and the reconstruction precision and mechanical preciseness of the mining-induced stress field are improved.

The invention provides a true triaxial stratified rock disturbance damage anisotropy model and a numeralization method, and the method comprises the following steps: S1, carrying out a true triaxial static test, and researching a peak intensity rule; s2, carrying out a true triaxial multistage disturbance test, and analyzing a disturbance critical intensity rule and anisotropic disturbance damage evolution characteristics; s3, establishing an anisotropic disturbance damage evolution equation; s4, constructing a stratified rock maximum failure constitutive equation under the true three-dimensional stress; s5, constructing a viscoelastic constitutive equation in which the true three-dimensional stress disturbance effect is introduced; s6, compiling the constitutive model established in S5 into a numeralization subprogram; s7, obtaining the maximum failure function parameter of the stratified rock in the peak state; s8, acquiring a three-dimensional disturbance yield function parameter of the stratified rock in a disturbance critical state; and S9, verifying the prediction effect and applicability of the model on the stratified rock disturbance deformation evolution. According to the invention, theoretical characterization of true three-dimensional stress, dynamic disturbance and spatial stratified coupling effect of stratified rock mass deformation and failure is realized.

The invention discloses a multi-source information fusion distribution transformer state evaluation method and system, and the method comprises the steps: collecting multi-source data, and obtaining a state quantity data set through preprocessing; constructing an electromagnetic thermal coupling model based on the state quantity data set, and outputting space physical field distribution; constructing a causal chain through displacement gradient mutation detection based on space physics field distribution, and outputting coordinates of a fault intrinsic source point; extracting a state response parameter by positioning a fault point based on the coordinates of the fault intrinsic source point, and obtaining an equipment health index through a critical physical parameter; and obtaining a risk score of the distribution transformer according to the equipment health index, and generating a state assessment report through a multi-dimensional risk assessment algorithm. According to the method, the electromagnetic thermal full-coupling model is constructed, and the constitutive equation is fused by adopting the cross-field energy analysis method, so that the hidden defect detection rate and the service life prediction accuracy of the distribution transformer are improved, the service cycle of key power equipment is prolonged, and the operation and maintenance cost is reduced.

The present application relates to a kind of pre-tensioned steel wire rope lateral impact response calculation method considering geometric and friction nonlinear coupling.First, the linear tensile constitutive model of pre-tensioned steel wire rope is constructed, Von Kármán large deflection theory is introduced, and the geometric hardening relationship of the nonlinear growth of axial tension with lateral deflection is established;Subsequently, a bilinear bending stiffness model is constructed to calculate the critical anti-sliding torque that evolves dynamically with tension;Based on the principle of energy conservation and Rayleigh-Ritz method, the system total potential energy functional of axial tensile potential energy and nonlinear bending potential energy is constructed, and the maximum impact deflection and tension response of the steel wire rope are obtained by solving the energy residual equation, the maximum response is substituted back into the constitutive equation, and the maximum nominal stress of the midspan cross section, the maximum axial tension and the extension length of the internal slip zone are calculated.The present application has very high calculation efficiency compared with full-size finite element simulation, and is suitable for the rapid design and safety evaluation of steel wire rope protection system.

The invention discloses an earthquake short-term and temporary prediction system and method based on physical constraint deep reinforcement learning, and the method comprises the steps: firstly carrying out the preprocessing and time-space fusion of a time sequence InSAR image and underground water level monitoring data, and generating a surface strain field and a water level rate field; then, a physical constitutive equation is constructed based on a pore elasticity theory, data driving and physical prior inversion region coupling coefficients are fused, and a physical guidance collaborative anomaly index is calculated; further constructing a deep reinforcement learning agent, and learning an optimal prediction strategy in a physical constraint environment by taking a collaborative anomaly index as a state and issuing early warning, delaying a decision and requesting more observations as actions; and finally, according to the action probability and the abnormal spatial features output by the intelligent agent, dynamically evaluating and predicting the confidence coefficient and the risk level. According to the method, deep fusion of a physical rule and a data driving strategy is realized, the accuracy, robustness and interpretability of earthquake short-term and temporary prediction are remarkably improved, and the false alarm rate is effectively reduced.

The invention relates to the technical field of mine safety monitoring, and discloses a device and method for measuring mining-induced stress, temperature and water pressure of a mine, the device comprises a high-strength metal shell, a hollow connecting rod, a water pressure measuring unit, a strain measuring unit, a temperature measuring unit and a single through optical fiber, and the surface of the shell is provided with a spiral resin grouting channel; a mechanical occlusion structure is constructed through a solid resin entity, and rock mass displacement is equivalently transmitted to a shell. The temperature compensation fiber bragg grating is coated with a heat insulation coating, in-situ rigid coupling is achieved by injecting liquid resin into a grouting channel, the central wavelength peak value of each grating is obtained through the wavelength division multiplexing technology, the environment temperature variable quantity is extracted based on the temperature compensation fiber bragg grating, and therefore the thermally induced drift distance of the strain grating is deducted, and the compensated strain value is obtained. And inverting and outputting the in-situ three-dimensional mining-induced stress state by mapping the constitutive equation set. According to the invention, synchronous high-fidelity acquisition of multi-physics field parameters is realized, and the intrinsic safety characteristic and the electromagnetic immunocompetence are realized.

The application discloses a kind of calculation methods for predicting cement-based material dry shrinkage viscoelastic deformation, comprising the following steps: establishing cement-based material structure model;Using Darcy's law, Fick's law and phase change law to describe the moisture transport behavior occurred in the drying process of cement-based material;Based on the basic law of thermodynamics, the constitutive equation of cement-based material in the drying process is established;Establish humidity-mechanical coupling equation, determine the instantaneous elastic deformation of cement-based material dry shrinkage;Based on Boltzmann superposition principle, determine the time-dependent viscous deformation of cement-based material dry shrinkage, obtain the total deformation of cement-based material dry shrinkage;Determine the calculation parameters, predict the dry shrinkage of target cement-based material under specific conditions.The present application solves the problem that the current cement-based material dry shrinkage viscoelastic deformation prediction model is often an empirical model fitted under specific experimental conditions, with low accuracy, no universality and scalability.

This invention relates to an equivalent accelerated testing method for plexiglass based on creep constitutive equations, belonging to the technical field of accelerated testing of polymer structures. Addressing the testing requirements for the creep performance of plexiglass structures, this invention shortens the testing cycle and saves testing costs through the design of testing temperature and pressure. Simultaneously, the reduced testing time indirectly saves manpower and material resources, and also reduces the frequency of random risks such as power outages and equipment failures. Therefore, the testing method of this invention has significant timeliness and economic efficiency, and can effectively improve the accuracy of quantitative analysis, possessing important value for engineering practice.

The invention relates to a method for calculating linear elastic critical stress of axisymmetric buckling of a large-diameter steel casing. The method comprises the following steps: constructing a constitutive equation and a deformation coordination equation of bending deformation of the axisymmetric steel casing; constructing a bending balance equation of the axisymmetric steel casing; a buckling equation of the axisymmetric steel casing is constructed on the basis of the bending theory, and a general solution of the buckling equation is obtained by solving a high-order differential equation; considering the working condition of the upper part of the steel casing, and introducing a mechanical boundary condition of axial uniform loading; and substituting a general solution form containing radial displacement into the boundary condition, giving a numerical solution by adopting a multi-interval dichotomy, and obtaining a critical buckling stress analytical solution of the cylindrical shell. The method has the beneficial effects that the limitation of a classic beam buckling theory and a buckling theory of only considering a cylindrical thin shell is broken through, the calculation precision of the overall buckling characteristics of the semi-buried steel casing can be improved, and meanwhile, the improvement of the buckling resistance of the steel casing by the characteristics of soil is considered.

This invention discloses a method for simulating and testing ceramic sintering stress and a method for reducing ceramic sintering stress. The simulation and testing method includes: 1. Measuring the grain size, relative density, and geometric dimensions before and after sintering; 2. Using Abaqus to establish the ceramic geometry and construct a transient heat conduction model; 3. Establishing the viscoelastic constitutive equation for the sintering shrinkage deformation of zirconia ceramics and constructing a sintering shrinkage model; 4. Sequentially coupling the transient heat conduction model and the sintering shrinkage model to perform joint simulation of solid-state sintering, obtaining the simulation results of ceramic sintering stress. The method for reducing ceramic sintering stress includes: 5. Establishing a finite element model of ceramic sintering shrinkage with proportionally distributed grain sizes and calculating the average sintering stress distribution of the grain size proportional distribution model; 6. Comparing the average sintering stress of sintering shrinkage models with different grain size proportions to determine the method for reducing sintering stress. This invention improves ceramic sintering quality and production efficiency.

The application discloses a kind of V-shaped slope stability calculation method and system, it is related to strip mining technical field.Based on three-dimensional numerical simulation technology, determine its failure mode first determine the spatial form equation of potential sliding body, then the sliding body is divided into regional division micro column, through constitutive relation and static equilibrium condition, the stress state of micro column is solved, the force of each row micro column is superposed along the direction of main sliding surface, and the two-dimensional equivalent shear strength parameters with three-dimensional effect on each row of main sliding surface micro column are obtained using equivalent idea, then the three-dimensional V-shaped slope stability coefficient is derived using rigid body limit equilibrium method.The application avoids the problems of high calculation cost, difficult parameter determination and complex calculation process in the traditional three-dimensional slope stability calculation method, solves the three-dimensional stability problem of this special form slope, provides more reliable theory and technology for the design, mining, prevention and management of slope, and has important practical significance for ensuring mining safety and efficient production.

The application discloses a kind of based on numerical simulation's silicon nitride sintering process parameter optimization method, including the following steps: to photo-curing 3D printing silicon nitride ceramic is successively implemented and sintered experiment is debound, micro characterization is carried out to the ceramic after sintering, and second characterization result is obtained;Establish the viscoelastic constitutive equation of silicon nitride ceramic sintering shrinkage deformation, based on the viscoelastic constitutive equation in Abaqus Sintering finite element model is constructed, to obtain the simulation result of transient temperature field and the simulation result of sintering shrinkage deformation;Second characterization result is corrected to finite element model, and verified finite element model is obtained;According to verified finite element model, the original sintering process curve is optimized, and the sintering process curve with the lowest cost and the greatest influence on sintering stress reduction is selected as the optimal sintering process, to realize the optimization of sintering process.The sintering process parameter optimization method not only reduces the cost, but also shortens the experimental period, and the production efficiency is high.

The invention discloses a water lubricated bearing rubber interface contact angle numerical simulation system based on a bionic microstructure, and relates to the technical field of mechanical engineering and fluid mechanics, and the system comprises a bionic microstructure parameter module which obtains geometric parameters such as the shape and depth of the microstructure; the multi-physics field coupling calculation module is used for constructing a fluid-solid-heat-electricity four-field bidirectional coupling model, and synchronously calculating a lubricating water flow field, a rubber solid field, a friction heat field, an interface electric field, correction water viscosity, a rubber elastic modulus and interface surface energy in combination with a Navier-Stokes equation, a rubber superelasticity constitutive model and the like; the contact angle solving module is used for solving a dynamic contact angle and a lag amount based on the multi-field parameters, a VOF model and a dynamic contact angle constitutive equation; and the result output module is used for outputting the parameters, the multi-field cloud picture and the contact angle change curve. The simulation precision is improved, data support is provided for water lubricated bearing bionic structure optimization, and the environment-friendly lubrication requirement is met.

The invention discloses a longitudinal wave dispersion and attenuation calculation method based on jet flow and wave-induced flow coupling. The method comprises the following steps: establishing a unified coupling model of fluid saturation periodic layered medium microscopic jet flow and mesoscopic wave-induced flow; setting a stiffness matrix and boundary conditions of the unified coupling model; establishing a unified coupling model constitutive equation; calculating each parameter of the stiffness matrix; calculating a longitudinal wave speed and a transverse wave speed when incident at any angle; and frequency dispersion and attenuation of the longitudinal wave velocity and the transverse wave velocity during incidence at any angle are calculated. According to the method, the change of the longitudinal wave speed and the transverse wave speed in the model is calculated by calculating the stiffness matrix of the fluid saturated periodic layered medium microscopic jet flow and mesoscopic wave induced flow unified coupling model, so that the speed dispersion and energy attenuation characteristics and the change rule of the longitudinal wave and the transverse wave when the longitudinal wave and the transverse wave are incident at any angle are analyzed.

The invention discloses a grouting coupling simulation method and system based on a diffusion model and time-varying rheology, and relates to the technical field of geotechnical engineering grouting numerical simulation. Current geological data are input into the diffusion model to generate grouting initial parameters; automatically identifying and dividing a plurality of solidification stages of the slurry based on the multi-source sensing data; based on a stage division result, performing dynamic inversion and analysis on parameters in the time-varying rheological constitutive equation of the slurry to obtain time-varying rheological parameters, and coupling the time-varying rheological parameters to a constitutive relation of a multi-physics field coupling control equation set in real time; and when the slurry density of a certain area in the computational domain is lower than a critical density threshold value, activating the fluid model for solving, when the slurry density reaches or exceeds the critical density threshold value, switching the area to a solid mechanical model for solving, and dynamically optimizing grouting parameters based on a reinforcement learning algorithm. Simulation parameters and a calculation model are dynamically adjusted through an AI system, and continuous and accurate simulation of the whole process of slurry from liquid pouring to solid phase change is achieved.

This invention discloses an efficient transient analysis method for electromagnetic-thermal-fluid multiphysics fields on integrated chips. Focusing on electromagnetic, thermal, and fluid fields as core research objects, and centering on typical scenarios of full electromagnetic-thermal-fluid coupling, it systematically integrates the governing equations, boundary conditions, and constitutive relations of each physical field to construct a unified set of coupled partial differential equations. Under the premise of verifying and satisfying the stability conditions of all physical field discretization schemes, simultaneous numerical solutions for the multiphysics fields are achieved through FDTD. This invention, through multi-faceted synergistic optimization, achieves comprehensive adaptation to complex structures, providing reliable technical support for solving various complex engineering multiphysics coupling problems.

The invention relates to a method for constructing a rock salt nonlinear damage creep constitutive model considering a temperature effect. The method comprises the following steps: constructing an element combination model formed by connecting an elastomer, a nonlinear viscous body and a generalized Kelvin body in series as a basic framework of the rock salt nonlinear damage creep constitutive model considering the temperature effect; introducing a damage variable related to time and temperature; establishing a constitutive equation of the nonlinear viscous body of the salt rock; based on the constitutive equation of the salt rock nonlinear viscous body, deducing a total creep strain expression of a salt rock nonlinear damage creep constitutive model considering the temperature effect in a one-dimensional stress state; and carrying out uniaxial compression creep tests on the salt rock sample at different temperatures by adopting a graded loading mode to obtain strain-time data and a corresponding creep curve of the salt rock sample at the corresponding temperature, and carrying out inversion to determine model parameters in the total creep strain expression. The invention also provides a long-term deformation prediction method of the salt-cavern underground gas storage cavern structure.

The invention provides a deep-sea sediment dynamic shear strain calculation method, device and equipment, and the method comprises the steps: firstly carrying out a test, collecting transient disturbance response data and long-term creep deformation data, and constructing a dynamic shear rheological constitutive equation comprising a static strain component and a dynamic strain component; each strain component is expressed through a time-related structural evolution parameter, then parameters in a constitutive equation are calibrated by using the collected data, and the parameters are substituted into the constitutive equation to obtain a calculation result, so that the structural evolution parameter is innovatively introduced to couple transient disturbance and long-term creep characteristics, and the calculation result is obtained through dynamic and static separation solution and multi-parameter collaborative prediction. The method realizes high-precision calculation of the dynamic shear strain, is suitable for working conditions of different shear stresses and loading frequencies, and provides reliable theoretical support for safe operation design of deep-sea mining vehicles.

The invention provides a woven composite material multi-scale analysis method based on clustering order reduction, and belongs to the technical field of composite material multi-scale damage evolution evaluation. The method comprises the following steps: 1, defining a microscopic damage constitutive model; defining a fiber damage constitutive equation and a matrix damage constitutive equation; 2, solving an RVE damage problem by using an SCA method; the method comprises the following steps: for a composite material RVE region, converting a control equation of elastic mechanics into a solving L-S equation by introducing reference stiffness; the SCA method comprises an offline stage and an online stage. Step 3, establishing an FE-SCA2 concurrent three-scale model; and the numerical value is solved. According to the method, the problem of low three-scale calculation efficiency is relieved while nonlinear calculation high precision is achieved, and the method has high application value in the field of composite material structure multi-scale calculation.

This invention relates to the field of rail transit technology, and more particularly to a method and system for calculating the coupled dynamics of high-speed rail vehicles and tracks. The constitutive equations of the fractional-order Zener model are transformed into a CA mortar layer model, and its numerator operator is expressed as a discrete series to obtain the target CA mortar layer model. The ground reaction force of the CA mortar layer acting on the track slab is then obtained. Based on the ground reaction force of the CA mortar layer acting on the track slab, the vibration differential equations of the track slab are constructed. The vibration differential equations of the track slab are transformed into a set of ordinary differential equations in modal coordinates containing fractional-order terms using the Ritz method. Taking a half-car model as the vehicle subsystem, the vibration differential equations of the rail in modal coordinates and the set of ordinary differential equations in modal coordinates containing fractional-order terms of the track slab are integrated into the track subsystem to construct the coupled dynamics model of the high-speed rail vehicle and track. This invention effectively improves the accuracy of vehicle-track coupled dynamics calculations.

The invention relates to a method and device for evaluating the deformation capacity of a current collector in an electrode, equipment, a medium and a program product, and the method comprises the steps: simulating the deformation process of the current collector due to the expansion of the electrode through a finite element simulation model of the current collector, and obtaining the deformation of different positions in the finite element simulation model; according to the stress-strain constitutive equation of the material used by the current collector and the deformation amount of different positions in the finite element simulation model, the maximum stress generated by the finite element simulation model is obtained, and the stress-strain constitutive equation represents the mathematical relationship between the stress and the strain of the material used by the current collector in the deformation process; and determining the deformability of the current collector according to the maximum stress generated by the finite element simulation model and the pre-tested fracture stress when the material used by the current collector is fractured, and representing the maximum deformation borne by the current collector in the working process of the electrode by the deformability. Therefore, the maximum deformation borne by the current collector in the working process of the electrode can be quickly evaluated at low cost.

The application provides a method for transplanting a FENE-P model to construct an OpenFOAM solver, which comprises the following steps: selecting source code of the FENE-P model, and confirming code corresponding to a constitutive equation of the FENE-P model; modifying TEqn.H of rheoTestFoam, and transplanting the code corresponding to the constitutive equation of the FENE-P model to TEqn.H; modifying creatFields.H of rheoTestFoam, and defining new variables and commenting irrelevant variables; selecting an environment to compile, and determining a position for compiling the OpenFOAM solver; and verifying the OpenFOAM solver after the compilation is completed. The application can help users to construct a solver according to self needs, which is a very important breakthrough for turbulence research.

The application discloses a tunnel surrounding rock creep damage constitutive model construction method based on an energy conservation theorem, relates to the technical field of geotechnical engineering, and comprises the following steps: S1, regarding the rock mass in the preset range of the tunnel surrounding rock excavation line as a closed system, sampling and processing the rock, carrying out triaxial compression creep test, and obtaining creep data and test results; S2, based on the energy conservation theorem, a constitutive equation for describing unstable creep of the tunnel surrounding rock is established, a creep constitutive basic model for the tunnel surrounding rock is determined based on a unified rheological mechanics model theory, the constitutive equation is embedded into the creep constitutive basic model, and a tunnel surrounding rock creep damage constitutive model is established; and S3, model parameters are divided into test parameters and analytical parameters, and the parameter values of the test parameters and the analytical parameters are determined respectively. The application can clearly reflect the nonlinear characteristics of tunnel surrounding rock creep, better simulate the tunnel surrounding rock creep behavior, and the correlation coefficient square is improved by 10% compared with traditional models in the simulation of unstable creep behavior.

The invention discloses an integral transformation cohesion fracture phase field simulation method and device based on staggered iteration. The method is applied to finite element simulation software and comprises the following steps: establishing a geometric model of a material to be simulated, and performing mesh generation on the geometric model to obtain a mesh model; determining a constitutive relation between strain and stress based on the energy degradation function, the elastic stiffness tensor of the to-be-simulated material and inherent mechanical parameters; determining a control equation based on the dissipative function functional, the energy storage function and the thermodynamic law; obtaining a residual equation according to the control equation and the constitutive relation; the intrinsic mechanical parameters comprise fracture energy, intrinsic characteristic length, Young modulus, tensile strength, shear modulus and shear strength; applying a load condition on the outer boundary of the grid model, and solving to obtain a phase field distribution result by gradually loading a load step based on staggered iteration; and for each load step, when the residual error calculated by the residual error equation reaches a convergence condition, determining that the iteration of the load step is completed. The method can be implemented in ABAQUS software, and is suitable for large-scale engineering application.

The invention discloses a coal mine fault stick-slip instability critical stress criterion method based on a speed-state friction law, and the method comprises the steps: building a mining overburden rock mechanical model, combining a fault speed-state friction constitutive equation, quantitatively calculating a dynamic friction coefficient, and then building a fault stick-slip instability critical stress criterion. Advanced and accurate early warning of fault slippage instability is achieved, and the defect that traditional static friction criterion early warning is low in reliability is overcome.

The invention belongs to the technical field of heat treatment process parameter optimization, and particularly relates to a wear-resistant steel ball structure and hardness distribution data obtaining method and system.The method comprises the steps that firstly, material characteristic parameters are obtained through calculation and experiments according to alloy steel components; constructing an axisymmetric three-dimensional steel ball model, integrating material characteristics and heat treatment process parameters, embedding heat transfer, phase change and stress-strain constitutive equations, and compiling to form a multi-physics field coupling finite element model; solving the model to obtain spatial and temporal change data of temperatures, phase change rate constants, transformation volume fractions and hardness of different positions of the steel ball, and fitting through MATLAB to obtain a structure and hardness evolution rule; and finally, outputting optimal wear-resistant steel ball parameters through parameterized scanning and model optimization. The problem that in the prior art, an effective tissue and hardness data obtaining means is lacked in the heat treatment process of the steel balls can be solved.