A numerical simulation method and system for irregular contact between a pipe inner wall and a lining layer

Abstract

This invention provides a numerical simulation method and system for irregular contact between the inner wall and lining of a pipeline. The method includes: first, establishing a three-dimensional model of the pipeline and the lining, assembling and positioning them, and extracting the inner wall of the pipeline and the outer wall of the lining as the contact interface, and establishing corresponding contact pairs; defining tangential contact properties for the contact pairs, specifying a user-defined friction subroutine, and setting user parameter arrays and state variable arrays; then, constructing an interface friction constitutive model based on the frictional physics mechanism of the contact interface; during the finite element incremental analysis, obtaining the current normal pressure, shear displacement increment, state variables, and user parameters through the user-defined friction subroutine, calculating the interface trial shear stress of the current incremental step, and determining the actual shear stress and corresponding tangential stiffness of the interface based on the contact state; and writing the historical relevant data of the current incremental step into the state variable array for subsequent incremental steps to call. This invention can more reasonably characterize the interface shear stress, slip state, and contact evolution process.

Description

Technical Field

[0001] This invention relates to the field of finite element simulation analysis technology, and in particular to a numerical simulation method and system for irregular contact between the inner wall and the inner lining of a pipe. Background Technology

[0002] During the repair of pipeline linings, the contact state between the inner wall of the pipeline and the lining layer will affect the interfacial stress transfer, relative slippage and overall stress response. Therefore, it is necessary to reasonably model the contact behavior between the two.

[0003] In existing finite element analysis, the interface relationship between the inner wall of a pipe and its lining is typically simulated by defining contact pairs. The FRIC subroutine in ABAQUS can be used to establish the relationship between interfacial shear stress and shear displacement to define the frictional behavior of the contact surface. However, the conventional default contact model has limited ability to describe complex interfacial shear behavior and cannot fully reflect the nonlinear evolution characteristics of interfacial shear stress caused by changes in normal pressure, slip process, and historical state.

[0004] In addition, existing modeling methods lack effective handling of the irregular contact characteristics between the inner wall and the inner lining of the pipe during finite element incremental analysis, such as how to pass interface model parameters through user parameter arrays, record interface history information through state variable arrays, and dynamically update interface shear stress and tangential stiffness accordingly.

[0005] Therefore, a numerical simulation method and system for irregular contact between the inner wall and the inner lining of a pipe is needed to achieve dynamic modeling of the irregular contact interface between the inner wall and the inner lining of the pipe, so as to more reasonably characterize the interface shear stress, slip state and contact evolution process. Summary of the Invention

[0006] The purpose of this invention is to provide a numerical simulation method and system for irregular contact between the inner wall and the inner lining of a pipe, aiming to solve the technical problem that existing methods are unable to accurately characterize the irregular, nonlinear, and historically correlated contact behavior between the inner wall and the inner lining of a pipe.

[0007] To achieve the above objectives, in a first aspect, the present invention provides a numerical simulation method for irregular contact between the inner wall of a pipe and its lining layer, the steps of which include:

[0008] S1. Establish a three-dimensional geometric model of the pipe and the inner lining, and assign corresponding material properties;

[0009] S2. Assemble and position the pipe and the inner lining, extract the inner wall of the pipe and the outer wall of the inner lining as the contact interface, and establish the corresponding contact pair.

[0010] S3. Define tangential contact properties for the contact pair, specify a user-defined friction subroutine, and set a user parameter array and a state variable array;

[0011] S4. Establish an interface friction constitutive model based on the tribophysical mechanism of the contact interface;

[0012] S5. During the finite element incremental analysis, the user-defined friction subroutine receives the current normal pressure, shear displacement increment, state variables and user parameters, calculates the interface trial shear stress under the current incremental step, and determines the actual interface shear stress and corresponding tangential stiffness based on the contact state.

[0013] S6. Write the historical relevant data generated in the current incremental step into the state variable array for subsequent incremental steps to call, and complete the numerical simulation of the irregular contact between the inner wall of the pipe and the inner lining.

[0014] As a further improvement to the above scheme, in step S2, the inner wall of the pipe with greater stiffness and / or coarser mesh is defined as the main contact surface, and the outer wall of the inner lining is defined as the secondary contact surface, so as to establish a surface-to-surface contact pair.

[0015] As a further improvement to the above scheme, the user parameter array includes at least one or more of the following: initial friction coefficient, shear stiffness, hardening parameter, and softening parameter.

[0016] As a further improvement to the above scheme, the state variable array is used to store historical data related to the interface, and the historical data related to the interface includes at least one or more of the following: equivalent plastic slip, current friction coefficient, damage variable, local slip history, and contact state identifier.

[0017] As a further improvement to the above scheme, in step S4, the interface friction constitutive model is any one of the slip weakening friction model, Coulomb friction model, rate-state friction model, or thermal-pore pressure coupled friction model.

[0018] As a further improvement to the above solution, in step S5, the user-defined friction subroutine is a FRIC subroutine;

[0019] The FRIC subroutine receives the current normal pressure PRESS, shear displacement increment DSHEAR, state variable array STATEV, and user parameter array PROPS from the finite element main program, and calculates the interface shear stress and tangential stiffness based on the interface friction constitutive model.

[0020] As a further improvement to the above scheme, in step S5, the trial shear stress under the current incremental step is first calculated in the FRIC subroutine, and then the trial shear stress is corrected according to the yield criterion to determine the actual shear stress of the interface and the corresponding tangential stiffness.

[0021] The determination of the actual shear stress and corresponding tangent stiffness of the interface is achieved using a return mapping algorithm.

[0022] As a further improvement to the above scheme, in step S6, the slip stage of the interface is determined based on the local slip amount between the current increment and the previous increment, and different shear stress update relationships are adopted according to different slip stages.

[0023] Local slip updates and interface shear stress calculations are performed along two tangential directions of the contact interface.

[0024] As a further improvement to the above scheme, the numerical simulation method also includes: meshing the pipe and the inner lining and performing finite element analysis to extract the interface shear stress, relative slip and state variable results, and comparing the obtained results with theoretical solutions and / or experimental data to verify and calibrate the interface friction constitutive model.

[0025] Secondly, the present invention also provides a numerical simulation system for irregular contact between the inner wall of a pipe and its lining, characterized in that it comprises:

[0026] The geometry modeling module is used to create three-dimensional geometric models of pipes and linings and assign material properties;

[0027] The contact interface construction module is used to extract the inner wall of the pipe and the outer wall of the inner lining as the contact interface and establish contact pairs;

[0028] The contact property configuration module is used to define tangential contact properties and specify user-defined friction subroutines;

[0029] This constitutive modeling module is used to build interface friction constitutive models;

[0030] The interface response calculation module is used to receive the current normal pressure, shear displacement increment, state variables and user parameters during the finite element incremental analysis process, and calculate the actual shear stress and corresponding tangential stiffness of the interface.

[0031] The state update module is used to write the historical relevant data generated by the current incremental step into the state variable array to complete the irregular contact numerical simulation.

[0032] Thirdly, the present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, is used to implement the steps of the numerical simulation method for irregular contact between the inner wall and the inner lining of a pipe as described in the first aspect.

[0033] Because the present invention adopts the above technical solutions, the beneficial effects of the present invention are as follows:

[0034] This invention provides a numerical simulation method for irregular contact between the inner wall and the inner lining of a pipe. Compared with the modeling method using default friction contact or constant friction coefficient contact, this invention introduces a user-defined friction subroutine in the contact analysis and establishes a friction constitutive model based on the interface physical mechanism. This makes the interface shear stress and tangential stiffness no longer fixed values, but can dynamically change with the current normal pressure, shear displacement increment and interface history state, thus making it more suitable for characterizing the complex and nonlinear contact response between the inner wall and the inner lining of the pipe.

[0035] Furthermore, by setting up an array of state variables and passing historical data between incremental steps, this invention enables the model to record historical interface slip, current friction state, and damage evolution information. This avoids simplifying interface behavior to a single instantaneous response and improves the ability of numerical simulation of irregular contact to represent the actual interface evolution process. Especially when the interface contact state changes, the state variables can still provide historical data for subsequent shear stress updates, giving the contact model stronger continuity and physical consistency.

[0036] Furthermore, the present invention updates the interface stress based on the trial shear stress and yield judgment in the subroutine, and can use the return mapping algorithm to determine the actual shear stress and corresponding tangent stiffness of the interface, which is beneficial to improve the rationality of solving the interface nonlinear response while ensuring the stability of the calculation.

[0037] Furthermore, this invention extracts interface shear stress, relative slip, and state variable results through post-processing, and compares the shear stress-shear displacement curves at key points with theoretical solutions or experimental data to verify the correctness of the subroutine and calibrate constitutive parameters. Therefore, this invention not only completes the establishment of the contact model but also forms a closed-loop analysis process of "modeling-solving-verification-calibration," which is beneficial to improving the engineering application value of the model in pipeline repair analysis scenarios.

[0038] In some preferred embodiments, the present invention determines the slip stage of the interface by using the local slip amount between the current increment and the previous increment, and adopts different shear stress update relationships according to different slip stages, which can more accurately reflect the changes in mechanical response of the interface during the evolution process from bonding, initiation to slip; at the same time, performing local slip amount update and shear stress calculation along the two tangential directions of the contact interface respectively is beneficial to improving the ability to express the directional response under complex contact conditions. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0040] Figure 1 This is a flowchart illustrating a numerical simulation method for irregular contact between the inner wall and lining of a pipe, as disclosed in this invention.

[0041] Figure 2 This is a schematic diagram of the pipe inner wall and inner lining layer disclosed in this invention, wherein, Figure 2 (a) is a schematic cross-sectional view of the inner wall of the pipe model. Figure 2 (b) is a three-dimensional schematic diagram of the inner lining model;

[0042] Figure 3 This is a flowchart illustrating the FRIC subroutine disclosed in this invention;

[0043] Figure 4 This is a schematic diagram of the finite element simulation deformation of the pipe lining disclosed in this invention.

[0044] Figure 5 This is a schematic diagram comparing the finite element simulation results and experimental results disclosed in this invention, wherein, Figure 5 (a) is a schematic diagram comparing the finite element and full-scale experimental curves outside the spigot and socket. Figure 5 (b) is a schematic diagram comparing the finite element and full-scale experimental curves inside the spigot and socket.

[0045] The objectives, features, and advantages of the invention will be further explained in conjunction with the implementation methods and with reference to the accompanying drawings. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0047] It should be noted that the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0048] Example 1

[0049] See Figures 1-5 This invention provides a numerical simulation method for irregular contact between the inner wall and the inner lining of a pipe, aiming to solve the technical problem that existing methods are unable to accurately characterize the irregular, nonlinear and historically related contact behavior between the inner wall and the inner lining of a pipe, thereby achieving a more reasonable description of the shear stress, slip state and contact evolution process of the contact interface.

[0050] See Figure 1 The specific implementation steps are as follows:

[0051] S1. Establish a three-dimensional geometric model of the pipe and the inner lining, and assign corresponding material properties.

[0052] A three-dimensional geometric model of the pipeline is established based on the structural dimensions of the object to be analyzed, and a three-dimensional geometric model of the inner lining layer that matches the pipeline is also established. The pipeline can be a metal pipeline, a composite material pipeline, or other tubular structure with internal wall load-bearing function, and the inner lining layer can be a repair lining, an anti-corrosion lining, a reinforcement lining, or other lining structure set inside the pipeline.

[0053] After establishing the geometric model, corresponding material properties are assigned to the pipe and the liner. These material properties may include elastic modulus, Poisson's ratio, density, and other mechanical parameters related to structural deformation analysis; if necessary, plastic parameters, viscoelastic parameters, or damage parameters may also be assigned. By establishing independent three-dimensional models of the pipe and the liner and assigning corresponding material properties, a clear geometric and material basis can be provided for subsequent contact analysis, which is beneficial to improving the rationality of the interface mechanical response analysis.

[0054] S2. Assemble and position the pipe and the inner lining, extract the inner wall of the pipe and the outer wall of the inner lining as the contact interface, and establish the corresponding contact pair.

[0055] The inner lining is assembled into the inside of the pipe, creating an interaction area between the outer wall of the inner lining and the inner wall of the pipe. Based on the spatial relationship after assembly, the surface of the inner wall of the pipe and the surface of the outer wall of the inner lining are extracted as the contact interface, and the corresponding contact pair is established in the finite element analysis model.

[0056] Depending on the requirements of the solution model, one side of the surface can be defined as the primary contact surface, and the other side as the secondary contact surface. By explicitly extracting the inner wall of the pipe and the outer wall of the lining as the contact interface and establishing contact pairs, it is possible to describe the contact differences caused by local fit, local gaps, and irregular surface undulations, providing a foundation for subsequent tangential force analysis and slip evolution analysis.

[0057] S3. Define tangential contact attributes for the contact pair, specify a user-defined friction subroutine, and set a user parameter array and a state variable array.

[0058] Tangential contact behavior is defined in the contact properties of the contact pair, and the calculation process of the interface friction response is implemented by a user-defined friction subroutine. Simultaneously, a user parameter array is set to store the parameters required for the interface friction constitutive model; a state variable array is set to store historical relevant data of the interface in each incremental step.

[0059] The user parameter array may include one or more of the following: friction coefficient parameters, interface tangential stiffness parameters, characteristic slip parameters, strength control parameters, and degradation parameters; the state variable array may include cumulative shear displacement, shear stress of the previous incremental step, contact state identifier, damage variables, and other information reflecting the loading history. By introducing a user-defined friction subroutine and setting the user parameter array and state variable array separately, the interface response calculation is not limited to the default friction model, but can be incrementally updated based on the interface's historical state, thus making it more suitable for describing the nonlinear and path-dependent behavior of irregular contact interfaces.

[0060] S4. Establish an interface friction constitutive model based on the tribophysical mechanism of the contact interface.

[0061] To address the contact characteristics between the inner wall of the pipe and the outer wall of the inner lining, a friction constitutive model is established to describe the tangential mechanical behavior of the interface. This interface friction constitutive model characterizes the variation of shear stress at the interface under normal pressure with increasing shear displacement.

[0062] In this embodiment, the interface friction constitutive model considers at least one or more of the following factors: the influence of normal pressure on the interface's shear resistance, the cumulative effect of shear displacement increment on the interface's experimental shear stress, the transition conditions from an adhesive state to a slip state, the nonlinear change in the interface friction response, and the influence of loading history on the current interface state. By establishing an interface friction constitutive model based on the frictional physics mechanism of the contact interface, the contact analysis results can not only reflect the current stress state but also the changing patterns of the interface during compression, adhesion, slip, and evolution, thus more reasonably characterizing the interface shear stress and slip state.

[0063] S5. During the finite element incremental analysis, the user-defined friction subroutine receives the current normal pressure, shear displacement increment, state variables and user parameters, calculates the interface trial shear stress under the current incremental step, and determines the actual interface shear stress and corresponding tangential stiffness based on the contact state.

[0064] In each incremental step of the finite element incremental analysis, the user-defined friction subroutine reads the normal pressure, shear displacement increment, historical information saved in the state variable array, and model parameters in the user parameter array at the current contact integration point, and calculates the interface trial shear stress under the current incremental step based on the interface friction constitutive model.

[0065] After obtaining the interface trial shear stress, it is determined based on the current contact state. If the interface is in an adhesive state, the interface trial shear stress is determined as the actual interface shear stress, and the tangential stiffness corresponding to the adhesive state is output; if the interface satisfies the slip condition, the interface trial shear stress is corrected according to the friction response relationship in the slip state to obtain the actual interface shear stress, and the tangential stiffness corresponding to the slip state is output.

[0066] The contact state may include an adhesive state and a slip state; in some embodiments, it may be further subdivided into an initial contact state, a critical transition state, and a stable slip state. By performing trial calculations, state determinations, and result corrections in each incremental step, dynamic solutions to the interface contact behavior can be achieved, enabling the model to reflect the state transitions of the interface under different load stages; simultaneously, by outputting tangential stiffness that matches the current state, the stability and convergence of the finite element incremental iterative calculation are improved.

[0067] S6. Write the historical relevant data generated in the current incremental step into the state variable array for subsequent incremental steps to call, and complete the numerical simulation of the irregular contact between the inner wall of the pipe and the inner lining.

[0068] After the current increment step calculation is completed, the historical relevant data obtained in this increment step is written into the state variable array for subsequent increment steps to continue using. The historical relevant data may include cumulative shear displacement, actual shear stress in the current increment step, contact state identifier, damage variables, and other data characterizing the interface evolution process.

[0069] In subsequent incremental steps, the user-defined friction subroutine continues to call the updated state variable array and performs new interface response calculations based on it, thereby achieving continuous evolution analysis of the contact interface and ultimately completing the numerical simulation of irregular contact between the pipe inner wall and the inner lining. By continuously writing and passing the historical relevant data generated in the current incremental step to subsequent incremental steps, the interface model can retain the force path and slip history information, thus avoiding simplifying the interface behavior into an instantaneous response model unrelated to history, and more accurately reflecting the historical relevant characteristics and evolution laws of the irregular contact interface.

[0070] This invention achieves dynamic modeling of the irregular contact interface between the pipe's inner wall and the inner lining by establishing a three-dimensional geometric model of the pipe and its inner lining, constructing contact pairs, defining tangential contact properties, introducing a user-defined friction subroutine, establishing an interface friction constitutive model, and continuously updating state variables during finite element incremental analysis. Compared to simplifying the interface to an ideal uniform contact or a fixed friction relationship, this invention can more reasonably characterize the interface shear stress, slip state, and contact evolution process.

[0071] In a preferred embodiment, after the assembly and positioning of the pipe and the inner lining are completed, the inner wall of the pipe and the outer wall of the inner lining are extracted as contact interfaces, and a surface-to-surface contact method is used to establish a contact pair between them. Specifically, the inner wall of the pipe, which has higher stiffness and / or a coarser mesh, is defined as the master surface, and the outer wall of the inner lining is defined as the slave surface. As the original load-bearing structure, the pipe usually has higher stiffness than the inner lining, and in the finite element discretization process, the pipe side often uses a relatively coarser mesh; accordingly, defining it as the master surface helps to improve the stability of the contact search and contact constraint application process, and reduce local penetration and contact identification errors in the contact calculation. At the same time, defining the outer wall of the inner lining, which is in contact with the master surface, as the slave surface allows the interface response on the inner lining side to better follow the changes in the contact state of the master surface, thereby more reasonably reflecting the actual contact relationship between the inner wall of the pipe and the inner lining. After establishing the surface-to-surface contact pair using the above master-slave surface definition method, it can provide a stable contact boundary basis for the subsequent loading of user-defined friction constitutive models, and also help improve the calculation rationality of interface shear stress, slip state and contact evolution process, thereby better serving the purpose of this invention to dynamically model the irregular contact behavior between the inner wall and the inner lining of the pipeline.

[0072] In a preferred embodiment, step S4 involves determining a mathematical constitutive model to describe the interfacial friction behavior based on the actual stress characteristics of the interface between the pipe's inner wall and the lining layer. This determined constitutive model is then written into a user-defined friction subroutine for subsequent incremental analysis. The constitutive model can be selected from any of the following based on the interface's physical mechanism: a slip-weakening friction model, a Coulomb friction model, a rate-state friction model, or a thermo-pore pressure coupled friction model. Simultaneously, the required parameters for the model are passed through the PROPS array, and the interface response is calculated in the subroutine using the current normal pressure PRESS, shear displacement increment DSHEAR, and state variable array STATEV. This setup ensures that the determination of the interfacial shear stress and tangential stiffness is based on a clear friction mechanism, rather than simply using fixed friction parameters for simplification. This provides a constitutive basis for the dynamic characterization of the irregular contact behavior between the pipe's inner wall and the lining layer.

[0073] Specifically, when the interface response between the inner wall of the pipe and the inner lining mainly exhibits shear bearing characteristics that gradually decrease with slip development, a slip-weakening friction model can be selected to allow the interface shear stress to be dynamically adjusted with changes in local slip, thus better reflecting the process of interface evolution from initial adhesion to slip. When it is necessary to highlight the correspondence between normal pressure and interface friction limit, a Coulomb friction model can be selected to make yield judgment and correction based on normal pressure for interface trial shear stress, making the calculation process easier to implement. When the interface friction behavior is strongly correlated with loading rate and historical state, a rate-state friction model can be selected to improve the ability to express historically related contact behavior. When the interface contact is simultaneously affected by factors such as temperature field and pore fluid pressure, a thermo-pore pressure coupled friction model can be selected to incorporate the interface friction changes under multiple fields into a unified modeling process. By selecting appropriate friction constitutive models for different interface conditions, it is beneficial to improve the matching degree between the contact model and actual working conditions.

[0074] In a preferred embodiment, regardless of which interface friction constitutive model is used, the interface response can be updated within a unified solution framework in the FRIC subroutine: first, the interface trial shear stress is calculated based on the input parameters in the current increment step; then, the trial shear stress is judged according to the corresponding yield criterion; and a return mapping algorithm is used to determine the true interface shear stress and corresponding tangential stiffness. Subsequently, the updated equivalent plastic slip, current friction coefficient, damage variables, and other historical relevant data are written into the STATEV array for use in the next increment step. This preserves the differences in physical mechanisms among different friction constitutive models while enabling unified solutions within the same finite element contact analysis framework. This improves the continuity and stability of model calculations and provides a more reasonable characterization of interface shear stress, slip state, and contact evolution process.

[0075] In a preferred embodiment, step S5 uses a user-defined friction subroutine to perform incremental calculations of the interface response. This user-defined friction subroutine is preferably the FRIC subroutine. Specifically, in each incremental step of the finite element solution, the FRIC subroutine receives the current normal pressure PRESS, shear displacement increment DSHEAR, state variable array STATEV, and user parameter array PROPS transmitted from the finite element main program. It then combines these with the interface friction constitutive model pre-established in step S4 to calculate the interface mechanical response under the current contact state. The PROPS array is used to transmit parameters corresponding to the interface friction constitutive model, which may include the initial friction coefficient, shear stiffness, and hardening or softening parameters. The STATEV array stores historical interface variables for reuse in subsequent incremental steps. As clearly stated in the documentation, the FRIC subroutine receives PRESS, DSHEAR, STATEV, and PROPS at the program entry point and dynamically calculates the interface shear stress and its tangential stiffness based on the friction model.

[0076] Furthermore, the FRIC subroutine first calculates the interface trial shear stress in the current increment step based on the current normal pressure, shear displacement increment, and user parameters, combined with the interface friction constitutive model. Then, it judges the trial shear stress according to the yield criterion and uses numerical methods such as the return mapping algorithm to determine the actual interface shear stress and the corresponding tangential stiffness. After completing the calculation for this increment step, the updated equivalent plastic slip, current friction coefficient, damage variables, or other historically relevant data are written into the STATEV array for use in the next increment step. Through this method, the interface shear stress and tangential stiffness no longer use fixed given values, but can be dynamically adjusted according to the current normal pressure, shear displacement increment, and historical interface state. This is beneficial for improving the characterization ability of the nonlinear, historically relevant, and staged contact behavior between the pipe inner wall and the inner lining. Simultaneously, the synchronous calculation of tangential stiffness also helps improve the continuity and stability of the contact solution process, making the established irregular contact model more consistent with the actual interface stress evolution process.

[0077] In a preferred embodiment, the FRIC subroutine in step S5 first calculates the trial shear stress in the current increment step based on the current normal pressure PRESS, shear displacement increment DSHEAR, state variable array STATEV, and user parameter array PROPS, combined with a pre-established interface friction constitutive model. Then, it judges the trial shear stress according to the yield criterion. When the trial shear stress exceeds the allowable shear bearing capacity of the interface, a return mapping algorithm is used to correct it to determine the actual interface shear stress and corresponding tangential stiffness that satisfy the yield condition. Through this method, the determination of the interface shear stress no longer relies on a fixed assignment but can simultaneously consider the current loading increment and the interface yield constraint, thereby improving the characterization ability of the nonlinear contact response between the pipe inner wall and the inner lining. Simultaneously, the synchronous update of the tangential stiffness and the corrected stress state also helps to improve the continuity and stability of the contact solution process.

[0078] In a preferred embodiment, the state variable array in step S6 is used not only to record the interface shear stress calculation results, but also to store the local slip amount between the current increment and the previous increment, and to determine the slip stage of the interface accordingly. Specifically, after the FRIC subroutine completes the interface response calculation for the current increment step, the local slip history amounts in the first tangential direction and the second tangential direction are written into the STATEV array respectively; subsequently, based on the comparison results of the local slip amounts corresponding to the current increment step and the previous increment step, it is determined whether the interface has crossed the preset slip threshold, and it is determined which stage the interface is currently in: the initial bonding stage, the slip transition stage, or the stable slip stage. After determining the slip stage, different shear stress update relationships are called for different stages: when the local slip amount has not yet reached the preset threshold, the shear stress update relationship corresponding to the initial bonding stage is used; when the local slip amount crosses the threshold and enters the subsequent slip stage, another shear stress update relationship corresponding to that stage is used. Through this phased updating method, the interfacial shear stress no longer evolves according to a single fixed law, but can dynamically switch with the development of local slippage. This is more conducive to reflecting the contact evolution characteristics between the inner wall of the pipe and the inner lining from adhesion, slippage initiation to continuous slippage, thereby improving the ability to characterize irregular, nonlinear and historically related contact behaviors.

[0079] Furthermore, local slip updates and interface shear stress calculations are performed along two tangential directions of the contact interface. Specifically, in the first tangential direction, the interface shear stress and corresponding stiffness are calculated based on the current incremental slip, the previous incremental slip history, and the shear stress update relationship corresponding to the current stage. In the second tangential direction, slip updates and interface shear stress calculations are performed independently using the same method. This approach is because the contact response between the pipe's inner wall and the lining may differ across tangential directions. Treating it only in a single direction or by combining them could weaken the directional response characteristics of the interface. Updating and calculating separately along both tangential directions allows for a more detailed characterization of the directional differences in interface shear stress and slip state under complex contact conditions, further improving the continuity and rationality of the entire contact model during incremental analysis.

[0080] In a preferred embodiment, after establishing the interface friction constitutive model and configuring the FRIC subroutine, the numerical simulation method further includes meshing the pipe and the liner and performing finite element analysis. Specifically, based on the analysis type and the response characteristics of the contact area, the pipe and the liner are meshed using either structured or unstructured meshes, and element types suitable for the solution process are selected to ensure sufficient mesh density and mesh compatibility in the contact area. On this basis, the completed subroutine is associated with the analysis job and the finite element solution is executed to obtain the interface response results during loading. This setup serves two purposes: firstly, it provides a stable discrete foundation for the numerical realization of the interface friction constitutive model, avoiding the impact of excessively sparse or poorly matched meshes in the contact area on the interface response calculation; secondly, it also improves the reliability of subsequent extraction results of interface shear stress, relative slip, and state variables.

[0081] After the finite element analysis is completed, the results of interface shear stress, relative slip, and state variables are further extracted. Shear stress-shear displacement relationship curves at key locations are then plotted. The obtained results are compared with theoretical solutions and / or experimental data to verify and calibrate the interface friction constitutive model. This method allows for determination of whether the current constitutive model and its parameters can adequately reflect the actual contact behavior between the pipe's inner wall and lining. When discrepancies exist in the comparison results, the relevant parameters in the user parameter array can be adjusted, and the analysis can be re-executed until the model response achieves a relatively consistent correspondence with the theoretical solution and / or experimental data. This not only completes the establishment of the interface contact model but also forms a closed-loop modeling process of "mesh generation - finite element analysis - result extraction - comparison and verification - parameter calibration," thereby improving the rationality of the interface friction constitutive model's representation of irregular, nonlinear, and historically related contact behaviors between the pipe's inner wall and lining.

[0082] See Figure 3 The implementation process of the FRIC subroutine can be summarized as follows: First, the state variables are initialized and their initial values ​​are set to 0 to record the historical stress state of the interface during the analysis process. Then, the basic physical parameters and user parameters of the interface are input, and the ultimate shear stress and shear stiffness of the interface are calculated based on these parameters. The ultimate shear stress serves as a threshold for determining whether slip has occurred on the interface, and the shear stiffness characterizes the interface's ability to resist tangential deformation at the current stage. Next, the current contact state is determined. When the state variable LM = 2, it indicates that the interface is in a fully bonded, non-slip state, and the program enters the shear stress calculation process under the bonded state. When LM ≠ 2, it indicates that slip has occurred on the interface, and the program enters the slip-allowed branch. When the interface can no longer maintain bond, the state variable LM is set to 0 to mark the interface entering the slip state. LM is the interface contact state identifier variable. After determining the current contact state, the actual shear stress of the interface is calculated based on the shear stiffness under the corresponding state. At the end of this incremental step, the current shear stiffness matrix is ​​stored and the state variables are updated to provide basic data for the interface response calculation in the next incremental step. Through the above processing, the interface state judgment, interface shear stress solution and historical state update can be integrated into the same subroutine flow, so that the interface response can change dynamically with the contact state and historical stress process, which is more conducive to characterizing the irregular, nonlinear and historically related contact behavior between the inner wall of the pipeline and the inner lining.

[0083] It should be noted that the finite element analysis is preferably implemented using the ABAQUS software platform, and the interface friction constitutive model is preferably loaded into the ABAQUS contact analysis process through a FRIC user subroutine written in Fortran.

[0084] To analyze the influence of lining parameters on the stress response of a pipeline with corrosion defects, a finite element analysis was performed on the pipeline based on the previously established model of the irregular contact surface between the pipeline inner wall and the lining. (See [link to relevant documentation]). Figure 2 , Figure 2 The left image in the diagram is a three-dimensional sectional view of the inner wall of the pipe. Figure 2The right-hand image shows a three-dimensional view of the inner lining layer. Specifically, the model parameters can be set as follows: pipe material is C30, pipe diameter is 1m, wall thickness is 100mm, corrosion length is 4m, corrosion width is 90°, corrosion depth is 40% of the wall thickness, Poisson's ratio of the inner lining layer is 0.2, pipe cover depth is 1m, and traffic load is 1.5MPa. Here, traffic load refers to the external additional load generated by surface vehicles and transmitted to the buried pipeline structure via the road surface and cover layer; in the finite element model, it can be equivalent to static pressure. Based on this, the interface response is calculated when the elastic modulus of the inner lining layer is 20GPa, 25GPa, 30GPa, 35GPa, and 40GPa, and the corresponding circumferential strain of the inner lining layer and pipe bending moment results are extracted. Through this parametric analysis method, the influence of changes in the stiffness of the inner lining layer on the stress state of the repaired pipeline can be examined, thus providing a numerical example to support the engineering application of the interface friction constitutive model.

[0085] Combination Figure 4 The finite element analysis results show that after the surface vehicle load is transferred to the pipeline structure through the overburden layer, the circumferential strain in the central region of the lining layer is more significant. As the elastic modulus of the lining layer gradually increases from 20 GPa to 40 GPa, the circumferential strain of the lining layer gradually decreases, indicating that, under the condition that other factors remain unchanged, increasing the elastic modulus of the lining layer helps to reduce the circumferential deformation level of the repair mortar lining layer. Furthermore, as the repair thickness increases, the circumferential strain of the lining layer also decreases significantly, indicating that increasing the stiffness and thickness of the lining layer is beneficial to improving the stress state of the pipeline after repair of the corrosion-defective pipeline. The above results demonstrate that the irregular contact surface model established based on this invention can more intuitively reflect the influence of changes in lining layer parameters on the pipeline structure response, thereby improving the applicability of the model in repair parameter analysis.

[0086] Combination Figure 5 The comparison between the finite element simulation results and the experimental results shows that the circumferential strain results obtained from the irregular contact surface model of the pipe inner wall and inner lining layer established through ABAQUS secondary development are basically consistent with the full-scale test results. This indicates that the established model and its parameter settings can match the actual test conditions well, thus verifying the rationality of using the model to characterize the contact behavior of the pipe inner wall and inner lining layer. Further analysis shows that the maximum circumferential strain at the socket position is greater than that at the spigot position. This is because the socket position is relatively higher and bears the larger load transferred from the external load first. In contrast, the spigot is inserted into the socket and connected to the socket through a rubber ring. It is not in direct contact with the external soil load, so the load acting on the spigot is relatively smaller. Therefore, the irregular contact model established in this invention can not only reflect the overall deformation law, but also distinguish the stress differences of different structural parts.

[0087] Furthermore, fromFigure 5 As can be seen from (a), the outer part of the pipe is mainly under compression in the ranges of 315°–45° and 135°–225°, while it is mainly under tension in the remaining areas; from Figure 5 As can be seen from (b), the inner wall of the pipe exhibits the opposite stress state. Meanwhile, the circumferential strain is close to zero near 45°, 135°, 225°, and 315°, indicating that the external load has little effect on the pipe hip and shoulder positions, and the effects at these locations can be approximated as negligible. Through this comparative analysis between the outer and inner walls, and between the socket and spigot, it is further demonstrated that the irregular contact surface model established in this invention can reflect the local response characteristics of different orientations and locations in greater detail, thus more reasonably characterizing the interface stress and contact evolution process between the inner wall and the inner lining of the pipe.

[0088] Example 2

[0089] This invention also provides a numerical simulation system for irregular contact between the inner wall and lining of a pipeline. This system can be implemented using a computer, a finite element analysis platform, and a user-defined subroutine runtime environment, and is used to execute the aforementioned numerical simulation method for irregular contact between the inner wall and lining of a pipeline. Specifically, the system includes a geometric modeling module, a contact interface construction module, a contact attribute configuration module, a site modeling module, an interface response calculation module, and a state update module. These modules work collaboratively according to the modeling process sequence to achieve dynamic modeling of the irregular contact behavior between the inner wall and lining of the pipeline.

[0090] The geometric modeling module is used to create three-dimensional geometric models of the pipe and the lining layer and assign material properties. In practice, the module creates corresponding three-dimensional solid models based on the structural dimensions of the pipe and the lining layer, and further defines material properties such as the elastic modulus, Poisson's ratio, and density of the pipe and lining materials. Then, it assigns the corresponding material sections to the relevant components. This module provides a unified and clear structural and material basis for subsequent contact interface creation and finite element analysis.

[0091] The contact interface construction module is used to extract the inner wall of the pipe and the outer wall of the liner as contact interfaces and establish contact pairs. Specifically, after completing the geometric model assembly and positioning, the contact interface construction module extracts the inner wall of the pipe and the outer wall of the liner to form a set of contact surfaces, and establishes contact pairs based on the set of contact surfaces. Preferably, the pipe surface with higher stiffness and / or coarser mesh is defined as the master surface, the liner surface is defined as the slave surface, and a surface-to-surface contact method is used for contact modeling. This module helps to improve the stability of the contact identification and contact constraint application process.

[0092] The contact attribute configuration module is used to define tangential contact attributes and specify user-defined friction subroutines, while configuring the user parameter array PROPS and the state variable array STATEV. In specific implementation, the contact attribute configuration module sets the tangential behavior of the contact pair to a user-defined mode and configures the parameters required for the interface friction constitutive model and the number of state variables, thereby providing an input interface for interface friction constitutive calculation and historical variable storage. Through this module, the interface friction constitutive model can be linked to the finite element solution process, providing conditions for the dynamic updating of the interface response.

[0093] The constitutive modeling module is used to establish an interfacial friction constitutive model based on the interface stress characteristics. Specifically, the module theoretically determines the mathematical model describing the interfacial friction behavior and embeds the corresponding constitutive relations into a user-defined friction subroutine. The interfacial friction constitutive model can be any of the following: a slip-weakening friction model, a Coulomb friction model, a rate-state friction model, or a thermo-pore pressure coupled friction model. Through this module, the solution for interfacial shear stress and tangential stiffness is established on a clear friction mechanism, which is beneficial for improving the characterization ability of nonlinear, history-dependent contact behaviors.

[0094] The interface response calculation module receives the current normal pressure PRESS, shear displacement increment DSHEAR, state variables, and user parameters during the finite element incremental analysis, and calculates the actual shear stress and corresponding tangential stiffness of the interface. Specifically, this module is preferably implemented through a FRIC subroutine. In each incremental step, it receives PRESS, DSHEAR, STATEV, and PROPS from the finite element main program, calculates the trial shear stress under the current incremental step based on the interface friction constitutive model, and then determines the actual shear stress and corresponding tangential stiffness of the interface using a return mapping algorithm based on the yield criterion. Through this module, the interface response can dynamically change with the current loading state and historical states.

[0095] The state update module is used to write historical relevant data generated in the current increment step into the state variable array to complete the numerical simulation of irregular contact. Specifically, the state update module writes the updated equivalent plastic slip, current friction coefficient, damage variables, and local slip history generated during the calculation process into the corresponding positions of the STATEV array, and continues to call them in subsequent increment steps. In a preferred embodiment, the slip stage of the interface can also be determined based on the local slip amount of the current increment and the previous increment, and the local slip amount is updated and the interface shear stress is calculated along the two tangential directions of the contact interface, respectively. Through this module, the model can not only reflect the instantaneous response at the current moment, but also reflect the historical evolution process of the interface from contact and initial slip to continuous slip.

[0096] In summary, the numerical simulation system for irregular contact between the inner wall and the lining of a pipe provided by this invention, through the coordinated cooperation of the geometric modeling module, the contact interface construction module, the contact attribute configuration module, the constitutive modeling module, the interface response calculation module, and the state update module, organically combines geometric modeling, contact interface establishment, interface friction constitutive solution, and historical state update, thereby enabling a more reasonable characterization of the interface shear stress, relative slip, and contact evolution process between the inner wall and the lining of the pipe.

[0097] Example 3

[0098] The present invention also provides an electronic device, including a memory for storing computer program instructions and a processor for executing the computer program instructions, wherein when the computer program instructions are executed by the processor, the device is triggered to execute some or all of the steps in Embodiment 1;

[0099] A processor may include one or more processing units, such as an application processor (AP), a modem processor, a graphics processing unit (GPU), an image signal processor (ISP), a controller, a video codec, a digital signal processor (DSP), a baseband processor, and / or a neural network processing unit (NPU). Different processing units may be independent devices or integrated into one or more processors.

[0100] The controller can serve as the nerve center and command center of an electronic device. Based on the instruction opcode and timing signals, the controller generates operation control signals to control the fetching and execution of instructions.

[0101] The processor may also include memory for storing instructions and data. In some embodiments, the memory in the processor is a cache memory. This memory can store instructions or data that the processor has just used or that are used repeatedly. If the processor needs to use the instruction or data again, it can retrieve it directly from the memory. This avoids repeated accesses, reduces processor waiting time, and thus improves system efficiency.

[0102] Example 4

[0103] The present invention also provides a storage medium having a computer program stored thereon, wherein, when the program is executed, it controls the device where the storage medium is located to perform some or all of the steps in Embodiment 1.

[0104] The storage medium may include high-speed RAM memory, and may also include nonvolatile memory, such as at least one disk storage device. It is understood that the storage medium can be any machine-readable medium capable of storing program code, such as random access memory (RAM), magnetic disk, hard disk, solid state disk (SSD), or nonvolatile memory.

[0105] Those skilled in the art will understand that embodiments of the present invention can be provided as methods or storage media. Therefore, embodiments of the present invention can take the form of entirely hardware embodiments, entirely software embodiments, or embodiments combining software and hardware aspects. Furthermore, embodiments of the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0106] The above are merely preferred embodiments of the present invention and do not limit the patent scope of the present invention. All equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A numerical simulation method for irregular contact between the inner wall and the inner lining of a pipe, characterized in that, The steps include: S1. Establish a three-dimensional geometric model of the pipe and the inner lining, and assign corresponding material properties; S2. Assemble and position the pipe and the inner lining, extract the inner wall of the pipe and the outer wall of the inner lining as the contact interface, and establish the corresponding contact pair. S3. Define tangential contact properties for the contact pair, specify a user-defined friction subroutine, and set a user parameter array and a state variable array; S4. Establish an interface friction constitutive model based on the tribophysical mechanism of the contact interface; S5. During the finite element incremental analysis, the user-defined friction subroutine receives the current normal pressure, shear displacement increment, state variables and user parameters, calculates the interface trial shear stress under the current incremental step, and determines the actual interface shear stress and corresponding tangential stiffness based on the contact state. S6. Write the historical relevant data generated in the current incremental step into the state variable array for subsequent incremental steps to call, and complete the numerical simulation of the irregular contact between the inner wall of the pipe and the inner lining.

2. The numerical simulation method for irregular contact between the inner wall and the inner lining of a pipe according to claim 1, characterized in that, In step S2, the inner wall of the pipe with greater stiffness and / or coarser mesh is defined as the primary contact surface, and the outer wall of the inner lining is defined as the secondary contact surface, so as to establish a surface-to-surface contact pair.

3. The numerical simulation method for irregular contact between the inner wall and the inner lining of a pipe according to claim 1, characterized in that, The user parameter array includes at least one or more of the following: initial friction coefficient, shear stiffness, hardening parameter, and softening parameter; The state variable array is used to store historical data related to the interface. The historical data includes at least one or more of the following: equivalent plastic slip, current friction coefficient, damage variable, local slip history, and contact state identifier.

4. The numerical simulation method for irregular contact between the inner wall and the inner lining of a pipe according to claim 1, characterized in that, In step S4, the interface friction constitutive model is any one of the following: slip weakening friction model, Coulomb friction model, rate-state friction model, or thermo-pore pressure coupled friction model.

5. The numerical simulation method for irregular contact between the inner wall and the inner lining of a pipe according to claim 1, characterized in that, In step S5, the user-defined friction subroutine is the FRIC subroutine; The FRIC subroutine receives the current normal pressure PRESS, shear displacement increment DSHEAR, state variable array STATEV, and user parameter array PROPS from the finite element main program, and calculates the interface shear stress and tangential stiffness based on the interface friction constitutive model.

6. The numerical simulation method for irregular contact between the inner wall and the inner lining of a pipe according to claim 5, characterized in that, In step S5, the trial shear stress under the current incremental step is first calculated in the FRIC subroutine, and then the trial shear stress is corrected according to the yield criterion to determine the actual shear stress of the interface and the corresponding tangential stiffness. The determination of the actual shear stress and corresponding tangent stiffness of the interface is achieved using a return mapping algorithm.

7. The numerical simulation method for irregular contact between the inner wall and the inner lining of a pipe according to claim 1, characterized in that, In step S6, the slip stage of the interface is determined based on the local slip amount between the current increment and the previous increment, and different shear stress update relationships are adopted according to different slip stages. Local slip updates and interface shear stress calculations are performed along two tangential directions of the contact interface.

8. The numerical simulation method for irregular contact between the inner wall and the inner lining of a pipe according to claim 1, characterized in that, The numerical simulation method also includes: meshing the pipe and the inner lining and performing finite element analysis to extract the interface shear stress, relative slip and state variable results, and comparing the results with theoretical solutions and / or experimental data to verify and calibrate the interface friction constitutive model.

9. A numerical simulation system for irregular contact between the inner wall and lining layer of a pipe, characterized in that, include: The geometry modeling module is used to create three-dimensional geometric models of pipes and linings and assign material properties; The contact interface construction module is used to extract the inner wall of the pipe and the outer wall of the inner lining as the contact interface and establish contact pairs; The contact property configuration module is used to define tangential contact properties and specify user-defined friction subroutines; This constitutive modeling module is used to build interface friction constitutive models; The interface response calculation module is used to receive the current normal pressure, shear displacement increment, state variables and user parameters during the finite element incremental analysis process, and calculate the actual shear stress and corresponding tangential stiffness of the interface. The state update module is used to write the historical relevant data generated by the current increment step into the state variable array to complete the numerical simulation of irregular contact.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, which, when executed by a processor, is used to implement the steps of the numerical simulation method for irregular contact between the inner wall and the lining layer of a pipe as described in any one of claims 1-8.

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