Construction method of numerical analysis model of fiber bridge in fiber concrete

Abstract

The present invention provides a method for constructing a numerical analysis model of fiber bridging of fiber concrete, which belongs to the technical field of fiber concrete. First, a nonlinear slip constitutive relationship of the fiber-matrix interface is established; secondly, a probability density function is used to describe the anisotropic distribution of the three-dimensional fiber orientation angle, and the randomness of the fiber embedding length is simulated in combination with the log-normal distribution, and a correction factor is introduced to quantify the interaction between fibers. Then, the debonding behavior of the microscopic interface is mapped to the macroscopic fracture surface through a heterogeneous data transfer protocol to achieve seamless coupling of multi-scale mechanical states; at the same time, the grid density in the crack tip area is dynamically optimized by combining the posterior error estimation and the local subdivision technology of the unstructured hexahedral grid. The present invention adopts the above method to effectively solve the limitations of the traditional model in the characterization of interface behavior, the idealized assumption of fiber distribution and the rigid division of the grid, and significantly improves the accuracy and reliability of the simulation of the fiber bridging effect.

Description

Technical Field

[0001] The present invention relates to the technical field of fiber concrete, and in particular to a method for constructing a numerical analysis model of fiber concrete fiber bridging. Background Art

[0002] Fiber-reinforced concrete (FRC) has been widely used in civil engineering, bridge reinforcement, and seismic structures due to its excellent crack resistance, toughness, and energy absorption capacity. The core mechanism behind this performance improvement stems from the fiber's bridging effect. When cracks form in the concrete matrix, the fibers transfer stress across the cracks, slowing crack propagation and improving the overall ductility of the material. In recent years, with the advancement of computational mechanics, numerical analysis models have become an important tool for studying the mechanical behavior of FRC, providing theoretical support for material design, performance prediction, and engineering applications.

[0003] However, existing numerical models still face many challenges in simulating the fiber bridging effect. First, the interfacial behavior between the fiber and the concrete matrix involves the multi-scale coupling problem of micro-slip and macro-fracture. Traditional methods usually achieve cross-scale modeling through homogenization assumptions or simplified constitutive relations, but such methods are difficult to accurately capture the nonlinear characteristics of local stress-slip during interfacial debonding, resulting in deviations in the prediction of the evolution of the macroscopic fracture surface. Secondly, the stress concentration phenomenon in the crack tip area is extremely sensitive to the meshing accuracy. Existing numerical models mostly use a fixed mesh strategy, which makes it difficult to achieve a dynamic balance between computational efficiency and local accuracy. Especially under complex crack propagation paths, coarse meshes may underestimate the stress gradient, while global fine meshes will significantly increase the computational cost.

[0004] Furthermore, the actual distribution of fibers in concrete exhibits significant randomness and spatial heterogeneity. Although some studies have attempted to describe fiber orientation angles and embedment lengths using statistical methods, these models are often based on idealized assumptions (e.g., uniform distribution or a single Gaussian distribution), ignoring the skewed characteristics of fiber distribution in actual engineering (e.g., lognormal distribution) and inter-fiber interactions. This simplification may limit the model's applicability to scenarios with high fiber content or non-uniform distribution. Furthermore, the parameter calibration of existing models often relies on theoretical derivation or limited experimental data, lacking a multi-objective optimization mechanism that integrates numerical inverse analysis, limiting the model's adaptability to different material combinations and complex boundary conditions.

[0005] To address these challenges, developing a numerical analysis method that balances multiscale coupling accuracy, dynamic mesh optimization, random fiber distribution modeling, and adaptive parameter correction has become an important research direction in fiber-reinforced concrete. The establishment of such a model not only deepens our understanding of fiber bridging mechanisms but also provides more reliable design and evaluation tools for engineering practice. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for constructing a numerical analysis model of fiber bridging in fiber concrete, which effectively solves the limitations of traditional models in the characterization of interface behavior, idealized assumptions of fiber distribution and grid rigidity division, significantly improves the accuracy and reliability of the simulation of fiber bridging effects, and provides an efficient theoretical tool for the design and engineering application of fiber concrete materials.

[0007] To achieve the above object, the present invention provides a method for constructing a numerical analysis model of fiber concrete fiber bridging, comprising the following steps:

[0008] Step S1, establishing a nonlinear slip constitutive model of the fiber-matrix interface and determining the relationship between the interface shear stress and the slip amount;

[0009] Step S2, generating a random distribution field of three-dimensional fiber direction angles and embedding lengths;

[0010] Step S3: combining the nonlinear slip constitutive model of the microscopic interface with the macroscopic phase field method, characterizing the interface behavior through the cohesion unit, and mapping the interface debonding behavior to the macroscopic fracture surface using a heterogeneous data transfer protocol based on the random distribution field of the fiber orientation angle and embedment length;

[0011] Step S4: In the multi-scale analysis, based on the a posteriori error estimation method, the unstructured hexahedral grid local subdivision technology is used to dynamically adjust the grid size of the crack tip area.

[0012] Preferably, in step S1, the nonlinear slip constitutive model is a piecewise bilinear softening model, and its expression is:

[0013] ;

[0014] in, represents the interfacial shear stress, represents the slip amount, represents the peak shear stress, represents the slip amount when the peak shear stress is reached, Represents the residual slip in the softening stage.

[0015] Preferably, in step S2, the three-dimensional fiber direction angle According to the following probability density distribution :

[0016] ;

[0017] in, represents the polar angle, represents the azimuth, represents the anisotropy coefficient, represents the second-order Legendre polynomial, which is expressed as:

[0018] .

[0019] Preferably, in step S2, the correction factor Corrected fiber orientation angle distribution function, correction factor The expression is

[0020] ;

[0021] in, Indicates the number of fibers per unit volume. represents the fiber diameter, Indicates the density of concrete; Indicates the fiber embedding length;

[0022] The corrected fiber orientation angle distribution function is:

[0023] .

[0024] Preferably, in step S2, the fiber embedding length follows the average value , the standard deviation is The lognormal distribution of :

[0025] ;

[0026] in, The fiber embedding length is The probability density when .

[0027] Preferably, in step S3, the mechanical parameters of the cohesion unit are determined by the following optimization formula:

[0028] ;

[0029] ;

[0030] in, represents the fracture energy, represents the peak load in the pull-out test, represents the critical debonding displacement, represents the width of the specimen, represents the peak bond stress, represents the elastic modulus of the fiber;

[0031] At the same time, the numerical back analysis correction coefficient is introduced By comparing the load-displacement curves of numerical simulation and test, iterative optimization The root mean square error (RMS) between the simulation results and the test results is less than 5%.

[0032] Preferably, in step S3, the heterogeneous data transmission protocol is implemented by the following steps:

[0033] Step S31, obtaining the debonding displacement field and stress field of the cohesion unit at the microscopic scale;

[0034] Step S32: Mapping the microscopic debonding displacement field and stress field onto the macroscopic fracture surface using an interpolation algorithm;

[0035] Step S33: updating the mechanical state of the macro fracture surface, including displacement and stress, according to the mapping results;

[0036] Step S34: Feedback the updated macroscopic fracture surface mechanical state to the microscopic scale to achieve coupling between the microscopic and macroscopic scales.

[0037] Preferably, the specific expression of the heterogeneous data transmission protocol is:

[0038] ;

[0039] in, Represents a point on the macroscopic fracture surface The displacement at Indicates the microscopic interface debonding The displacement of a cohesion unit, represents the interpolation function, represents the displacement gradient at the microscopic level, Indicates the The coordinates of the cohesion unit.

[0040] Preferably, in step S4, the unstructured hexahedral grid local subdivision technology includes the following steps:

[0041] Step S41, determining the crack tip area that needs to be subdivided;

[0042] Step S42: Calculate the required grid density for the area based on the a posteriori error estimation result;

[0043] Step S43: using an unstructured hexahedral mesh generation algorithm to perform mesh subdivision on the target area;

[0044] Step S44: perform quality inspection and optimization on the subdivided mesh to ensure that the mesh quality meets the requirements of numerical analysis.

[0045] Preferably, the posterior error estimate uses the following energy norm form:

[0046] ;

[0047] in, represents the stress field obtained by numerical calculation, represents the stress field based on experiments or high-precision benchmark solutions, represents the analysis area;

[0048] when Exceeding the preset threshold When , the subdivision of the unstructured hexahedral mesh in the crack tip area is triggered, and the subdivision criterion is:

[0049] ;

[0050] in, and Represents the mesh size before and after subdivision, represents the local error estimate, Indicates the convergence order, and its value range is [1,3].

[0051] Therefore, the present invention adopts the above-mentioned method for constructing a numerical analysis model of fiber concrete fiber bridging, and the beneficial technical effects are as follows:

[0052] (1) Improved coupling accuracy between micro-interfaces and macro-fracture surfaces: This invention uses an innovative heterogeneous data transfer protocol to accurately map the debonding behavior of micro-interfaces to macro-fracture surfaces, resolving the problem of insufficient data transfer accuracy in existing multi-scale coupling models. This improvement enables the model to more realistically reflect the impact of interface behavior on macro-mechanical properties, providing more reliable prediction results for the mechanical analysis of fiber reinforced concrete.

[0053] (2) Adaptive mesh adjustment in the crack tip region: In multi-scale analysis, this paper uses a posterior error estimation method combined with unstructured hexahedral mesh local subdivision technology to achieve dynamic adjustment of the mesh size in the crack tip region. This method overcomes the large computational errors and low efficiency of traditional fixed mesh methods in stress concentration areas, thereby improving the accuracy of numerical simulations and the efficiency of computing resources.

[0054] (3) Simulation of random distribution of fiber embedment length and orientation angle: This paper takes into account the actual distribution characteristics of fibers in concrete, adopts a lognormal distribution to describe the fiber embedment length, and uses an improved probability density function to simulate the distribution of three-dimensional fiber orientation angles. This avoids the limitations of simple uniform distribution or single Gaussian distribution in traditional methods, enabling the model to more accurately simulate the spatial distribution of fibers, thereby improving the simulation accuracy of the complex mechanical behavior of fiber concrete.

[0055] (4) Optimization and Verification of Model Parameters: By introducing numerical back-analysis correction coefficients and iteratively optimizing model parameters based on experimental data, this invention addresses the limitations of existing methods for determining model parameters. This parameter optimization method, based on a combination of experimental and numerical simulation, significantly improves the accuracy and reliability of the model, making it more applicable to different types of fiber and concrete matrix combinations.

[0056] (5) Consideration of fiber interactions: This paper introduces a correction factor for the first time to account for the effects of fiber interactions on fiber distribution, filling the gap in the prior art that ignores fiber interactions. This innovation enables the model to more realistically simulate the fiber distribution state at high fiber content, expanding the model's application range.

[0057] (6) Improvement of the nonlinear slip constitutive model: The present invention adopts a piecewise bilinear softening model to describe the nonlinear slip behavior of the fiber-matrix interface. Compared with the traditional single-stage linear or nonlinear model, it can more carefully characterize the mechanical properties of the interface in the elastic stage and the softening stage, providing more accurate theoretical support for the study of the interface behavior of fiber concrete. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is a flow chart of a method for constructing a numerical analysis model of fiber bridges in fiber concrete according to the present invention;

[0059] Figure 2 is the interface shear stress-slip relationship curve;

[0060] Figure 3 is the probability density distribution curve of fiber embedment length. DETAILED DESCRIPTION

[0061] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0062] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0063] Example 1

[0064] like Figure 1 As shown, a method for constructing a numerical analysis model of fiber concrete fiber bridges includes the following steps:

[0065] Step S1, establishing a nonlinear slip constitutive model of the fiber-matrix interface and determining the relationship between the interface shear stress and the slip amount;

[0066] The nonlinear slip constitutive model is a piecewise bilinear softening model, and its expression is:

[0067] ;

[0068] in, represents the interfacial shear stress, represents the slip amount, represents the peak shear stress, represents the slip amount when the peak shear stress is reached, Represents the residual slip in the softening stage.

[0069] Figure 2 is the interface shear stress-slip relationship curve, the curve shows that in the initial stage (0≤ ≤ ), the interfacial shear stress increases linearly with the slip amount, and after reaching the peak shear stress ( = ), with the further increase of slip, the interfacial shear stress gradually decreases, showing a softening behavior.

[0070] Step S2, generating a random distribution field of three-dimensional fiber direction angles and embedding lengths;

[0071] Step 2.1, 3D fiber orientation angle According to the following probability density distribution :

[0072] ;

[0073] in, represents the polar angle, represents the azimuth, represents the anisotropy coefficient, represents the second-order Legendre polynomial, which is expressed as:

[0074] .

[0075] An X-ray tomography analysis was performed on polypropylene fiber concrete in a bridge project to obtain the fiber direction distribution data. The anisotropy coefficient was determined by statistical analysis of the scanning data. =0.3.

[0076] Through the correction factor Corrected fiber orientation angle distribution function, correction factor The expression is:

[0077] ;

[0078] in, Indicates the number of fibers per unit volume, with a value of 500 fibers / mm 3 , Indicates the fiber diameter, which is 0.5 mm. Indicates the density of concrete, the value is 2400kg / m 3 ; Indicates the fiber embedding length, which is 15mm; Substitute the above parameters to calculate the correction factor =1.2.

[0079] The corrected fiber orientation angle distribution function is:

[0080] .

[0081] Step 2.2: The fiber embedding length follows the mean value , the standard deviation is The lognormal distribution of :

[0082] ;

[0083] in, The fiber embedding length is By sampling and analyzing the polypropylene fiber concrete in the above bridge project, the mean value of the fiber embedding length was obtained statistically. =12mm, standard deviation =3mm.

[0084] Figure 3 This is the probability density distribution curve of the fiber embedding length. The curve shows the characteristics of log-normal distribution and shows the probability density of the fiber at different embedding lengths.

[0085] Step S3: combining the nonlinear slip constitutive model of the microscopic interface with the macroscopic phase field method, characterizing the interface behavior through the cohesion unit, and mapping the interface debonding behavior to the macroscopic fracture surface using a heterogeneous data transfer protocol based on the random distribution field of the fiber orientation angle and embedment length;

[0086] The mechanical parameters of the cohesion unit are determined by the following optimization formula:

[0087] ;

[0088] ;

[0089] in, represents the fracture energy, Indicates the peak load in the pull-out test, which is 500N. Indicates the critical debonding displacement, which is 0.05 mm. Indicates the width of the specimen, which is 50 mm. represents the peak bond stress, represents the elastic modulus of the fiber, which is 3000 MPa;

[0090] At the same time, the numerical back analysis correction coefficient is introduced By comparing the load-displacement curves of numerical simulation and test, iterative optimization The RMS error between the simulation results and the test results was kept below 5%. After multiple rounds of iterative optimization, the numerical back-analysis correction factor was finally determined to be 1.08. At this point, the RMS error between the simulation results and the test results was 4.8%, meeting the accuracy requirements.

[0091] The heterogeneous data transmission protocol is implemented through the following steps:

[0092] Step S3.1: Obtain the debonding displacement and stress fields of the cohesion unit at the microscopic scale. Numerical simulation is used to obtain the displacement and stress data of the cohesion unit during the debonding process, which reflect the mechanical behavior of the microscopic interface.

[0093] Step S3.2: Use an interpolation algorithm to map the microscopic debonding displacement and stress fields to the macroscopic fracture surface. A bilinear interpolation algorithm is used to interpolate the displacement and stress data at the microscopic interface to each node on the macroscopic fracture surface, ensuring smoothness and accuracy of data transfer.

[0094] Step S3.3: Update the mechanical state of the macroscopic fracture surface, including displacement and stress, based on the mapping results. Substitute the interpolated displacement and stress data as the new mechanical state of the macroscopic fracture surface into the macroscopic phase field method calculation.

[0095] Step S3.4: Feedback the updated macroscopic fracture surface mechanical state to the microscale, achieving micro- and macro-scale coupling. Through this feedback mechanism, the behavior of the microscopic interface and the evolution of the macroscopic fracture surface interact, forming a multi-scale dynamic coupling analysis.

[0096] The specific expression of the heterogeneous data transmission protocol is:

[0097] ;

[0098] in, Represents a point on the macroscopic fracture surface The displacement at Indicates the microscopic interface debonding The displacement of a cohesion unit, represents the interpolation function, represents the displacement gradient at the microscopic level, Indicates the The coordinates of the cohesion unit.

[0099] Step S4: In the multi-scale analysis, based on the a posteriori error estimation method, the unstructured hexahedral grid local subdivision technology is used to dynamically adjust the grid size of the crack tip area.

[0100] The unstructured hexahedral mesh local subdivision technique includes the following steps:

[0101] Step S4.1: Determine the crack tip region to be subdivided. By analyzing the stress field during the numerical simulation process, identify the region where stress concentration and crack propagation are likely to occur as the crack tip region to be subdivided.

[0102] Step S4.2: Calculate the required grid density for the area based on the a posteriori error estimation result;

[0103] The posterior error estimate uses the following energy norm form:

[0104] ;

[0105] in, represents the stress field obtained by numerical calculation, represents the stress field based on experiments or high-precision benchmark solutions, represents the analysis area;

[0106] when Exceeding the preset threshold (5%), the subdivision of the unstructured hexahedral grid in the crack tip area is triggered, and the subdivision criterion is:

[0107] ;

[0108] in, and Represents the mesh size before and after subdivision, represents the local error estimate, Indicates the convergence order, and its value range is [1,3].

[0109] Step S4.3: using an unstructured hexahedral mesh generation algorithm to subdivide the target area;

[0110] Step S4.4: Check and optimize the quality of the subdivided mesh to ensure that the mesh quality meets the requirements of numerical analysis.

[0111] It is worth noting that the contents not elaborated in detail in the present invention are all prior art and are well known to those skilled in the art.

[0112] Therefore, the present invention adopts the above-mentioned method for constructing a numerical analysis model of fiber bridging of fiber concrete, which effectively solves the limitations of traditional models in interface behavior characterization, idealized assumptions of fiber distribution and grid rigid division, significantly improves the accuracy and reliability of fiber bridging effect simulation, and provides an efficient theoretical tool for fiber concrete material design and engineering application.

[0113] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for constructing a numerical analysis model of fiber bridges in fiber concrete, characterized in that: The following steps are involved: Step S1, establishing a nonlinear slip constitutive model of the fiber-matrix interface and determining the relationship between the interface shear stress and the slip amount; Step S2, generating a random distribution field of three-dimensional fiber direction angles and embedding lengths; Step S3: combining the nonlinear slip constitutive model of the microscopic interface with the macroscopic phase field method, characterizing the interface behavior through the cohesion unit, and mapping the interface debonding behavior to the macroscopic fracture surface using a heterogeneous data transfer protocol based on the random distribution field of the fiber orientation angle and embedment length; Step S4: in the multi-scale analysis, based on the a posteriori error estimation method, the unstructured hexahedral grid local subdivision technology is used to dynamically adjust the grid size of the crack tip area; In step S1, the nonlinear slip constitutive model is a piecewise bilinear softening model, and its expression is: ； in, represents the interfacial shear stress, represents the slip amount, represents the peak shear stress, represents the slip amount when the peak shear stress is reached, Indicates the residual slip in the softening stage; In step S3, the heterogeneous data transmission protocol is implemented through the following steps: Step S31, obtaining the debonding displacement field and stress field of the cohesion unit at the microscopic scale; Step S32: Mapping the microscopic debonding displacement field and stress field onto the macroscopic fracture surface using an interpolation algorithm; Step S33: updating the mechanical state of the macro fracture surface, including displacement and stress, according to the mapping results; Step S34: Feedback the updated macroscopic fracture surface mechanical state to the microscopic scale to achieve coupling between the microscopic and macroscopic scales; The specific expression of the heterogeneous data transmission protocol is: ； in, Represents a point on the macroscopic fracture surface The displacement at Indicates the microscopic interface debonding The displacement of a cohesion unit, represents the interpolation function, represents the displacement gradient at the microscopic level, Indicates the The coordinates of the cohesion unit.

2. The method for constructing a numerical analysis model of fiber concrete fiber bridging according to claim 1, characterized in that: In step S2, the three-dimensional fiber direction angle According to the following probability density distribution : ； in, represents the polar angle, represents the azimuth, represents the anisotropy coefficient, represents the second-order Legendre polynomial, which is expressed as: 。 3. The method for constructing a numerical analysis model of fiber concrete fiber bridging according to claim 2, characterized in that: In step S2, the correction factor Corrected fiber orientation angle distribution function, correction factor The expression is: ； in, Indicates the number of fibers per unit volume. represents the fiber diameter, Indicates the density of concrete; Indicates the fiber embedding length; The corrected fiber orientation angle distribution function is: 。 4. The method for constructing a numerical analysis model of fiber bridges in fiber concrete according to claim 3, characterized in that: In step S2, the fiber embedding length follows the average value , the standard deviation is The lognormal distribution of : ； in, The fiber embedding length is The probability density when .

5. The method for constructing a numerical analysis model of fiber concrete fiber bridging according to claim 4, characterized in that: In step S3, the mechanical parameters of the cohesion unit are determined by the following optimization formula: ； ； in, represents the fracture energy, represents the peak load in the pull-out test, represents the critical debonding displacement, represents the width of the specimen, represents the peak bond stress, represents the elastic modulus of the fiber; At the same time, the numerical back analysis correction coefficient is introduced By comparing the load-displacement curves of numerical simulation and test, iterative optimization The root mean square error (RMS) between the simulation results and the test results is less than 5%.

6. The method for constructing a numerical analysis model of fiber concrete fiber bridging according to claim 1, characterized in that: In step S4, the unstructured hexahedral mesh local subdivision technique includes the following steps: Step S41, determining the crack tip area that needs to be subdivided; Step S42: Calculate the required grid density for the area based on the a posteriori error estimation result; Step S43: using an unstructured hexahedral mesh generation algorithm to perform mesh subdivision on the target area; Step S44: perform quality inspection and optimization on the subdivided mesh to ensure that the mesh quality meets the requirements of numerical analysis.

7. The method for constructing a numerical analysis model of fiber bridges in fiber concrete according to claim 6, characterized in that: The posterior error estimate uses the following energy norm form: ； in, represents the stress field obtained by numerical calculation, represents the stress field based on experiments or high-precision benchmark solutions, represents the analysis area; when Exceeding the preset threshold When , the subdivision of the unstructured hexahedral mesh in the crack tip area is triggered, and the subdivision criterion is: ； in, and Represents the mesh size before and after subdivision, represents the local error estimate, Indicates the convergence order, and its value range is [1,3].

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