A calculation method for the uniaxial tensile constitutive model of UHPC based on fiber content and orientation

Abstract

The present invention relates to the field of constitutive model calculation for UHPC materials, and specifically to a method for calculating a uniaxial tensile constitutive model for UHPC based on fiber content and orientation, comprising the following steps: S1, constructing a three-dimensional microscopic numerical model of UHPC; S2, performing a uniaxial tensile simulation on a specimen using the three-dimensional microscopic numerical model to obtain a stress-strain curve data set for the specimen; S3, dividing the applicable scope of the constitutive model according to the stress-strain curve data set; S4, constructing a constitutive model based on the volume fraction of steel fibers in the UHPC and the orientation angle of the steel fibers, wherein the constructed constitutive model is a strain hardening constitutive model, a strain softening constitutive model, or a displacement softening constitutive model. The present invention constructs a uniaxial tensile constitutive model for UHPC that takes into account steel fiber content and orientation, effectively improving the calculation accuracy of the tensile strength of UHPC and solving the problem of insufficient accuracy of existing UHPC tensile constitutive models in macroscopic finite element analysis calculations.

Description

Technical Field

[0001] The present invention relates to the field of UHPC material constitutive model calculation, and in particular to a UHPC uniaxial tension constitutive model calculation method based on fiber content and orientation. Background Art

[0002] UHPC, the full name of which is Ultra-high-performance concrete, is made mainly of materials such as silicate cement, silica fume, quartz powder, steel fiber or synthetic fiber, high-efficiency water reducer, and water mixed in a certain proportion. It is a fiber-reinforced cement-based composite material with ultra-high compressive strength and high tensile strength, and is widely used in engineering practice. According to research, the amount of steel fiber and the orientation of steel fibers have a great influence on the tensile properties of UHPC. As the amount of steel fiber increases, the number of effective bridging fibers increases, and the post-crack tensile strength of UHPC is significantly improved. Compared with the fiber content, the orientation of the fiber mainly affects the interaction force between the fiber and the UHPC matrix interface, and thus affects the tensile strength of UHPC after cracking. Therefore, with an increase in the amount of steel fiber and a good fiber orientation, the uniaxial stress-strain curve of UHPC will show obvious strain hardening characteristics, and the tensile strength of UHPC will also be significantly increased.

[0003] As a relatively new material, research on tensile constitutive models for UHPC is still in its infancy, with the focus on the influence of parameters such as different fiber types and fiber content. When using this type of constitutive model for finite element calculations and analysis of UHPC components, the specific influence of fiber orientation on the tensile strength of UHPC is not taken into account, and results consistent with experiments are often not obtained. This leads to insufficient accuracy in finite element analysis calculations, which urgently needs to be addressed. Summary of the Invention

[0004] To avoid and overcome the technical problems existing in the prior art, the present invention provides a method for calculating the uniaxial tension constitutive model of UHPC based on fiber content and orientation. This method constructs a uniaxial tension constitutive model for UHPC that takes into account the steel fiber content and orientation, effectively improving the calculation accuracy of the tensile strength of UHPC.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A calculation method for the uniaxial tension constitutive model of UHPC based on fiber content and orientation includes the following steps:

[0007] S1. Construct a three-dimensional mesoscopic numerical model of UHPC;

[0008] S2. Perform uniaxial tensile simulation on the specimen using a three-dimensional microscopic numerical model to obtain a stress-strain curve dataset of the specimen;

[0009] S3. Classify the constitutive model type based on the stress-strain curve data set;

[0010] S4. Based on the volume fraction of steel fibers in UHPC and the orientation angle of steel fibers, a constitutive model is constructed. The constructed constitutive model is a strain hardening constitutive model, a strain softening constitutive model, or a displacement softening constitutive model.

[0011] As a further solution of the present invention: the strain hardening constitutive model is:

[0012]

[0013] Among them, σ t1 In the strain hardening constitutive model, any UHPC strain ε t The corresponding UHPC uniaxial tensile stress;

[0014] ε t represents the UHPC strain;

[0015] ε t,1 is the strain corresponding to UHPC cracking;

[0016] ε t,2 is the strain corresponding to the termination of strain hardening of UHPC;

[0017] ε t,3 is the strain corresponding to the onset of strain softening of UHPC;

[0018] ε t,4 is the ultimate tensile strain of UHPC;

[0019] E e Indicates that when ε t ≤ε t,1 UHPC elastic modulus at ;

[0020] E h Indicates that when ε t,1 <ε t ≤ε t,2 Elastic modulus of UHPC in the hardening stage;

[0021] f t,1 is the stress corresponding to UHPC cracking;

[0022] f t,2 is the critical point stress corresponding to the transition from strain hardening to strain softening of UHPC;

[0023] α2 and α3 are calibration coefficients;

[0024] e is Euler's number.

[0025] As a further solution of the present invention:

[0026] E e =37+295V f ;

[0027] ε t,1 =0.01+0.5V f ;

[0028] Among them, V f is the volume fraction of steel fiber in UHPC;

[0029] E h =α1E e ;

[0030]

[0031] α1 represents the fitting coefficient;

[0032] μ represents the mean of the Gaussian distribution of the angle between the arrangement direction of steel fibers in UHPC and the tensile direction;

[0033]

[0034] ε t,3 =ε t,2 +0.001;

[0035]

[0036] As a further solution of the present invention: the strain softening constitutive model is:

[0037]

[0038] Among them, σ t2 In the strain softening constitutive model, any UHPC strain ε t The corresponding UHPC uniaxial tensile stress;

[0039] ε t represents the UHPC strain;

[0040] ε t,1 is the strain corresponding to UHPC cracking;

[0041] E e Indicates that when ε t ≤ε t,1 UHPC elastic modulus at ;

[0042] ε t,4 is the ultimate tensile strain of UHPC;

[0043] f t,1is the stress corresponding to UHPC cracking;

[0044] α2 and α3 are calibration coefficients;

[0045] e is Euler's number.

[0046] As a further solution of the present invention:

[0047] E e =37+295V f ;

[0048] ε t,1 =0.01+0.5V f ;

[0049] Among them, V f is the volume fraction of steel fiber in UHPC;

[0050]

[0051] As a further solution of the present invention: the displacement softening constitutive model is:

[0052]

[0053] Among them, σ t3 represents any UHPC strain ε in the displacement softening constitutive model t The corresponding UHPC uniaxial tensile stress;

[0054] ε t represents the UHPC strain;

[0055] E e Indicates that when ε t ≤ε t,1 UHPC elastic modulus at ;

[0056] ε t,1 is the strain corresponding to UHPC cracking;

[0057] ε t,5 is the strain corresponding to the termination of UHPC displacement softening;

[0058] ε t,4 is the ultimate tensile strain of UHPC;

[0059] f t,1 is the stress corresponding to UHPC cracking;

[0060] e is Euler's number.

[0061] As a further solution of the present invention:

[0062] E e=37+295V f ;

[0063] ε t,1 =0.01+0.5V f ;

[0064] ε t,5 =ε t,1 +0.05%;

[0065] Among them, V f is the volume fraction of steel fiber in UHPC.

[0066] As a further solution of the present invention: in step S1:

[0067] S11, determining the volume of the UHPC sample, the volume fraction of steel fibers in the sample, and the size of the steel fibers, and generating a UHPC mortar cohesive unit;

[0068] S12, dividing the probability density distribution of steel fiber orientation along the uniaxial tensile direction into equal-width intervals;

[0069] S13, randomly determining the center coordinates of the fibers within the sample and generating steel fibers until the volume fraction of the generated steel fibers reaches a set value, generating an orientation angle for the steel fibers in each interval according to a probability distribution, and calculating the positions of the two endpoints of the steel fibers based on the orientation angles of the steel fibers;

[0070] S14. Verify whether the generated steel fibers intersect with the specimen boundary or other steel fibers;

[0071] If there is an intersection, return to step S13;

[0072] If there is no intersection, output the three-dimensional microscopic numerical model of UHPC.

[0073] As a further solution of the present invention: a zero-thickness six-node three-dimensional cohesive element is established through ABAQUS, the length of the steel fiber is set to 13 mm, the diameter is 0.2 mm, and the volume fraction of the steel fiber is 1% or 2% or 3%.

[0074] As a further solution of the present invention, the UHPC specimens to which the strain hardening constitutive model is applicable must meet the following conditions:

[0075] The volume fraction of steel fiber is 1% and the mean of the Gaussian distribution of the angle between the arrangement direction of steel fiber in UHPC and the tensile direction is between 20° and 35°;

[0076] Alternatively, the steel fiber volume fraction is 2% and the mean of the Gaussian distribution of the angle between the arrangement direction of the steel fibers in the UHPC and the tensile direction is between 20° and 40°;

[0077] Alternatively, the steel fiber volume fraction is 3% and the mean of the Gaussian distribution of the angle between the arrangement direction of the steel fibers in the UHPC and the tensile direction is between 20° and 45°;

[0078] The UHPC specimens applicable to the strain softening constitutive model must meet the following conditions:

[0079] The volume fraction of steel fiber is 1% and the mean of the Gaussian distribution of the angle between the arrangement direction of steel fiber in UHPC and the tensile direction is between 40° and 50°;

[0080] Alternatively, the steel fiber volume fraction is 2% and the mean of the Gaussian distribution of the angle between the arrangement direction of the steel fibers in the UHPC and the tensile direction is between 50° and 70°;

[0081] Alternatively, the steel fiber volume fraction is 3% and the mean of the Gaussian distribution of the angle between the arrangement direction of the steel fibers in the UHPC and the tensile direction is between 50° and 70°;

[0082] The UHPC specimens applicable to the displacement softening constitutive model must meet the following conditions:

[0083] The volume fraction of steel fiber is 1% and the mean of the Gaussian distribution of the angle between the arrangement direction of steel fiber in UHPC and the tensile direction is between 50° and 70°.

[0084] Compared with the prior art, the present invention has the following beneficial effects:

[0085] 1. The present invention constructs a UHPC uniaxial tensile constitutive model that takes into account the steel fiber content and orientation, effectively improving the calculation accuracy of the UHPC tensile strength and solving the problem of insufficient accuracy of the existing UHPC tensile constitutive model in macroscopic finite element analysis calculations.

[0086] 2. The present invention considers the effect of fiber orientation on the tensile properties of UHPC from a microscopic perspective and clarifies the quantitative relationship between fiber orientation and the strain hardening characteristics of UHPC.

[0087] 3. The constitutive model construction method proposed in the present invention is also applicable to different types of fibers and different concrete materials, providing a basis for the refined theoretical analysis of fiber-reinforced concrete. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 Schematic diagram of the structure of the tensile specimen of the present invention.

[0089] Figure 2 This is the Gaussian probability distribution diagram of the steel fiber orientation angle of the sample with a steel fiber volume fraction of 1%.

[0090] Figure 3 for Figure 2The corresponding cross-sectional binary image of the sample.

[0091] Figure 4 This is the Gaussian probability distribution diagram of the steel fiber orientation angle of the sample with a steel fiber volume fraction of 2%.

[0092] Figure 5 for Figure 4 The corresponding cross-sectional binary image of the sample.

[0093] Figure 6 This is the Gaussian probability distribution diagram of the steel fiber orientation angle of the sample with a steel fiber volume fraction of 3%.

[0094] Figure 7 for Figure 6 The corresponding cross-sectional binary image of the sample.

[0095] Figure 8 for Figure 2 Comparison of the calculated predicted constitutive curve and the experimental constitutive curve of the corresponding sample.

[0096] Figure 9 for Figure 4 Comparison of the calculated predicted constitutive curve and the experimental constitutive curve of the corresponding sample.

[0097] Figure 10 for Figure 6 Comparison of the calculated predicted constitutive curve and the experimental constitutive curve of the corresponding sample. DETAILED DESCRIPTION

[0098] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0099] See also Figures 1 to 10 In an embodiment of the present invention, a calculation method for the uniaxial tensile constitutive model of UHPC based on fiber content and orientation is provided.

[0100] The steps include:

[0101] S1. Construct a three-dimensional mesoscopic numerical model of UHPC. The constructed three-dimensional mesoscopic numerical model simultaneously considers the steel fiber orientation, matrix multi-cracks and steel fiber-matrix interaction in UHPC.

[0102] S11. Determine the volume of the UHPC specimen, the volume fraction of the steel fiber in the specimen, and the size of a single steel fiber, and generate a UHPC mortar cohesive unit. The UHPC mortar cohesive unit is a zero-thickness, six-node three-dimensional cohesive unit established in the finite element software ABAQUS. In this embodiment, a total of 75 specimens were established. The steel fibers used in the specimens were smooth, short, straight steel fibers with a length of 13 mm and a diameter of 0.2 mm. The steel fiber dosages were 25 groups each of 1%, 2%, and 3%.

[0103] S12. Divide the probability density distribution of steel fiber orientation into equal-width intervals along the uniaxial tensile direction of the tensile test; steel fiber orientation can be defined as the angle between the arrangement direction of steel fibers in UHPC and the tensile direction.

[0104] The orientation of steel fibers can be determined by cutting the specimen to obtain a statistical histogram of the fiber angle of the cut section. The Gaussian probability density distribution of the fiber angle is obtained by fitting the histogram, and the corresponding mean and variance are obtained. The applicable ranges of the three types of constitutive models can be obtained by querying the mean and variance.

[0105] S13, randomly determining the center coordinates of the fibers within the sample and generating steel fibers until the volume fraction of the generated steel fibers reaches a set value, generating an orientation angle for the steel fibers in each interval according to a probability distribution, and calculating the positions of the two endpoints of the steel fibers based on the orientation angles of the steel fibers;

[0106] S14. Based on the calculated steel fiber position, verify whether the generated steel fiber intersects with the specimen boundary or other steel fibers.

[0107] If there is an intersection, return to step S13 and regenerate the steel fiber;

[0108] If there is no intersection, the three-dimensional microscopic numerical model of UHPC is output. In this embodiment, the generated steel fibers are divided into six groups according to the orientation angles of the steel fibers, and corresponding material properties are assigned to each group of steel fibers according to the orientation range of the steel fibers.

[0109] The steel fibers are divided into six groups, with steel fiber orientation angles of 0°~7.5°, 7.5°~22.5°, 22.5°~37.5°, 37.5°~52.5°, 52.5°~67.5° and 67.5°~90°, corresponding to the steel fiber pull-out force-displacement relationships at inclination angles of 0°, 15°, 30°, 45°, 60° and 90°, respectively.

[0110] S2. Perform uniaxial tensile simulation on the sample using a three-dimensional microscopic numerical model, and obtain a stress-strain curve data set of the sample based on the numerical simulation results. In this embodiment, a total of 75 groups of stress-strain curves of the sample are extracted.

[0111] S3. Classify the constitutive model type based on the stress-strain curve data set;

[0112] S4. Based on the volume fraction of steel fibers and the orientation angle of steel fibers in UHPC, the strain hardening constitutive model, strain softening constitutive model and displacement softening constitutive model are constructed.

[0113] The strain hardening constitutive model is:

[0114]

[0115] Among them, σ t1 In the strain hardening constitutive model, any UHPC strain ε t The corresponding UHPC uniaxial tensile stress;

[0116] ε t represents the UHPC strain;

[0117] ε t,1 is the strain corresponding to the cracking of UHPC, which corresponds to the starting point of strain hardening.

[0118] ε t,1 =0.01+0.5V f ;

[0119] ε t,2 is the strain corresponding to the termination of strain hardening of UHPC;

[0120]

[0121] ε t,3 is the strain corresponding to the onset of strain softening of UHPC;

[0122] ε t,3 =ε t,2 +0.001;

[0123] ε t,4 is the ultimate tensile strain of UHPC, and its value is the strain value when the specimen reaches 85% of the peak stress.

[0124] E e Indicates that when ε t ≤ε t,1 UHPC elastic modulus at ;

[0125] E e =37+295V f ;

[0126] V f is the volume fraction of steel fiber in UHPC;

[0127] E h Indicates that when εt,1 <ε t ≤ε t,2 Elastic modulus of UHPC in the hardening stage;

[0128] E h =α1E e ;

[0129]

[0130] f t,1 is the stress corresponding to UHPC cracking;

[0131] f t,2 is the critical point stress corresponding to the transition from strain hardening to strain softening of UHPC;

[0132] α2 and α3 are calibration coefficients, which are obtained by fitting the values.

[0133]

[0134] e is Euler's number.

[0135] The applicable scope of the strain hardening constitutive model is as follows:

[0136] The volume fraction of steel fiber is 1% and the mean of the Gaussian distribution of the angle between the arrangement direction of steel fiber in UHPC and the tensile direction is between 20° and 35°;

[0137] Alternatively, the steel fiber volume fraction is 2% and the mean of the Gaussian distribution of the angle between the arrangement direction of the steel fibers in the UHPC and the tensile direction is between 20° and 40°;

[0138] Alternatively, the volume fraction of the steel fiber is 3% and the Gaussian distribution mean of the angle between the arrangement direction of the steel fiber in the UHPC and the tensile direction is between 20° and 45°.

[0139] The strain softening constitutive model is:

[0140]

[0141] Among them, σ t2 In the strain softening constitutive model, any UHPC strain ε t The corresponding UHPC uniaxial tensile stress;

[0142] ε t represents the UHPC strain;

[0143] ε t,1 It is the strain corresponding to the cracking of UHPC; UHPC enters the strain softening process after cracking.

[0144] Ee Indicates that when ε t ≤ε t,1 UHPC elastic modulus at ;

[0145] E e =37+295V f ;

[0146] ε t,1 =0.01+0.5V f ;

[0147] V f is the volume fraction of steel fiber in UHPC;

[0148] ε t,4 is the ultimate tensile strain of UHPC, and its value is the strain value when the specimen reaches 85% of the peak stress.

[0149] f t,1 is the stress corresponding to UHPC cracking;

[0150] α2 and α3 are calibration coefficients, which are obtained by fitting the values.

[0151]

[0152] e is Euler's number.

[0153] The UHPC specimens applicable to the strain softening constitutive model must meet the following conditions:

[0154] The volume fraction of steel fiber is 1% and the mean of the Gaussian distribution of the angle between the arrangement direction of steel fiber in UHPC and the tensile direction is between 40° and 50°;

[0155] Alternatively, the steel fiber volume fraction is 2% and the mean of the Gaussian distribution of the angle between the arrangement direction of the steel fibers in the UHPC and the tensile direction is between 50° and 70°;

[0156] Alternatively, the volume fraction of the steel fiber is 3% and the mean value of the Gaussian distribution of the angle between the arrangement direction of the steel fiber in the UHPC and the tensile direction is between 50° and 70°.

[0157] The displacement softening constitutive model is:

[0158]

[0159] Among them, σ t3 represents any UHPC strain ε in the displacement softening constitutive model t The corresponding UHPC uniaxial tensile stress;

[0160] ε t represents the UHPC strain;

[0161] E e Indicates that when ε t ≤ε t,1 UHPC elastic modulus at ;

[0162] E e =37+295V f ;

[0163] V f is the volume fraction of steel fiber in UHPC.

[0164] ε t,1 is the strain corresponding to UHPC cracking;

[0165] ε t,1 =0.01+0.5V f .

[0166] ε t,5 is the strain corresponding to the termination of UHPC displacement softening;

[0167] ε t,5 =ε t,1 +0.05%.

[0168] ε t,4 is the ultimate tensile strain of UHPC, and its value is 0.8% to 1.2%.

[0169] f t,1 is the stress corresponding to UHPC cracking;

[0170] e is Euler's number.

[0171] The UHPC specimens applicable to the displacement softening constitutive model must meet the following conditions:

[0172] The volume fraction of steel fiber is 1% and the mean of the Gaussian distribution of the angle between the arrangement direction of steel fiber in UHPC and the tensile direction is between 50° and 70°.

[0173] In this example, the raw materials of the UHPC sample are mixed in the following proportions:

[0174] Portland cement 1000kg / m 3 , silica fume 250kg / m 3 , quartz sand 1250kg / m 3 , water reducing agent 10kg / m 3 , water 240kg / m 3 The steel fiber length is 13 mm and the diameter is 0.2 mm.

[0175] The appearance of UHPC specimens is as follows Figure 1As shown in the figure, the specimen is flat, wide at both ends and narrow in the middle, with an inclined transition between the middle section and the two ends, giving it an overall dog-bone shape. Three groups of specimens were made, with steel fiber volume fractions of 1%, 2%, and 3% respectively.

[0176] When performing a tensile test on a specimen, the specimen is clamped on an MTS (Mechanical Testing & Simulation) electro-hydraulic testing machine. The upper and lower ends of the specimen are connected to the fixture of the testing machine through two clamping rods. A spherical hinge is provided at the connection end, and axial tension is applied to the specimen through the testing machine.

[0177] The tensile displacement of the specimen was measured using two highly sensitive displacement gauges within a narrow 80mm region in the middle of the specimen. Displacement loading was applied at a rate of 0.2mm / min. After the test, the specimen was sectioned, and the fiber angle perpendicular to the tensile direction was statistically analyzed using image processing. The mean and variance of the Gaussian probability distribution were then fitted.

[0178] In the test results, Figure 2 The Gaussian probability distribution diagram of the steel fiber orientation angle of the sample with a steel fiber volume fraction of 1% is shown in the figure. The average value of the steel fiber orientation angle is 53°. The cross-sectional binary diagram of the sample is shown in the figure. Figure 3 shown.

[0179] Figure 4 The Gaussian probability distribution diagram of the steel fiber orientation angle of the sample with a steel fiber volume fraction of 2% is shown in Figure 2. The average steel fiber orientation angle is 56°. The cross-sectional binary diagram of the sample is shown in Figure 2. Figure 5 shown.

[0180] Figure 6 The Gaussian probability distribution diagram of the steel fiber orientation angle of the sample with a steel fiber volume fraction of 3% is shown in Figure 2. The average steel fiber orientation angle is 43°. The cross-sectional binary diagram of the sample is shown in Figure 2. Figure 7 shown.

[0181] Figure 3 The corresponding specimens are subjected to the displacement softening constitutive model, and the constitutive relationship curve obtained from the test is consistent with the predicted curve simulated by calculation in this embodiment. Figure 8 As shown, the two sets of curves are basically consistent.

[0182] Figure 5 The corresponding specimens were subjected to the strain softening constitutive model, and the constitutive relationship curve obtained from the test was consistent with the predicted curve simulated by calculation in this embodiment. Figure 9 As shown, the two sets of curves are basically consistent.

[0183] Figure 7 The corresponding specimens are subjected to the strain hardening constitutive model, and the constitutive relationship curve obtained from the test is consistent with the predicted curve simulated by calculation in this embodiment. Figure 10As shown, the two sets of curves are basically consistent.

[0184] It can be seen that the calculation prediction curves of the three types of constitutive models are consistent with the constitutive relationship curves obtained from the experiment, which can verify the reliability of the calculation method of this embodiment.

[0185] The basic principles of the present application have been described above in conjunction with specific embodiments. However, it should be noted that the advantages, strengths, and effects mentioned in this application are merely illustrative and not restrictive, and it should not be assumed that these advantages, strengths, and effects are required of each embodiment of this application. In addition, the specific details disclosed above are merely illustrative and facilitating understanding, and are not restrictive. The above details do not limit this application to necessarily being implemented using the above specific details.

[0186] The block diagrams of the devices, devices, equipment, and systems involved in this application are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As will be appreciated by those skilled in the art, these devices, devices, equipment, and systems can be connected, arranged, or configured in any manner. Words such as "include," "comprise," "have," and the like are open-ended words, meaning "including but not limited to," and can be used interchangeably therewith. The words "or" and "and" used herein refer to the words "and / or" and can be used interchangeably therewith, unless the context clearly indicates otherwise. The word "such as" used herein refers to the phrase "such as but not limited to," and can be used interchangeably therewith.

Claims

1. A calculation method for the uniaxial tension constitutive model of UHPC based on fiber content and orientation, characterized in that: The steps include: S1. Construct a three-dimensional mesoscopic numerical model of UHPC; S2. Perform uniaxial tensile simulation on the specimen using a three-dimensional microscopic numerical model to obtain a stress-strain curve dataset of the specimen; S3. Classify the constitutive model type based on the stress-strain curve data set; S4. Based on the volume fraction of steel fibers and the orientation angle of steel fibers in UHPC, a constitutive model is constructed. The constructed constitutive model is a strain hardening constitutive model. The strain hardening constitutive model is: Among them, σ t1 In the strain hardening constitutive model, any UHPC strain ε t The corresponding UHPC uniaxial tensile stress; ε t represents the UHPC strain; ε t,1 is the strain corresponding to UHPC cracking; ε t,2 is the strain corresponding to the termination of strain hardening of UHPC; ε t,3 is the strain corresponding to the onset of strain softening of UHPC; ε t,4 is the ultimate tensile strain of UHPC; E e Indicates that when ε t ≤ε t,1 UHPC elastic modulus at ; E h Indicates that when ε t,1 <ε t ≤ε t,2 Elastic modulus of UHPC in the hardening stage; f t,1 is the stress corresponding to UHPC cracking; f t,2 is the critical point stress corresponding to the transition from strain hardening to strain softening of UHPC; α2 and α3 are calibration coefficients; e is Euler's number.

2. The method for calculating the uniaxial tensile constitutive model of UHPC based on fiber content and orientation according to claim 1, characterized in that: AND e =37+295V f ; e t,1 =0.01+0.5V f ; Among them, V f is the volume fraction of steel fiber in UHPC; E h =α1E e ; α1 represents the fitting coefficient; μ represents the mean of the Gaussian distribution of the angle between the arrangement direction of steel fibers in UHPC and the tensile direction; e t,3 =e t,2 +0.001; 3. A method for calculating the uniaxial tensile constitutive model of UHPC based on fiber content and orientation according to claim 1 or 2, characterized in that: In step S1: S11, determining the volume of the UHPC sample, the volume fraction of steel fibers in the sample, and the size of the steel fibers, and generating a UHPC mortar cohesive unit; S12, dividing the probability density distribution of steel fiber orientation along the uniaxial tensile direction into equal-width intervals; S13, randomly determining the center coordinates of the fibers within the sample and generating steel fibers until the volume fraction of the generated steel fibers reaches a set value, generating an orientation angle for the steel fibers in each interval according to a probability distribution, and calculating the positions of the two endpoints of the steel fibers based on the orientation angles of the steel fibers; S14. Verify whether the generated steel fibers intersect with the specimen boundary or other steel fibers; If there is an intersection, return to step S13; If there is no intersection, output the three-dimensional microscopic numerical model of UHPC.

4. A method for calculating the uniaxial tensile constitutive model of UHPC based on fiber content and orientation according to claim 1 or 2, characterized in that: A zero-thickness six-node three-dimensional cohesive element was established using ABAQUS. The length of the steel fiber was set to 13 mm, the diameter was 0.2 mm, and the volume fraction of the steel fiber was set to 1%, 2%, or 3%.

5. A method for calculating the uniaxial tensile constitutive model of UHPC based on fiber content and orientation according to claim 1 or 2, characterized in that: The UHPC specimens applicable to the strain hardening constitutive model must meet the following conditions: The volume fraction of steel fiber is 1% and the mean of the Gaussian distribution of the angle between the arrangement direction of steel fiber in UHPC and the tensile direction is between 20° and 35°; Alternatively, the steel fiber volume fraction is 2% and the mean of the Gaussian distribution of the angle between the arrangement direction of the steel fibers in the UHPC and the tensile direction is between 20° and 40°; Alternatively, the volume fraction of the steel fiber is 3% and the Gaussian distribution mean of the angle between the arrangement direction of the steel fiber in the UHPC and the tensile direction is between 20° and 45°.

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