A method of meso-modelling and analysis of a uhpc structure

Abstract

This invention relates to a method for mesoscopic modeling and analysis of UHPC structures, comprising: Step 1) determining the coordinates of lattice nodes based on the dimensional characteristic parameters of the UHPC components, and connecting the lattice nodes to obtain the framework of the lattice model; Step 2) determining the number of steel fibers and the mesoscopic two-dimensional parameters of each component of the UHPC based on the material gradation of each component used in the UHPC material; Step 3) generating a mesoscopic random distribution model of steel fibers based on a random distribution algorithm, and generating connecting rods based on the coordinates of the steel fiber nodes and the coordinates of the lattice nodes to obtain the lattice model; Step 4) importing the lattice model into the ABAQUS secondary development platform, performing load calculations, and judging the stress state of each lattice element according to the failure criterion based on the load calculation results. If the judgment result indicates failure, the lattice element is replaced with a zero element with both elastic modulus and strength of 0. Compared with the prior art, this invention comprehensively considers the mesoscopic structural characteristics of UHPC and provides a refined numerical simulation approach.

Description

Technical Field

[0001] This invention relates to the field of material simulation and numerical analysis, and in particular to a method for mesoscopic modeling and analysis of UHPC structures. Background Technology

[0002] Unified high-performance concrete (UHPC) is a multiphase composite material composed of a matrix and steel fibers. Due to the presence of steel fibers, when the UHPC matrix cracks, the steel fibers passing through the cracks act as a "bridging" agent, transferring stress between the cracks through their interaction with the matrix. This results in a highly complex failure mechanism. Currently, numerical models of UHPC are based on macroscopic mechanical models that simulate homogeneous materials, failing to accurately represent the actual failure process. Furthermore, in macroscopic mechanical experiments, the size effect becomes increasingly pronounced as the structure's dimensions increase. Often, a macroscopic constitutive numerical model applicable at one size becomes inapplicable at another, which is related to the increasing number of internal defects in the material. Simulating the structure at the mesoscopic level can effectively avoid the size effect at the macroscopic mechanical level. Therefore, to obtain accurate failure mechanisms and mechanical responses, research at the mesoscopic level is imperative.

[0003] A review of existing technologies revealed that the microstructure analysis of UHPC materials primarily focuses on the random distribution of steel fibers. In the Chinese patent "A Method for Analyzing the Microstructure Behavior of Fiber-Modified Asphalt Concrete Based on Random Finite Element Method" (authorization number: CN201710591145.7), Xu Xunqian et al. constructed a three-dimensional random distribution model of fibers based on the Latin hypercube stratified sampling method and a random generation algorithm. This method can quickly generate fiber microstructure geometric distribution parameters and establish a microstructure numerical analysis model. Regarding microstructure analysis methods, in the Chinese patent "A Method for Analyzing Concrete Microstructure Models Based on APDL Language" (authorization number: CN201711098345.5), Yang Xu et al. used the APDL parametric design language as a platform. By inputting the material properties of each concrete component and the loading method of the specimen, they performed modeling and intelligent mesh generation, then solved the model, judged the element information read after loading, and killed the element if the condition for element failure was met, finally obtaining the output result. This method, because it directly kills elements, is prone to convergence problems. Existing patents on the microstructure of UHPCs mainly focus on microstructure modeling methods, while microstructure computational analysis methods have not yet been addressed. Summary of the Invention

[0004] The purpose of this invention is to provide a method for microstructure modeling and analysis of UHPC structures, which comprehensively considers the microstructure characteristics of UHPC materials, establishes a lattice model suitable for numerical analysis, and performs refined numerical analysis on it.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] A method for mesoscopic modeling and analysis of UHPC structures includes the following steps:

[0007] Step 1) Determine the coordinates of the lattice nodes based on the dimensional characteristic parameters of the UHPC components, and connect the lattice nodes to obtain the frame of the lattice model, wherein the lattice model includes lattice nodes and lattice units that are interconnected between the lattice nodes.

[0008] Step 2) Determine the number of steel fibers and the microscopic two-dimensional parameters of each component of UHPC based on the material gradation of each component used in UHPC material;

[0009] Step 3) Generate a steel fiber mesoscopic random distribution model based on the random distribution algorithm, the number of steel fibers, and the mesoscopic two-dimensional parameters of each component of UHPC. Generate connecting rods based on the steel fiber node coordinates and the lattice node coordinates to obtain the lattice model.

[0010] Step 4) Import the lattice model into the ABAQUS secondary development platform, perform load calculations, and based on the load calculation results, determine the stress state of each lattice element according to the failure criterion. If the determination result is failure, replace the lattice element with a zero element whose elastic modulus and strength are both 0.

[0011] The characteristic parameters of the UHPC components include the overall dimensions, boundary conditions, and load conditions of the UHPC structure.

[0012] The method for determining the coordinates of the lattice nodes is as follows: based on the concept of the lattice model, the structure is divided into several grids, and each lattice node is randomly distributed in the corresponding grid.

[0013] The number of steel fibers is calculated based on the volume of the UHPC component, the volume content of steel fibers, and the volume of steel fibers:

[0014] n s =V U ρ s / V s

[0015] Where, n s V represents the number of steel fibers. U ρ is the volume of the UHPC component. s V represents the volume content of steel fibers. s This represents the volume of the steel fiber.

[0016] The microscopic two-dimensional parameters of each component of the UHPC include the elastic modulus, Poisson's ratio, and strength of each material.

[0017] The two-dimensional spatial steel fiber parameters in the two-dimensional parameters are obtained by reducing and transforming the steel fiber based on the material characteristic parameters of the steel fiber in three-dimensional space and the projection of the steel fiber.

[0018] The reduction conversion includes the following steps:

[0019] For any steel fiber passing through the computational plane, determine the projected length of the steel fiber on the computational plane:

[0020] l cosα=l xoy

[0021] Where l is the actual length of the steel fiber, α is the angle between the steel fiber and the calculation plane, and l xoy It is the planar projection length of the steel fiber;

[0022] Based on the spatial distribution characteristics of steel fibers, the average projected length of steel fibers in two-dimensional space is determined:

[0023]

[0024] Using the reduction in elastic modulus E instead of the reduction in horizontal projected length, the conversion relationship is as follows:

[0025] E1ε1=E2ε2

[0026]

[0027] Where E1 is the true elastic modulus of the steel fiber, E2 is the elastic modulus of the steel fiber in two-dimensional space, ε1 is the true strain of the steel fiber, and ε2 is the strain of the steel fiber in two-dimensional space.

[0028] The spatial distribution characteristics of the steel fibers include:

[0029] The steel fibers are distributed uniformly and randomly in space;

[0030] The angle α between each steel fiber passing through the calculation plane and the calculation plane is random, and the probability of each angle is the same.

[0031] The process of generating the microscopic random distribution model of steel fibers includes the following steps:

[0032] Step 3-1) Determine the distribution range and quantity of steel fibers;

[0033] Step 3-2) Each steel fiber includes 2 nodes. For the i-th steel fiber, an initial node is randomly generated within the distribution range of the steel fiber. The position of the initial node is determined by a random number x. i and y i The coordinates of the second node are determined by taking the initial node as the origin of the polar coordinates and based on the actual length of the steel fiber and the random polar coordinate angle ρ.

[0034] Step 3-3) Determine whether the coordinates of the second node exceed the pre-configured matrix range. If so, delete the coordinates and regenerate the coordinates of the second node of the steel fiber.

[0035] Steps 3-4) Repeat steps 3-2)-3-3) until all steel fiber nodes are generated.

[0036] Step 4) includes the following steps:

[0037] Step 4-1) Import the lattice model into the ABAQUS computing platform;

[0038] Step 4-2) Use Python to perform secondary development on the lattice model, assigning pre-configured boundary and load constraints;

[0039] Step 4-3) Use the Standard module to perform load calculations on the lattice model;

[0040] Step 4-4) Based on the load calculation results, the stress state of each lattice element is judged according to the failure criterion. If the judgment result is failure, the lattice element is replaced with a zero element with an elastic modulus and strength of 0.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] (1) This invention comprehensively considers the microstructural characteristics of UHPC materials and fully utilizes the features of the lattice model and rod system model to simulate the microstructure of steel fibers, which is not available in traditional continuous finite element models. This modeling method is simpler and faster. At the same time, this invention uses connecting rods to simulate the connection between steel fibers and the UHPC matrix, and uses the failure of the connecting rods to simulate the failure process of steel fibers and matrix. The failure process is more refined, providing a new and effective simulation method for UHPC microstructure simulation.

[0043] (2) This invention uses the ABAQUS platform for secondary development and performs linear elastic calculations on the UHPC lattice model. It uses the failure criteria to replace the elements. Therefore, the model can simulate the sequential failure process of UHPC material based on the sequential failure of the steel fiber and matrix connecting rods, providing a good calculation model for the refined numerical simulation of UHPC material. Attached Figure Description

[0044] Figure 1 This is a flowchart of the method of the present invention;

[0045] Figure 2 A schematic diagram of the basic elements of a lattice model;

[0046] Figure 3 This is a schematic diagram of the reduction and conversion of steel fiber parameters;

[0047] Figure 4 The diagram shows the dimensions of the UHPC and the axial tensile test, where (a) shows the dimensions of the UHPC and (b) shows the axial tensile test.

[0048] Figure 5 A lattice model as one embodiment;

[0049] Figure 6 This is a schematic diagram of a two-bar connection method;

[0050] Figure 7 For steel fiber micro-stochastic model and matrix combination model, (a) is steel fiber micro-stochastic model and (b) is combination model;

[0051] Figure 8 A comparison diagram of the damage change process;

[0052] Figure 9 This is a schematic diagram of the failure of the connecting rod. Detailed Implementation

[0053] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0054] This embodiment uses the axial tensile test of UHPC as an example to provide a method for mesoscopic modeling and analysis of UHPC structures, such as... Figure 1 As shown, it includes the following steps:

[0055] Step 1) Determine the coordinates of the lattice nodes based on the dimensional characteristic parameters of the UHPC components, and connect the lattice nodes to obtain the frame of the lattice model, wherein the lattice model includes lattice nodes and lattice units that are interconnected between the lattice nodes.

[0056] The characteristic parameters of the UHPC components include the overall dimensions, boundary conditions, and load conditions of the UHPC structure.

[0057] A lattice model is a mesoscopic numerical model that simulates a continuous structure using discrete rods. The basic structure of a lattice model includes lattice nodes and the interconnected rod-like lattice elements (rods). The locations of the lattice nodes and the element dimensions are determined as follows: based on the concept of a lattice model, such as... Figure 2 As shown, the structure is first divided into several grids. The position of each lattice node can be randomly distributed in the corresponding structural grid. After the lattice nodes are determined, adjacent lattice nodes are connected to form lattice units.

[0058] First, determine the dimensions of its two-dimensional lattice model based on the dimensions of the test specimen, such as... Figure 4 As shown in (a). The UHPC axial tensile test is as follows: Figure 4 As shown in (b), the end loading area of ​​this model is 200×200mm. The transition section of this model has been simplified using a straight line. Furthermore, to ensure that the axial force can be directly transmitted to the test section of the model, the degrees of freedom of the lattice nodes in the transition section are set to 0, and all end elements are set as rigid bodies. In the 200mm×50mm test section in the middle, this example uses n=0.5 degrees of freedom to generate the middle node model, while the degrees of freedom of the edge nodes are set to n=0. The final axial tension lattice model is shown below. Figure 5 As shown.

[0059] Step 2) Determine the number of steel fibers and the microscopic two-dimensional parameters of each component of UHPC based on the material gradation of each component used in UHPC material;

[0060] The number of steel fibers is calculated based on the volume of the UHPC component, the volume content of steel fibers, and the volume of steel fibers:

[0061] n s =V U ρ s / V s

[0062] Where, n s V represents the number of steel fibers. U ρ is the volume of the UHPC component. s V represents the volume content of steel fibers. s This represents the volume of the steel fiber.

[0063] The microscopic two-dimensional parameters of each component of UHPC include the elastic modulus, Poisson's ratio, and strength of each material, all of which can be determined based on experimental and literature data. The material parameters in this embodiment are shown in Table 1.

[0064] Table 1 Properties of UHPC Lattice Elements

[0065]

[0066] Since the steel fibers were originally randomly distributed in the UHPC specimen in three-dimensional space, it is necessary to reduce and transform the UHPC steel fiber parameters in a two-dimensional plane in order to establish a three-dimensional lattice analysis model.

[0067] The three-dimensional spatial distribution of steel fibers is as follows Figure 3 As shown in the figure, the plane through which the steel fiber passes is set as the calculation plane, and the material properties of the steel fiber are converted according to the projection of the steel fiber.

[0068] For any steel fiber passing through the computational plane, determine the projected length of the steel fiber on the computational plane:

[0069] l cosα=l xoy

[0070] Where l is the actual length of the steel fiber, α is the angle between the steel fiber and the calculation plane, and l xoy It is the planar projection length of the steel fiber;

[0071] Based on the spatial distribution characteristics of steel fibers, the average projected length of steel fibers in two-dimensional space is determined:

[0072]

[0073] To ensure that the deformation of the steel fiber in two dimensions is the same as the actual deformation, this invention uses a reduction in the elastic modulus E instead of a reduction in the horizontal projected length. The conversion relationship is as follows:

[0074] E1ε1=E2ε2

[0075]

[0076] Where E1 is the true elastic modulus of the steel fiber, E2 is the elastic modulus of the steel fiber in two-dimensional space, ε1 is the true strain of the steel fiber, and ε2 is the strain of the steel fiber in two-dimensional space.

[0077] The spatial distribution characteristics of the steel fibers include:

[0078] The steel fibers are distributed uniformly and randomly in space;

[0079] The angle α between each steel fiber passing through the calculation plane and the calculation plane is random, and the probability of each angle is the same.

[0080] Step 3) Generate a steel fiber mesoscopic random distribution model based on the random distribution algorithm, the number of steel fibers, and the mesoscopic two-dimensional parameters of each component of UHPC. Generate connecting rods based on the steel fiber node coordinates and the lattice node coordinates to obtain the lattice model.

[0081] Step 3-1) Determine the distribution range and quantity of steel fibers;

[0082] Step 3-2) Each steel fiber includes 2 nodes. For the i-th steel fiber, an initial node is randomly generated within the distribution range of the steel fiber. The position of the initial node is determined by a random number x. i and y i The coordinates of the second node are determined by taking the initial node as the origin of the polar coordinates and based on the actual length of the steel fiber and the random polar coordinate angle ρ.

[0083] Step 3-3) Determine whether the coordinates of the second node exceed the pre-configured matrix range. If so, delete the coordinates and regenerate the coordinates of the second node of the steel fiber.

[0084] Steps 3-4) Repeat steps 3-2)-3-3) until all steel fiber nodes are generated.

[0085] In the lattice model, connections between nodes create lattice elements. Connecting the coordinates of steel fiber nodes to the coordinates of lattice nodes generates connecting members, while connecting the coordinates of lattice nodes together generates material elements. Connecting members and material elements are assigned different element and material properties. Once all lattice elements have been assigned element and material properties, a complete lattice model is obtained.

[0086] The failure process of UHPC material is actually the continuous breakdown of the connection between the steel fibers and the matrix after the matrix cracks until the steel fibers are completely pulled out. Therefore, in order to accurately simulate the failure process of UHPC and the separation process of the steel fibers from the UHPC matrix, this embodiment uses a double-bar configuration for simulation, such as... Figure 6 As shown, the steel fiber unit node is connected to the two nearest lattice nodes.

[0087] See the model diagram of the generated steel fiber. Figure 7 (a) The model after steel fibers and matrix are combined is shown in [reference]. Figure 7 (b)

[0088] Step 4) Import the lattice model into the ABAQUS secondary development platform, perform load calculations, and based on the load calculation results, determine the stress state of each lattice element according to the failure criterion. If the determination result is failure, replace the lattice element with a zero element whose elastic modulus and strength are both 0.

[0089] Step 4-1) Import the lattice model into the ABAQUS computing platform;

[0090] Step 4-2) Use Python to perform secondary development on the lattice model, assigning pre-configured boundary and load constraints;

[0091] Step 4-3) Use the Standard module to perform load calculations on the lattice model;

[0092] Step 4-4) Based on the load calculation results, the stress state of each lattice element is judged according to the failure criterion. If the judgment result is failure, the lattice element is replaced with a zero element with an elastic modulus and strength of 0.

[0093] The final analysis results are as follows Figure 8As shown, the lattice model initially generated cracks in three regions: the middle, upper-middle, and lower-middle sections of the UHPC test segment. Subsequently, as the loading displacement gradually increased, multiple cracks developed simultaneously, and the failure cracks were evenly distributed throughout the entire UHPC test segment. This mode of simultaneous development of multiple cracks demonstrates that the steel fibers and connecting rods in the lattice model effectively played their role, enabling the smooth transmission of tensile stress between cracks.

[0094] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for mesoscopic modeling and analysis of UHPC structures, characterized in that, Includes the following steps: Step 1) Determine the coordinates of the lattice nodes based on the dimensional characteristic parameters of the UHPC components, and connect the lattice nodes to obtain the frame of the lattice model, wherein the lattice model includes lattice nodes and lattice units that are interconnected between the lattice nodes. Step 2) Determine the number of steel fibers and the microscopic two-dimensional parameters of each component of UHPC based on the material gradation of each component used in UHPC material; Step 3) Generate a steel fiber mesoscopic random distribution model based on the random distribution algorithm, the number of steel fibers, and the mesoscopic two-dimensional parameters of each component of UHPC. Generate connecting rods based on the steel fiber node coordinates and the lattice node coordinates to obtain the lattice model. Step 4) Import the lattice model into the ABAQUS secondary development platform, perform load calculations, and based on the load calculation results, determine the stress state of each lattice element according to the failure criterion. If the determination result is failure, replace the lattice element with a zero element whose elastic modulus and strength are both 0. The microscopic two-dimensional parameters of each component of the UHPC include the elastic modulus, Poisson's ratio, and strength of each material; The two-dimensional spatial steel fiber parameters in the two-dimensional parameters are obtained by reducing and transforming the steel fiber based on the material characteristic parameters of the steel fiber in three-dimensional space and the projection of the steel fiber. The reduction conversion includes the following steps: For any steel fiber passing through the computational plane, determine the projected length of the steel fiber on the computational plane: in, This is the actual length of the steel fiber. The angle between the steel fiber and the calculation plane. It is the planar projection length of the steel fiber; Based on the spatial distribution characteristics of steel fibers, the average projected length of steel fibers in two-dimensional space is determined: Using elastic modulus The reduction in the horizontal projection length is replaced by the reduction in the horizontal projection length, and the conversion relationship is as follows: in, This represents the true elastic modulus of steel fibers. The elastic modulus of steel fiber in two-dimensional space. For the actual strain of steel fibers, For two-dimensional steel fiber strain.

2. The method for mesoscopic modeling and analysis of a UHPC structure according to claim 1, characterized in that, The characteristic parameters of the UHPC components include the overall dimensions, boundary conditions, and load conditions of the UHPC structure.

3. The method for mesoscopic modeling and analysis of a UHPC structure according to claim 1, characterized in that, The method for determining the coordinates of the lattice nodes is as follows: based on the concept of the lattice model, the structure is divided into several grids, and each lattice node is randomly distributed in the corresponding grid.

4. The method for mesoscopic modeling and analysis of a UHPC structure according to claim 1, characterized in that, The number of steel fibers is calculated based on the volume of the UHPC component, the volume content of steel fibers, and the volume of steel fibers: in, The number of steel fibers. For the volume of the UHPC component, This refers to the volume content of steel fibers. This represents the volume of the steel fiber.

5. The method for mesoscopic modeling and analysis of a UHPC structure according to claim 1, characterized in that, The spatial distribution characteristics of the steel fibers include: The steel fibers are distributed uniformly and randomly in space; The angle between each steel fiber passing through the calculation plane and the calculation plane The value of is random, and the probability of each included angle is the same.

6. The method for mesoscopic modeling and analysis of a UHPC structure according to claim 1, characterized in that, The process of generating the microscopic random distribution model of steel fibers includes the following steps: Step 3-1) Determine the distribution range and quantity of steel fibers; Step 3-2) Each steel fiber includes 2 nodes, for the first... i A steel fiber is randomly generated within its distribution range, and an initial node is determined by a random number. and Determined, with the initial node as the origin of polar coordinates, based on the actual length of the steel fiber and the random polar coordinate angle. Determine the coordinates of the second node; Step 3-3) Determine whether the coordinates of the second node exceed the pre-configured matrix range. If so, delete the coordinates and regenerate the coordinates of the second node of the steel fiber. Steps 3-4) Repeat steps 3-2) to 3-3) until all steel fiber nodes are generated.

7. The method for mesoscopic modeling and analysis of a UHPC structure according to claim 1, characterized in that, Step 4) includes the following steps: Step 4-1) Import the lattice model into the ABAQUS computing platform; Step 4-2) Use Python to perform secondary development on the lattice model, assigning pre-configured boundary and load constraints; Step 4-3) Use the Standard module to perform load calculations on the lattice model; Step 4-4) Based on the load calculation results, the stress state of each lattice element is judged according to the failure criterion. If the judgment result is failure, the lattice element is replaced with a zero element with an elastic modulus and strength of 0.

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