A near-field dynamic simulation method for low-velocity impact fracture of ultra-high performance concrete

Abstract

The application discloses a kind of near-field dynamics simulation methods for ultra-high performance concrete low-speed impact fracture, including establishing the complete discrete model of UHPC component, and the coupling of concrete gel matrix and steel fiber is realized by Embedded method;By introducing a transition unit, the classic finite element unit is connected by key with PeriFEM local unit and the force on the key is modified, the coupling of two methods is realized;Introduce continuous local unit, the motion equation of local unit is derived using explicit central difference algorithm, and the explicit algorithm based on continuous local unit is constructed, used to solve motion equation and calculate the damage condition of UHPC matrix.The simulation method provided by the application can effectively simulate the fracture process of UHPC under low-speed impact, and provides a new solution for the coupling of near-field dynamics and finite element.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation of concrete materials, specifically involving a near-field dynamic simulation method for low-velocity impact fracture of ultra-high performance concrete. Background Technology

[0002] In recent years, with the continuous advancement of urbanization in my country, major infrastructure construction such as roads, bridges, and marine engineering has developed rapidly. These large-scale projects are closely related to concrete materials. Modern engineering construction has also placed higher demands on the performance of concrete. Ultra-high performance concrete (UHPC), as a new type of building material, has broad application prospects in the engineering field due to its excellent properties such as high compressive strength and low permeability. However, the application of UHPC in practical engineering has progressed relatively slowly. One of the main reasons is the lack of systematic theoretical support and standardized guidance for key performance indicators such as ultimate strength and residual strength after cracking. Therefore, in-depth research on the damage and failure mechanism of UHPC materials is of great significance for engineering applications and design.

[0003] Currently, modeling of steel fiber reinforced ultra-high performance concrete (UHV-U) is generally based on the classical finite element method (FEM). While the FEM performs well in handling conventional mechanical problems of linear, homogeneous materials, it requires the introduction of failure criteria for crack initiation and propagation when dealing with fracture problems, increasing computational complexity and uncertainty. In contrast, peridynamics (PD), as a meshless method, handles nonlocal interactions between material points through an integral interaction model, naturally addressing discontinuities. It exhibits significant advantages, particularly in simulating crack initiation, propagation, and multi-crack interactions. However, PD has high computational costs, especially when dealing with large-scale engineering problems, where computational efficiency becomes a bottleneck. Therefore, combining the advantages of peridynamics and the finite element method, organically integrating the nonlocal interaction capabilities of PD with the computational efficiency of FEM, is one of the important directions for research on damage and failure processes and fracture mechanisms. Summary of the Invention

[0004] This invention provides a near-field dynamics simulation method for low-velocity impact fracture of ultra-high performance concrete. This method is based on the Peridynamics-based finite element method (PFE), employing continuous local elements to establish an explicit PFE algorithm. Furthermore, the PFE method is coupled with classical finite element methods, further improving computational efficiency without compromising accuracy.

[0005] The technical solution adopted by this invention to solve its technical problem is:

[0006] A near-field dynamics simulation method for low-velocity impact fracture of ultra-high performance concrete, specifically including the following steps:

[0007] S1: Establish a fully discrete model of ultra-high performance concrete components;

[0008] S2: Couple the PeriFEM region and the classical finite element region according to the region division;

[0009] S3: Define material properties, add virtual boundary layers, and apply boundary conditions and external loads according to the working conditions;

[0010] S4: Establish an explicit algorithm for PeriFEM based on continuous local elements, and give the motion equations of the local elements based on the explicit central difference algorithm;

[0011] S5: Solve the motion equations of UHPC material points and calculate UHPC damage based on the PeriFEM explicit algorithm based on continuous local elements proposed in step S4.

[0012] Furthermore, the specific steps for establishing a fully discrete model of the ultra-high performance concrete component in step S1 are as follows:

[0013] S11: Determine the size of the UHPC specimen, uniformly discretize the specimen according to the discrete interval, and store the coordinates of the UHPC matrix material points;

[0014] S12: Divide the model calculation area into two parts. The area that may cause damage and fracture is calculated using the near-field dynamics method, while the area that will not cause damage and fracture is calculated using the classical finite element method.

[0015] S13: Calculate the number of fibers deployed, generate the midpoint and angle parameters of random fibers, and calculate the coordinates of the two endpoints of the fibers based on the fiber length;

[0016] S14: The steel fiber is coupled onto the steel fiber ultra-high performance concrete gel matrix using the Embedded method, so that the displacement of the matrix is ​​completely consistent with the displacement of the steel fiber.

[0017] Furthermore, step S2 specifically involves:

[0018] S21: When coupling the PeriFEM region and the classical finite element region, a series of transitional near-field dynamic elements are generated on the local elements of the PeriFEM method near the classical finite element region. These transitional near-field dynamic elements are based on local elements at one end and classical finite element elements at the other end;

[0019] S22: Determine the particle distribution; the Gaussian integral points on the finite element region are the particles in the near-field dynamic region.

[0020] S23: Establish the coupling mode between classical finite element elements and local elements. The transition near-field dynamic element only exerts a force on the local element, while the residual of the classical finite element element is zero. The displacement of the four mass points of the transition element on the classical finite element element is determined by the nodal displacement and shape function of the classical finite element method.

[0021] Furthermore, step S4 specifically involves:

[0022] S41: Constructing continuous local elements for near-field dynamics based on classical finite element method, with adjacent elements sharing nodes;

[0023] S42: Based on step 1, the explicit central difference algorithm is used to establish the near-field dynamic equations of motion for the steel fiber reinforced ultra-high performance concrete material points. First, it is assumed that at the nth time step, the displacement variable of material point x is:

[0024]

[0025] Here, κ and ζ are positive real and complex numbers, respectively. Stability studies require that for any κ, |ζ|≤1. If this condition is satisfied, then the wave will not grow unbounded over time, thus preventing non-convergence.

[0026] The equations of motion are established using the explicit central difference algorithm:

[0027]

[0028] In the formula, ρ (k) Represents the material point x (k) quality; ξ (k)(j) Indicates the relative position of two substance points; v c(j) and V (j) These represent the volume correction factor and the material point volume, respectively; additionally, in the formula... and Representing the material point x respectively (k) and x (j) Volumetric strain at the nth time step;

[0029] Substituting the displacement variable and replacing the exponent with sine and cosine, we can simplify to obtain:

[0030]

[0031] in

[0032]

[0033] In the formula, a, b, and d are near-field dynamic material parameters, which can be calibrated through simple load conditions; t is time; and δ is the near-field range size.

[0034] Furthermore, step S5 specifically involves:

[0035] S51: First, the equations of motion of the UHPC material points are solved. Formula (3) is a system of quadratic equations in one variable. Solving it, we can obtain:

[0036]

[0037] Substituting into formula (2) allows us to solve for the displacement variable at each time step. It should be noted that, to satisfy the condition for any κ, then:

[0038]

[0039] Formula (6) introduces a safety factor less than 1. The smaller this safety factor, the more accurate the data obtained by the explicit algorithm, but the more iterations are required to complete the calculation. Safety Factor The value is selected based on a comprehensive consideration of accuracy requirements and computational costs;

[0040] S52: During the time integral, calculate the elongation of unbroken bonds in all near-field dynamic elements, compare it with the critical compressive elongation and critical tensile elongation to determine whether these bonds are broken, and introduce a scalar function μ(t,ξ) to correct the force density vector for simulating bond failure.

[0041]

[0042] Based on the number of broken bonds, the effective damage at any damage point x can be defined as:

[0043]

[0044] In the formula, V is the volume of a material point, and H is the integration region;

[0045] S53: After time integration is completed, displacement contour maps and damage contour maps are generated, and the results are post-processed. The displacement contour map is generated based on ABAQUS's built-in functions, while the damage contour map is generated through ABAQUS's VUMAT subroutine.

[0046] By employing the above technical solutions, the present invention has the following beneficial effects compared to the prior art:

[0047] 1. In this invention, the fibers are coupled to the steel fiber-reinforced ultra-high performance concrete gel matrix using an embedded method. This ensures that the displacement of the gel matrix is ​​completely synchronized with the displacement of the steel fibers. When the gel matrix experiences strain, the steel fibers also experience strain. The stress generated by the strain of the steel fibers is distributed across the surrounding gel matrix, reinforcing the gel matrix. Based on this method, the interaction between the steel fibers and the concrete gel matrix can be well simulated.

[0048] 2. An explicit PeriFEM algorithm based on continuous local elements was established using the explicit central difference method. The local elements in this algorithm are continuous elements, making coupling with the classical finite element method simple and convenient.

[0049] 3. This invention introduces a transition element to connect classical finite element elements and PeriFEM local elements via a key and modifies the forces on the key, thereby achieving coupling between the two methods. This coupling effectively reduces computational costs without affecting the accuracy of the numerical simulation. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the geometric model of the three-point bending drop hammer impact test according to an embodiment of the present invention;

[0051] Figure 2 This is a schematic diagram illustrating the coupling between steel fibers and the gel matrix in an embodiment of the present invention;

[0052] Figure 3 This is a schematic diagram illustrating the coupling between the PeriFEM method and the classical finite element method in an embodiment of the present invention.

[0053] Figure 4 This is a flowchart of the PeriFEM explicit algorithm based on continuous local units according to an embodiment of the present invention.

[0054] Figure 5 These are matrix damage cloud maps at different time steps in an embodiment of the present invention. Detailed Implementation

[0055] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0056] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0057] This invention provides a near-field dynamics simulation method for low-velocity impact fracture of ultra-high performance concrete, see reference. Figure 1A schematic diagram of the geometric model for a three-point bending drop hammer impact test, taking ultra-high performance concrete as an example. The model uses a rectangular cross-section beam with dimensions of 700mm × 150mm. The clear span of the beam is 600mm, and the span-to-depth ratio is 4 / 1, meeting the requirements for a three-point bending specimen. A hammer with a mass of 126.6kg is placed at the mid-span. A pre-fabricated crack with a width of 4mm and a depth of 45mm is placed at the mid-span.

[0058] First, a fully discrete model of the ultra-high performance concrete (UHPC) component is established. The fully discrete model includes a fiber model and a gel matrix. The establishment of the fully discrete model of the UHPC component is divided into the following steps:

[0059] 1. Determine the dimensions of the UHPC specimen. The model uses a rectangular cross-section beam with dimensions of 700mm × 150mm, a clear span of 600mm, and a span-to-depth ratio of 4 / 1. The specimen is uniformly discretized according to the discretization interval, and the coordinates of the UHPC matrix material points are stored.

[0060] 2. See Figure 1 The model calculation region is divided into two parts: the 160mm mid-span region, which may cause damage and fracture, is calculated using the near-field dynamics method, while the region that will not cause damage and fracture is calculated using the classical finite element method.

[0061] 3. Deploy fibers within the cross-sectional area. See also Figure 1 In the three-point bend test, arranging fibers only at the mid-span saves a lot of computational complexity and has no significant impact on the calculation results. Therefore, the model arranges random fibers in the near-field dynamic region of 160mm at the mid-span, generates the midpoint and angle parameters of the random fibers, and calculates the coordinates of the two endpoints of the fibers based on the fiber length.

[0062] 4. Fibers are coupled onto a steel fiber ultra-high performance concrete gel matrix using an embedded method. Figure 2 This diagram illustrates the coupling between the steel fiber and the gel matrix. The Embedded method is a fully coupled approach that ensures the displacement of the matrix is ​​perfectly synchronized with the displacement of the steel fiber. When the gel matrix undergoes strain, the steel fiber also undergoes strain. The stress generated by the strain of the steel fiber is distributed across the surrounding gel matrix, reinforcing the gel matrix.

[0063] The PeriFEM region and the classical finite element region are coupled according to the region division. (See also...) Figure 3A series of peridynamic elements are generated on the local elements of the PeriFEM method near the classical finite element region. These peridynamic elements are based on the local elements at one end and the classical finite element elements at the other. These elements are called transition peridynamic elements. These transition peridynamic elements exert forces only on the local elements, while the residuals on the classical finite element elements are zero, meaning there are no forces acting on them. The displacements of the four mass points of these transition peridynamic elements on the classical finite element elements are naturally determined solely based on the nodal displacements and shape functions of the classical finite element method.

[0064] The next step is to define material properties, add a virtual boundary layer, and apply initial boundary conditions. Displacement boundary conditions or other boundary conditions are then applied based on the working conditions. The mechanical parameters of the steel fiber and mortar matrix are shown in Table 1.

[0065] Table 1 Mechanical parameters of steel fiber and mortar matrix (a) Mechanical parameters of mortar matrix

[0066]

[0067] (b) Fiber mechanical parameters table

[0068]

[0069] Next, an explicit algorithm for the PeriFEM method based on continuous local elements is established. The motion equations of the local elements are given based on the explicit central difference algorithm. The specific steps are as follows:

[0070] 1. Based on the classical finite element method, a continuous local element for near-field dynamics is constructed, with adjacent elements sharing nodes.

[0071] 2. Based on step 1, establish the near-field dynamic equations of motion for the steel fiber reinforced ultra-high performance concrete material points. First, assume that at the nth time step, the displacement variable of material point x is:

[0072]

[0073] Here, κ and ζ are positive real and complex numbers, respectively. Stability studies require that for any κ, |ζ|≤1. If this condition is satisfied, then the wave will not grow unbounded over time, thus causing non-convergence.

[0074] The motion equations of the material points in steel fiber reinforced ultra-high performance concrete are established using the explicit central difference algorithm:

[0075]

[0076] In the formula, ρ (k) Represents the material point x (k) quality; ξ (k)(j)Indicates the relative position of two substance points; v c(j) and V (j) These represent the volume correction factor and the material point volume, respectively; additionally, in the formula... and Representing the material point x respectively (k) and x (j) Volumetric strain at the nth time step;

[0077] Substituting the displacement variable and replacing the exponent with sine and cosine, we can simplify to obtain:

[0078]

[0079] in

[0080]

[0081] In the formula, a, b, and d are near-field dynamic material parameters, which can be calibrated through simple load conditions; t is time; and δ is the near-field range size.

[0082] Finally, the motion equations of the UHPC material points were solved and UHPC damage was calculated. Figure 4 A flowchart is provided, and the specific steps are as follows:

[0083] 1. First, the equations of motion of the UHPC material points are solved. Equation (3) is a system of quadratic equations in one variable. Solving it, we can obtain:

[0084]

[0085] Substituting into formula (2) allows us to solve for the displacement variable at each time step. If we want the condition to be satisfied for any κ, then:

[0086]

[0087] Formula (6) introduces a safety factor less than 1. The smaller this safety factor, the more accurate the data obtained by the explicit algorithm, but the more iterations are required to complete the calculation. The value is selected based on a comprehensive consideration of accuracy requirements and computational costs;

[0088] 2. During the time integral, calculate the elongation of unbroken bonds in all near-field dynamic elements and compare it with the critical compressive elongation and critical tensile elongation to determine whether these bonds are broken. Introduce a scalar function μ(t,ξ) to correct the force density vector for simulating bond failure.

[0089]

[0090] Based on the number of broken bonds, the effective damage at any damage point x can be defined as:

[0091]

[0092] In the formula, V is the volume of a material point, and H is the integration region;

[0093] 3. After time integration, displacement and damage contour maps can be generated, and the results can be post-processed. The displacement contour map is generated using ABAQUS's built-in functions, while the damage contour map is generated using the ABAQUS VUMAT subroutine. In the PeriFEM method, the ratio of the number of fractured bonds to the total number of bonds on a local element is defined as the damage value of that local element. Generally, a macroscopic crack is considered to form when the damage value > 0.5. Figure 5 Damage contour maps of the matrix of the specimen at 0.2 ms, 0.4 ms, 0.6 ms, 0.8 ms and 1.0 ms are presented. The fracture development of the gel matrix can clearly reflect the fracture behavior of steel fiber ultra-high performance concrete after impact.

[0094] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A near-field dynamics simulation method for low-velocity impact fracture of ultra-high performance concrete, characterized in that, Specifically, the following steps are included: S1: Establish a fully discrete model of ultra-high performance concrete components; S2: Couple the PeriFEM region and the classical finite element region according to the region division; S3: Define material properties, add virtual boundary layers, and apply boundary conditions and external loads according to the working conditions; S4: Establish an explicit algorithm for PeriFEM based on continuous local elements, and give the motion equations of the local elements based on the explicit central difference algorithm; S5: Solve the motion equations of UHPC material points and calculate UHPC damage based on the PeriFEM explicit algorithm based on continuous local elements proposed in step S4. Step S1 is as follows: S11: Determine the size of the UHPC specimen, uniformly discretize the specimen according to the discrete interval, and store the coordinates of the UHPC matrix material points; S12: Divide the model calculation area into two parts. The area that may cause damage and fracture is calculated using the near-field dynamics method, while the area that will not cause damage and fracture is calculated using the classical finite element method. S13: Calculate the number of fibers deployed, generate the midpoint and angle parameters of random fibers, and calculate the coordinates of the two endpoints of the fibers based on the fiber length; S14: The steel fiber is coupled onto the steel fiber ultra-high performance concrete gel matrix using the Embedded method, so that the displacement of the matrix is ​​completely consistent with the displacement of the steel fiber. Step S2 is as follows: S21: When coupling the PeriFEM region and the classical finite element region, a series of transitional near-field dynamic elements are generated on the local elements of the PeriFEM method near the classical finite element region. These transitional near-field dynamic elements are based on local elements on one end and classical finite element elements on the other end. S22: Determine the particle distribution and identify the Gaussian integral points on the finite element region as the particles in the near-field dynamic region; S23: Establish the coupling mode between classical finite element elements and local elements. The transition near-field dynamic element only exerts a force on the local element, while the residual of the classical finite element element is zero. The displacement of the four mass points of the transition element on the classical finite element element is determined by the nodal displacement and shape function of the classical finite element method.

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