A key-type near-field dynamics-based concrete rate effect constitutive modeling method

Abstract

The application provides a key type near field dynamics based concrete rate effect constitutive modeling method, comprising: establishing a simulation model of concrete under impact, including an impact object and a concrete structure; modeling the simulation model, determining coordinates of all material points, completing group binding, and performing surface correction; calculating a dynamic enhancement coefficient of the key according to a deformation rate of the key and a concrete strength; calculating a dynamic limit deformation rate of the key according to the dynamic enhancement coefficient of the key; calculating a dynamic force function constitutive model of the key according to the limit deformation rate of the key; obtaining a dynamic damage judgment formula of the key according to the limit deformation rate of the key; calculating the stress and motion of the material point, and completing time circulation; outputting the calculation result and completing visualization of the result. The application reconstructs the limit elongation rate, the force function constitutive and the damage calculation of the key by introducing the dynamic enhancement coefficient, can reasonably restore the strain rate effect of the concrete material, restore the damage process of the concrete under the impact load, and ensure the calculation efficiency of the model.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of simulation, and particularly relates to a concrete rate effect constitutive modeling method based on bond type near-field dynamics. BACKGROUND

[0002] Concrete is a commonly used building material and is widely used in various engineering structures, such as buildings, bridges, roads, etc. However, concrete may suffer severe damage when subjected to impact or explosive loads, and this impact effect may lead to the collapse of structures and loss of life and property, posing a significant threat to structural safety. Therefore, studying the damage law of concrete under impact is crucial for improving the impact resistance of concrete structures and ensuring safety.

[0003] Near-field dynamics theory is a newly emerging non-local continuous mechanics theory system internationally. This theory uses a spatial integral equation to replace the partial differential equation to describe the stress state of matter, avoiding the singularity of differential calculation in traditional continuous mechanics when encountering discontinuous problems, so it is particularly suitable for simulating the spontaneous fracture process of materials and is widely used in the study of material fracture behavior. Near-field dynamics is divided into "bond type", "regular state type" and "irregular state type". The regular state type and the irregular state type of near-field dynamics are more accurate for simulating complex materials, but they have low computational efficiency and also have zero energy oscillation problems. Bond type near-field dynamics is relatively simple, has high computational efficiency, and studies have shown its effectiveness in simulating concrete fracture. Strain rate effect is one of the key issues that need to be considered in impact simulation.

[0004] Most of the existing near-field dynamics impact studies use the introduction of rate effect constitutive or the addition of damping to realize the strain rate effect. Among them, the method of using local damping was first used to realize the strain rate effect, but the use of local damping may lead to non-physical effects, so some scholars proposed that damping can be applied to the bond to avoid non-physical effects. However, the problem that cannot be avoided by both methods is that the damping values are empirical values, and there is no reasonable calculation formula, so their rationality needs to be improved. In recent years, some scholars have proposed that the deformation rate of the bond can be used as a parameter to reflect the strain rate of the material, and a rate effect constitutive model has been established in state type near-field dynamics. This method can be calculated from the strain rate effect constitutive model of traditional continuous homogeneous mechanics, and its rationality is relatively high. However, this method is realized based on state type near-field dynamics, and still retains the problem of low computational efficiency of state type near-field dynamics, so a new method is urgently needed to efficiently and reasonably restore the strain rate effect of materials. SUMMARY

[0005] The purpose of the present application is to provide a concrete rate effect constitutive modeling method based on bond type near-field dynamics.

[0006] The technical scheme of the present application is as follows:

[0007] A concrete rate effect constitutive modeling method based on key type near field dynamics, the method comprising the following steps:

[0008] Step one, establish a simulation model of concrete under impact, including impact object and concrete structure;

[0009] Step two, model the simulation model, determine the coordinates of all material points, complete the binding of the family, and perform surface correction;

[0010] Step three, calculate the dynamic enhancement coefficient of the key according to the deformation rate of the key and the strength of the concrete;

[0011] Step four, calculate the dynamic ultimate deformation rate of the key according to the dynamic enhancement coefficient of the key;

[0012] Step five, calculate the dynamic force function constitutive model of the key according to the ultimate deformation rate of the key;

[0013] Step six, obtain the dynamic damage criterion formula of the key according to the ultimate deformation rate of the key;

[0014] Step seven, calculate the motion of the mass point and complete the time loop;

[0015] Step eight, output the calculation results and complete the visualization of the results;

[0016] Further, in step three, the dynamic enhancement coefficient of the key is calculated by the following formula:

[0017]

[0018] In the formula, is the deformation rate of the key, is the maximum deformation rate under quasi-static state, In the formula, the calculation of the related variables is as follows:

[0019] δ=1 / (10+6f c / f0)

[0020] log(θ)=6δ-2

[0021]

[0022] In the formula, f0=10MPa, ξ is the initial direction vector between two points, η is the direction vector of displacement between two points, is the derivative of the direction vector of relative displacement between two points with respect to time.

[0023] Further, in step four, the dynamic ultimate deformation rate of the key includes the dynamic linear elongation rate and the dynamic ultimate elongation rate of the key, and the calculation formula is:

[0024]

[0025] In the formula, the quasi-static linear limit S0 = f t / E, where E is the elastic modulus of concrete, f t G represents the tensile strength of concrete. F This refers to the fracture energy of concrete.

[0026] Furthermore, in step five, the formula for calculating the dynamic force function constitutive model of the key based on the key's limit deformation rate is as follows;

[0027]

[0028] In the formula, C is the micromodulus function, ξ is the initial direction vector between the two points, and η is the direction vector of the displacement between the two points.

[0029] Furthermore, in step six, the dynamic damage determination formula for the bond under dynamic conditions is obtained based on the bond's limiting elongation.

[0030]

[0031] In the formula, S 0d S is the elastic limit value of the bond. cd μ represents the bond breaking limit, where μ = 1 indicates that the bond has not broken, and μ = 0 indicates that the bond has broken. When the bond elongation is greater than S... cd When the bond breaks.

[0032] Compared with the prior art, the present invention has the following advantages:

[0033] This invention can reasonably reflect the strain rate effect of concrete materials while ensuring computational efficiency. Compared with state-based near-field dynamics, this invention avoids problems such as low computational efficiency and zero-energy oscillations. At the same time, it uses a dynamic enhancement coefficient to restore the strain rate effect of concrete materials. This dynamic enhancement coefficient has clear experimental support and is more reasonable than the method of using damping to reflect the strain rate effect. Attached Figure Description

[0034] The accompanying drawings illustrate various embodiments generally by way of example rather than limitation, and are used, together with the specification and claims, to explain embodiments of the invention. Where appropriate, the same reference numerals are used in all drawings to refer to the same or similar parts. Such embodiments are illustrative and are not intended to be exhaustive or exclusive embodiments of the apparatus or method.

[0035] Figure 1 A schematic diagram of the bilinear force function of the present invention is shown;

[0036] Figure 2The integral domain for calculating the fracture energy of the present application is shown;

[0037] Figure 3 The schematic diagram of the contact process of the drop hammer and the concrete of the present application is shown;

[0038] Figure 4 The schematic diagram of the method flow of the present application is shown;

[0039] Figure 5 The schematic diagram of the fracture process of the present application is shown;

[0040] Figure 6 The schematic diagram of the fracture process of the present application is shown;

[0041] Figure 7 The schematic diagram of the fracture process of the present application is shown;

[0042] Figure 8 The experimental results of the present application are shown. DETAILED DESCRIPTION

[0043] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0044] The present application provides a key type near-field dynamics based concrete rate effect constitutive modeling method, comprising:

[0045] A simulation model of a concrete member under impact is established, including an impact object and a concrete beam; the parameters involved in the model include the diameter D and mass M of the impact object; the length L, width W and height H of the concrete plate.

[0046] The simulation model is modeled, the number of mass points required by the model is determined according to the distance dx between the mass points, and the coordinates of all mass points are determined. At the same time, the distance between different points is calculated according to the coordinates, the labels of the points with a distance less than the radius of the cluster are recorded, and the binding of the cluster is completed.

[0047] In near-field dynamics, displacement instead of displacement derivative is used to establish equations, and the motion equation of the mass point is as follows:

[0048]

[0049] Where, ρ is the mass density of the material, u(x, t) is the position vector of point x at time t, H x is the cluster of point x, which is composed of mass points within a radius of δ around it. f is the pair force formed between point x and point x`, and b is the volume force received by point x.

[0050] In bond-based peridynamics, the bond force f depends on the relative displacement of the points x and x', the initial relative position ξ and the relative displacement η of the points x and x' as follows:

[0051] ξ = x' - x η = u(x', t) - u(x, t)

[0052]

[0053] For concrete material, considering its softening effect under high stress, a bilinear force function constitutive model is adopted as shown in Figure 1 with the following formula:

[0054]

[0055] In the formula, C is the micro-modulus function, and the calculation formula is as follows:

[0056]

[0057] The calculation of the critical elongation of the bond can be obtained by establishing the energy equivalence relationship between the traditional continuum model and the peridynamics model. For the fracture surface as shown in Figure 2 , the energy equivalence relationship can be written as:

[0058]

[0059] These parameters of the bilinear damage model can be determined by the fracture energy G F and the experimental load-displacement curve. The linear elastic critical elongation S0 and the fracture limit elongation S c can be defined as:

[0060]

[0061] Where f t represents the tensile strength of concrete, and G F is the fracture energy of material I-type fracture. At the same time, the fracture of the bond is represented by a scalar value μ, which is calculated as follows:

[0062]

[0063] In the peridynamics theory, the damage of the particle is determined by calculating the percentage of broken bonds in the total number of bonds, which is calculated as follows:

[0064]

[0065] The deformation rate of the bond is calculated as follows:

[0066]

[0067] wherein ξ is the initial direction vector between two points, η is the direction vector of displacement between two points, is the derivative of the direction vector of displacement between two points with respect to time.

[0068] In order to reflect the strain rate effect of concrete, the dynamic increase factor DIF of the bond is introduced based on the deformation rate of the bond.

[0069]

[0070] wherein is the deformation rate of the bond, wherein δ = 1 / (10 + 6f c / f0), log(θ) = 6δ - 2, f0 = 10 MPa, the ultimate deformation of the bond is calculated as follows:

[0071]

[0072] The implementation steps are shown as follows. Figure 4

[0073] First step: a near-field dynamic rate effect simulation model of a falling weight impact concrete beam is established, the diameter of the falling weight impact head is D = 60 mm, the mass is M = 38.4 kg; the concrete material adopts C60 concrete, the compressive strength is f c = 60 MPa, the tensile strength is f t = 4.6 MPa, the fracture energy is G F = 96.4 N / m, the elastic modulus E = 25 GPa, the density is p1 = 2400 kg / m -3 ; the steel bar diameter is 6 mm, the yield strength f y = 482 MPa, the elastic modulus E = 208 GPa, and the density is p2 = 7750 kg / m -3 .

[0074] Second step: generate material points, the length of the concrete beam is L = 600 mm, the height H = 100 mm, the width W = 70 mm, the material point spacing is dx = 5 mm, the near-field range is δ = 3dx = 15 mm. The particles are evenly generated in the concrete range, the particle number is N = 33600, the distance between point i and all other points is calculated, and the distance less than δ is recorded in the family of point i. The time interval for calculation is taken as dt = 3x10 -7 s, the calculation step number is taken as nt = 5000, and the motion equation of the particle is:

[0075]

[0076] wherein p is the density of the material, b is the body force, V is the volume of the material represented by the particle. f is the force function of the bond. ​

[0077] The boundary conditions are applied to the concrete beam, and the constraint of the beam is simply supported constraint. A row of points is selected at the position of 250mm from the mid-span along the width direction on both sides of the beam, and the height direction displacement value is fixed at 0mm. A row of points is selected on one side, and the length and width direction displacement values are fixed at 0mm. Meanwhile, the speed of the drop hammer is set to 10.8m / s, and the kinetic energy E = 1 / 2mv 2 = 2239.5J.

[0078] Third step: surface correction is performed on the model. The equal parameter value of the micro modulus function of the model is the near-field range H δ of the mass point, which is calculated completely in the material. When the near-field range of the mass point is not in the material, correction is needed. The correction parameter is called surface correction coefficient S S(i) .

[0079]

[0080] Fourth step: a contact algorithm of the drop hammer and the mass point is established to restore the contact process of the drop hammer and the concrete, as shown in the following formula. The drop hammer moves at the initial speed v0. When the mass point overlaps the drop hammer, the mass point position is repositioned first to generate a displacement vector. The mass point is moved to the surface of the drop hammer along the velocity direction, and the displacement vector is divided by the time to obtain the velocity increment of the mass point. The calculation formula of the force is as follows: Figure 3

[0081]

[0082] wherein V is the volume represented by the mass point, v is the velocity of the mass point, and p is the material density. The real material has incompressibility, but the mass point itself does not have volume in the near-field dynamics. Therefore, in order to prevent the mass point from overlapping or even penetrating at high speed impact, a short-range repulsive force needs to be set. The calculation formula is as follows:

[0083]

[0084] wherein C sh = 1.5C, C is the value of the corresponding micro modulus function, and d is the action range of the short-range repulsive force, as shown in the following formula:

[0085] d = min{0.9|x j -x i |, 1.35Ax}

[0086] Fifth step: the near-field dynamics bond force after displacement and the mass point displacement are calculated.

[0087] The elongation of the bond is calculated:

[0088] ​

[0089] where ξ is the initial relative position and η is the relative displacement. Define μ as the damage history function of the bond, and the calculation formula is as follows:

[0090]

[0091] In the formula, S0 is the elastic limit value of the bond, S c is the breaking limit value of the bond, μ = 1 indicates that the bond has not been broken, μ = 0 indicates that the bond has been broken, and when the elongation of the bond is greater than S c , the bond is broken. The model considers the high compressive strength and low tensile strength of the concrete material, and the direct cause of local cracking of the concrete material is tensile cracking in a certain direction. Therefore, the model only sets the tensile breaking limit value, and does not set the breaking limit value for compression.

[0092] In the approach dynamics theory, the damage of the particle is determined by calculating the percentage of broken bonds in the total number of bonds, and the calculation is shown in the following formula:

[0093]

[0094] Where φ represents the damage degree, and its range is 0 ≤ φ ≤ 1, all the bonds are not damaged initially, φ = 0 indicates no damage, and φ = 1 indicates that all the bonds between the PD point and the points in the family are damaged.

[0095] The rate effect model of near-field dynamics established by the application adds a dynamic enhancement coefficient to the elastic limit S0 and the breaking limit S c of the bond, and obtains the dynamic elastic limit S 0d and the dynamic breaking limit S cd , and the calculation formula is as follows:

[0096]

[0097] Where DIF is the dynamic enhancement coefficient of the bond, and the calculation formula is as follows:

[0098]

[0099] Where, is the deformation rate of the bond, is the maximum deformation rate of the quasi-static state, and when the value exceeds the value, the dynamic enhancement effect of the material needs to be considered. In the formula, δ = 1 / (10 + 6f c / f0), log(θ) = 6δ-2, and f0 = 10 MPa.

[0100] Finally, the results are outputted and visualized, by which the simulation of the near-field dynamic rate effect of the drop hammer impact concrete beam is realized. Figures 5-7 The crack patterns at three time instants predicted by the numerical method are shown and compared with the experimental results, as shown in Figure 8 Fig. 4. As shown in Figure 5 Fig. 4, a compressive damage pattern can be observed in the middle of the beam, and the concrete below the impact point is crushed. Then, four cracks extend from the side of the crushed damage zone to the vertical and oblique downward directions, respectively. Two vertical cracks and two oblique cracks form a shear plug below the impact point. In addition, Figure 7 Concrete spalling is also observed below the impact point in Fig. 4.

[0101] The above merely describes preferred specific embodiments of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art should be covered within the protection scope of the present application according to the technical solution and the inventive concept of the present application, and any equivalent replacement or change is within the technical range disclosed by the present application.

Claims

1. A method for constitutive modeling of concrete rate effect based on bond-type near-field dynamics, characterized in that, The method includes the following steps: Step 1: Establish a simulation model of concrete under impact, including the impactor and the concrete structure; Step 2: Generate specific data for the simulation model, determine the coordinates of all material points, complete the binding of the families, and perform surface correction. Step 3: Calculate the dynamic reinforcement coefficient of the key based on the key deformation rate and concrete strength; Step 4: Calculate the dynamic limit deformation rate of the bond based on the dynamic reinforcement coefficient of the bond; Step 5: Calculate the dynamic force function constitutive model of the key based on the dynamic limit deformation rate of the key; Step 6: Based on the dynamic limit deformation rate of the bond, obtain the dynamic damage judgment formula for the bond. Step 7: Calculate the forces and motion of the particle and complete the time loop; Step 8: Output the calculation results and visualize them. In step three, the formula for calculating the dynamic enhancement coefficient of the bond is: ， In the formula, The deformation rate of the bond, The maximum deformation rate is quasi-static. The calculation of the relevant variables in the formula is shown below: ， In the formula, , For compressive strength, Let be the initial direction vector between the two points. Let be the direction vector of the displacement between the two points. Let be the derivative of the direction vector of the relative displacement between two points with respect to time.

2. The method for constructing a concrete rate effect model based on bond-type near-field dynamics according to claim 1, characterized in that, In step four, the dynamic limiting deformation rate of the bond includes the dynamic linear elongation and the dynamic limiting elongation, calculated using the following formula: ， In the formula, the quasi-static linear limit , E This refers to the elastic modulus of concrete. The tensile strength of concrete, This refers to the fracture energy of concrete.

3. The method for constructing a concrete rate effect model based on bond-type near-field dynamics according to claim 1, characterized in that, In step five, the formula for calculating the dynamic force function constitutive model of the key based on the key's limit deformation rate is as follows; ， In the formula, For the micromodulus function, Let be the initial direction vector between the two points. Let be the direction vector of the displacement between the two points.

4. The method for constructing a concrete rate effect model based on bond-type near-field dynamics according to claim 1, characterized in that, In step six, the dynamic damage determination formula for the bond under dynamic conditions is obtained based on the bond's limiting elongation: ， In the formula, S 0d The elastic limit value of the bond. S cd This represents the bond breaking limit. μ =1 indicates that the bond has not been broken. μ =0 indicates that the bond has broken, when the bond elongation is greater than 0. S cd At that time, the bond breaks.

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