Modeling method of engineering cement-based composite material under impact load based on near-field dynamics

Abstract

The invention discloses a near-field dynamics-based modeling method for an engineering cement-based composite material under an impact load, and the method comprises the steps: constructing an engineering cement-based composite material full-discrete model, and discretizing a cement matrix and fibers in the engineering cement-based composite material full-discrete model into a plurality of space material points; constructing an impact crack propagation model based on near-field dynamics through the plurality of space material points; correcting the impact crack propagation model in combination with a failure criterion of a model strain rate effect to obtain a corrected impact crack propagation model; and analyzing the engineering cement-based composite material under the impact load through the corrected impact crack propagation model. The method can effectively predict and analyze the mechanical behavior and damage problem of the ECC under the impact load.

Description

Technical Field

[0001] The invention relates to the technical field of peri-field dynamics and impact problems, and in particular to a modeling method of an engineering cement-based composite material under impact load based on peri-field dynamics. Background Art

[0002] Engineering cementitious composite (ECC) is a fiber-reinforced cement-based composite material that exhibits ultra-high toughness under tensile and shear loads. ECC is mainly used for engineering structure reinforcement and has good crack dispersion ability. Therefore, ECC has great research significance in material damage under load, especially fracture failure. However, when cracks initiate and propagate inside ECC, the originally continuous displacement and stress fields are no longer continuous. Traditional mechanical models and numerical simulation methods have great limitations in dealing with fracture, damage and other problems.

[0003] Peridynamics (PD) is an emerging mechanical theory system established in recent years based on the idea of ​​non-local action. It can avoid the singularity problem caused by derivatives at discontinuities and realize a natural description of the crack propagation process. The core idea of ​​PD is non-local interaction, which discretizes the calculation area into a finite number of material points, which contain all physical and mechanical information. By solving spatial integral equations instead of spatial differential equations to describe the mechanical behavior of material points, PD avoids the singularity of differential equations in traditional continuous deformation analysis methods when solving discontinuous problems. Discretization is a major model for analyzing the mechanical behavior of ECC, including semi-discrete and full discretize.

[0004] In order to predict and analyze the fracture and crack propagation problems of ECC, some scholars have developed a semi-discrete model based on the unconventional state-based peridynamic theory to simulate the bridging force between fiber and concrete. In order to give full play to the unique advantages of peridynamics in analyzing discontinuous problems and more accurately and efficiently predict and analyze the mechanical behavior of ECC under impact loads, it is necessary to develop a fully discrete model and algorithm based on peridynamics. Summary of the invention

[0005] The purpose of the present invention is to propose a modeling method for engineering cement-based composites under impact loads based on peridynamics. The model can effectively simulate the impact failure behavior of engineering cement-based composites, and can study the influence of factors such as fiber volume fraction and fiber aspect ratio on the dynamic fracture of materials. It can effectively predict and analyze the mechanical behavior and damage problems of ECC under impact loads, and provides a new idea for studying the fracture failure mechanism of materials.

[0006] To achieve the above object, the present invention provides a modeling method for engineering cement-based composite materials under impact load based on peridynamics, comprising:

[0007] Constructing a fully discrete model of an engineering cement-based composite material, and discretizing the cement matrix and the fibers in the fully discrete model of the engineering cement-based composite material into a plurality of spatial material points respectively;

[0008] By using the plurality of spatial material points, an impact crack propagation model is constructed based on peri-field dynamics;

[0009] The impact crack growth model is modified by combining the failure criterion of the model strain rate effect to obtain a modified impact crack growth model;

[0010] The modified impact crack growth model is used to analyze engineering cement-based composite materials under impact load.

[0011] Preferably, constructing the fully discrete model of the engineering cement-based composite material includes: matrix modeling, fiber modeling, and fiber-matrix interface modeling;

[0012] The process of matrix modeling includes:

[0013] Considering the softening behavior of the material and the damage caused by compression deformation, the damage correction factor λ of the bond is introduced to correct the point force function f in the PMB model to obtain the corrected constitutive force function, and the stress-strain response during the crack propagation process is obtained based on the corrected constitutive force function;

[0014] Among them, the value range of the damage correction factor λ of the bond is 0 to 1, and the modified constitutive force function is:

[0015] F=(1-λ)f

[0016] F is the modified constitutive force function.

[0017] Preferably, the fiber modeling process comprises:

[0018] The fiber is modeled as a one-dimensional peridynamic rod, neglecting the effects of bending and rotation, showing the strengthening effect of the fiber during crack propagation, including the micromodulus of the fiber bond;

[0019] Among them, the micro modulus c of the fiber bond f for:

[0020]

[0021] In the formula, E f is the elastic modulus of the fiber before failure, δ is the near field range of the fiber point, A f is the cross-sectional area of ​​a fiber unit;

[0022] Critical tensile strain S of fiber bond c The fiber tensile strength σ ft Decide:

[0023]

[0024] If the elongation of the fiber bond exceeds the critical elongation S cr , the bond force is irreversibly set to zero, indicating that the bond has failed.

[0025] Preferably, the process of fiber-matrix interface modeling comprises:

[0026] Determine the relationship between the interfacial pair force f and the interfacial shear stress τ between the fiber and the matrix, calculate the fiber pull-out displacement, obtain the key mechanism of the interaction between the fiber and the matrix, and obtain the interfacial micro-force;

[0027] The relationship between the interfacial pairing force f and the interfacial shear stress τ between the fiber and the matrix is:

[0028]

[0029] Where τ is the shear stress scalar value, d f is the fiber diameter, t is the interface thickness between the fiber and the matrix;

[0030] The fiber pull-out displacement is calculated as follows:

[0031]

[0032] Where Δ is the displacement vector, x f ,y f are the fiber points on the reference configuration, y m 、x m are the base points on the reference configuration, n f is the direction vector of the fiber element.

[0033] Preferably, the process of constructing the fully discrete model of the engineering cement-based composite material also includes considering the fiber friction effect and correcting the interface force between the fiber and the matrix according to the fiber direction, specifically:

[0034] Consider a fiber unit that is inclined relative to the crack surface. The angle between the fiber direction vector and the crack surface normal vector is θ. Let the bridging force contributed by the fiber be P θ , considering the friction effect of the fiber, the bridging force contributed by the fiber is:

[0035] P θ =e gθ P θ＝0

[0036] Where g is the friction coefficient, P θ＝0 is the bridging force contributed by the fiber when θ = 0, and e is the natural logarithm;

[0037] Considering the fiber friction effect, when the fiber intersects the matrix crack, the interfacial force between the fiber and the matrix is ​​corrected according to the fiber direction. The corrected interfacial shear stress τ θ for:

[0038]

[0039] Based on the embedment depth L of the fiber during extraction e The change of the interface micro-force f int After correction, the actual interface micro-force f int * for:

[0040]

[0041] Among them, L e is the initial embedding depth of the fiber, and Δ is the scalar value of the pull-out displacement.

[0042] Preferably, the cement matrix and the fibers in the fully discrete model of the engineering cement-based composite material are discretized into a plurality of spatial material points, including:

[0043] The cement matrix and the fiber are uniformly discretized into a number of material points with a discretization size of Δx; wherein the material points within the near-field domain of each material point satisfy the peridynamic motion equation, and the integral form in the peridynamic motion equation is converted into a summation form, specifically:

[0044]

[0045] In the formula, ρ represents density, is the acceleration, f is the interaction force between material points, V p The volume of any material point in the near field, is the external force on the material point, P is the neighboring material point, is the displacement vector of the neighboring material point P at time step n, x P is the initial spatial coordinate of the neighboring material point P, x i is the initial space coordinate of material point i.

[0046] Preferably, the impact crack propagation model is constructed based on the peridynamics by using the plurality of spatial material points, including:

[0047] Using the explicit time integration algorithm, the rigid body moves at a preset speed. The particles in the impact object are squeezed to a new position outside the impact object, forming a contact surface between the impact object and the particles. k At the next time step (t+Δt), the particle x is relocated to a new position. k The speed v k for:

[0048]

[0049] In the formula, is the displacement vector corrected at time (t+Δt), is the displacement vector at time t, Δt is the corresponding time increment, and at time (t+Δt), the particle x k Reaction force to impact object for:

[0050]

[0051] In the formula, For mass x k The velocity vector before repositioning at time (t+Δt), ρ k and V k are density and volume respectively;

[0052] The reaction force F received by the impact object at the time (t+Δt) is obtained by summing the reaction forces received by all particles in the impact object. k for:

[0053]

[0054] in,

[0055] Preferably, the modified impact crack growth model describes the fracture mechanism of the microscopic interaction force inside the material through a bond breaking model;

[0056] Wherein, the bond breaking model is:

[0057]

[0058] In the formula, and are the dynamic critical tensile and compressive elongations of the bond, and are the compression and extension rates of the bond, respectively; and are the quasi-static tensile strain rate and compressive strain rate, α, γ, δ, η are material constants, and f cu is the unconfined compressive strength of the cubic concrete specimen, E cdand E td are the dynamic compression and tension elastic moduli, respectively, c is the compressive strength of concrete, f t is the tensile strength of concrete.

[0059] Compared with the prior art, the present invention has the following advantages and technical effects:

[0060] The present invention will provide guidance and suggestions based on scientific evidence and theory for crack initiation and propagation, structural design and life prediction, material selection and design in actual engineering, and provide important data support and reference value for studying the fracture and failure mechanism of materials. It can effectively predict and analyze the mechanical behavior and damage problems of ECC under impact loads.

[0061] The present invention applies PD to the ECC impact model for the first time, which can more effectively predict and analyze the mechanical behavior and damage problems of ECC under impact load. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0063] Figure 1 It is an overall flow chart of a modeling method of an engineering cement-based composite material under impact load based on peri-field dynamics in an embodiment of the present invention;

[0064] Figure 2 Schematic diagram of a fiber unit in a two-dimensional peridynamic model in an embodiment of the present invention;

[0065] Figure 3 is the exponential friction attenuation model of the fiber-matrix interface used in the embodiment of the present invention;

[0066] Figure 4 Schematic diagram of relative movement between the fiber unit and the matrix in an embodiment of the present invention;

[0067] Figure 5 is a schematic diagram of a fiber unit inclined relative to a cracking surface in an embodiment of the present invention;

[0068] Figure 6 This is a schematic diagram of discretization of engineering cement-based materials in an embodiment of the present invention;

[0069] Figure 7 Schematic diagram of updating the position of a material point when an impacting object contacts an impacted object in an embodiment of the present invention;

[0070] Figure 8 This is a flow chart of peridynamic calculation in an embodiment of the present invention;

[0071] Fig. 9 A schematic diagram of the geometric dimensions and boundary conditions of the model in an embodiment of the present invention;

[0072] Fig.10 A crack propagation path diagram of the calculation results provided in an embodiment of the present invention;

[0073] Fig.11 It is a strain energy density diagram of the calculation results provided in the embodiment of the present invention. DETAILED DESCRIPTION

[0074] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0075] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0076] The present invention proposes a modeling method for engineering cement-based composite materials under impact load based on peri-field dynamics, such as Figure 1 ,include:

[0077] Constructing a fully discrete model of an engineering cement-based composite material, and discretizing the cement matrix and the fibers in the fully discrete model of the engineering cement-based composite material into a plurality of spatial material points respectively;

[0078] By using the plurality of spatial material points, an impact crack propagation model is constructed based on peri-field dynamics;

[0079] The impact crack growth model is modified by combining the failure criterion of the model strain rate effect to obtain a modified impact crack growth model;

[0080] The modified impact crack growth model is used to analyze engineering cement-based composite materials under impact load.

[0081] The present invention will provide guidance and suggestions based on scientific evidence and theory for crack initiation and propagation, structural design and life prediction, material selection and design in actual engineering, and provide important data support and reference value for studying the fracture and failure mechanism of materials. It can effectively predict and analyze the mechanical behavior and damage problems of ECC under impact loads.

[0082] Furthermore, a fully discrete model of engineered cementitious composites (ECC) is constructed, including matrix modeling, fiber modeling, and fiber-matrix interface modeling. Compared with the traditional continuous model, this modeling method can better handle discontinuous problems such as material rupture and crack propagation.

[0083] Furthermore, the process of matrix modeling includes:

[0084] Considering the softening behavior of the material and the damage caused by compression deformation, the damage correction factor λ of the bond is introduced to correct the point force function f in the PMB model to obtain the corrected constitutive force function, and the stress-strain response during the crack propagation process is obtained based on the corrected constitutive force function;

[0085] The value range of the bond damage correction factor λ is from 0 to 1, and the modified constitutive force function is:

[0086] F=(1-λ)f

[0087] F is the modified constitutive force function.

[0088] Specifically, the cement matrix is ​​modeled. In this embodiment, the softening behavior of the material and the damage caused by compression deformation are considered, and the damage correction factor λ of the bond is introduced to correct the point force function f in the PMB model so that the interaction bond shows a cumulative damage process. The corrected constitutive force function is:

[0089] F=(1-λ)f

[0090] Among them, the value range of the bond damage correction factor λ is 0 to 1, and the function between it and the elongation s is:

[0091]

[0092] In the formula, the bond is divided into three stages from stretching to failure: elastic stage, damage stage, and yield softening stage. 0t It represents the ultimate elastic elongation under tensile load, which can be expressed as the tensile strength f of cement matrix. t And elastic modulus E is used to express it, s f It represents the parameter that affects the slope of the softening branch, s ut is the critical elongation.

[0093] Further, the process of fiber modeling includes:

[0094] The fiber is modeled as a one-dimensional peridynamic rod, neglecting the effects of bending and rotation, showing the strengthening effect of the fiber during crack propagation, including the micromodulus of the fiber bond;

[0095] Among them, the micro modulus c of the fiber bond f for:

[0096]

[0097] In the formula, E f is the elastic modulus of the fiber before failure, δ is the near field range of the fiber point, A f is the cross-sectional area of ​​a fiber unit.

[0098] Critical tensile strain S of fiber bond c The fiber tensile strength σ ft Decide:

[0099]

[0100] If the elongation of the fiber bond exceeds the critical elongation S cr , the bond force is irreversibly set to zero, indicating that the bond has failed.

[0101] Specifically, the fiber is modeled as a one-dimensional peridynamic rod, neglecting effects such as bending and rotation.

[0102] Micromodulus of fiber bond c f for:

[0103]

[0104] In the formula, E f is the elastic modulus of the fiber before failure, and δ is the near field range of the fiber point, such as Figure 2 As shown in the figure, in the two-dimensional peridynamic model, a single fiber unit represents N fibers arranged along the thickness direction, and the cross-sectional area of ​​a fiber unit is:

[0105]

[0106] Where, d f is the fiber diameter.

[0107] By modeling the fiber as a one-dimensional peridynamic rod, the effects of its bending and rotation are neglected, thereby strengthening the role of the fiber in the crack propagation process. This is of great significance for simulating the tensile and reinforcement behavior of fibers in composite materials.

[0108] Furthermore, the process of fiber-matrix interface modeling includes:

[0109] Determine the relationship between the interfacial pair force f and the interfacial shear stress τ between the fiber and the matrix, calculate the fiber pull-out displacement, obtain the key mechanism of the interaction between the fiber and the matrix, and obtain the interfacial micro-force;

[0110] The relationship between the interfacial pairing force f between the fiber and the matrix and the interfacial shear stress τ is:

[0111]

[0112] Where τ is the shear stress scalar value, d f is the fiber diameter, t is the interface thickness between the fiber and the matrix;

[0113] The fiber pull-out displacement is calculated as follows:

[0114]

[0115] Where Δ is the displacement vector, x f ,y f are the fiber points on the reference configuration, y m 、x m are the base points on the reference configuration, n f is the direction vector of the fiber element.

[0116] The modeling results of the matrix include the deformation and failure mode of the material under the action of external forces, especially the stress-strain response during the crack propagation process. Specifically, it is the constitutive force function F. The results of fiber modeling show the strengthening effect of fibers during crack propagation, including the micro modulus of fiber bonds. The modeling results of the interface are the key mechanisms of the interaction between fibers and the matrix, and the interface micro forces are obtained. The fully discrete model is constructed by discretizing the fibers and the matrix, including the discretization of the interface, and solving the equations after discretization.

[0117] Specifically, the interface action mode between the fiber and the matrix is ​​determined as follows:

[0118] In the framework of peridynamic theory, the total force density exerted by the matrix point on the fiber point within the near field range of a fiber point is: The total pull-out force P of N fibers is f It can be expressed as:

[0119]

[0120] Where, L e is the fiber embedding length.

[0121] Assume that a fiber point and its near field H f The pairwise force function between all matrix points in the fiber point is f, then the matrix point in the near field of the fiber point applies the body force density to the fiber point for:

[0122]

[0123] The relationship between the interfacial pairing force f between the fiber and the matrix and the interfacial shear stress τ is:

[0124]

[0125] The interface constitutive model used in this embodiment is a classical exponential friction decay interface model, such as Figure 3 As shown:

[0126] in:

[0127]

[0128] Where Δ is the pull-out displacement vector and τ is the shear stress scalar value.

[0129] Let the scalar value of the pull-out displacement be Δ, and ignore the deformation of the fiber during the pull-out process and its Poisson's ratio effect, then:

[0130]

[0131] Where k is the fiber bulk interface bonding modulus, ζ is the interface damage coefficient, η is the shape coefficient describing the exponential decline section of the interface constitutive relationship, and the critical debonding pullout Δ 0 for:

[0132]

[0133] In the formula, τ max is the interfacial debonding strength, τ f is the initial friction of the interface.

[0134] Calculate the fiber pull-out displacement as follows:

[0135] The relative motion between the fiber unit and the matrix is ​​as follows Figure 4 As shown, the equivalent bonding point of the fiber point on the matrix point is defined as:

[0136]

[0137] In the formula, is the fiber point on the reference configuration, x f Substrate point within the near field, dV m is the volume element represented by the matrix point.

[0138] The fiber and the matrix undergo relative displacement under the pull-out force. f Move to y in the deformed configuration f , its equivalent matrix bonding point in the deformed configuration is:

[0139]

[0140] In the formula, H′ f is the near field range H in the reference configuration f The corresponding area on the deformed configuration, is a point on the reference configuration Corresponding points on the deformation configuration. Assuming that the fiber direction of the ECC material does not change during the fiber pull-out process, the fiber pull-out displacement relative to the matrix is:

[0141]

[0142] When calculating the pull-out displacement vector of the fiber relative to the matrix, its direction is the same as the initial direction of the fiber. Therefore, when the fiber is acted upon by a small force from the matrix, the direction of the force is also the same as the initial direction of the fiber. That is, in the model of this embodiment, the force on the fiber is parallel to the initial direction of the fiber, and the fiber unit will not bend.

[0143] Furthermore, the fully discrete model of engineering cement-based composites is constructed, which also includes considering the fiber friction effect and correcting the interface force between the fiber and the matrix according to the fiber direction, specifically:

[0144] Consider a fiber unit that is inclined relative to the crack surface. The angle between the fiber direction vector and the crack surface normal vector is θ. Let the bridging force contributed by the fiber be P θ , considering the friction effect of the fiber, the bridging force contributed by the fiber is:

[0145] P θ =e gθ P θ＝0

[0146] Where g is the friction coefficient, P θ＝0 is the bridging force contributed by the fiber when θ = 0;

[0147] Considering the fiber friction effect, when the fiber intersects the matrix crack, the interfacial force between the fiber and the matrix is ​​corrected according to the fiber direction. The corrected interfacial shear stress τ θ for:

[0148]

[0149] Based on the embedment depth L of the fiber during extraction e The change of the interface micro-force f int After correction, the actual interface micro-force f int * for:

[0150]

[0151] Among them, L e is the initial embedding depth of the fiber, and Δ is the scalar value of the pull-out displacement.

[0152] Specifically, Figure 5 As shown, consider a fiber unit inclined relative to the crack surface, the angle between the fiber direction vector and the crack surface normal vector is θ, and the bridging force contributed by the opening is Pθ , considering the friction effect of the fiber, the pull-out force or bridging force of the fiber is:

[0153] P θ =e gθ P θ＝0

[0154] Where g is the friction coefficient, P θ＝0 is the bridging force contributed by the fiber when θ = 0. Considering this friction effect, when the fiber intersects the matrix crack, the interfacial force between the fiber and the matrix is ​​corrected according to the fiber direction.

[0155] Corrected interface shear stress τ θ for:

[0156]

[0157] Based on the embedment depth L of the fiber during extraction e The change of the interface micro-force f int After correction, the actual interface micro-force f int * for:

[0158]

[0159] Among them, L e is the initial embedding depth of the fiber, and Δ is the scalar value of the pull-out displacement.

[0160] The model takes into account the friction effect between the fiber and the matrix and modifies the interface force according to the fiber direction, which provides support for more accurate dynamic analysis, especially in the micro-force calculation of fiber pullout and interface force.

[0161] Furthermore, the cement matrix and fibers in the ECC model are discretized into several spatial material points, including:

[0162] The cement matrix and fiber are evenly discretized into several material points with a discrete size of Δx. Among them, the material points within the near-field domain of each material point satisfy the peridynamic motion equation. The integral form in the peridynamic motion equation is converted into a summation form, which is specifically:

[0163]

[0164] In the formula, ρ represents density, is the acceleration, f is the interaction force between material points, V p The volume of any material point in the near field, is the external force on the material point, is the displacement vector of the neighboring material point P at time step n, x Pis the initial spatial coordinate of the neighboring material point P, x i is the initial space coordinate of material point i.

[0165] Specifically, Figure 6 As shown, the object is evenly discretized into material points with a discrete size of Δx. The material points within the near field of each material point satisfy the peridynamic motion equation. The integral form in the peridynamic motion equation is converted into the summation form, and its control equation is given as follows:

[0166]

[0167] In the formula, ρ represents density, is the acceleration, f is the interaction force between material points, V p The volume of any material point in the near field, The external force acting on a material point.

[0168] Furthermore, an impact crack propagation model is constructed based on the plurality of spatial material points and peri-field dynamics, including:

[0169] like Figure 7 As shown, a rigid impact object will not be deformed during impact and will move as a rigid body at a certain speed. The particles in the impact object will be squeezed to a new position outside the impact object.

[0170] Using the explicit time integration algorithm, the rigid body moves at a preset speed. The particles in the impact object are squeezed to a new position outside the impact object, forming a contact surface between the impact object and the particles. k At the next time step (t+Δt), the particle x is relocated to a new position. k The speed v k for:

[0171]

[0172] In the formula, is the displacement vector corrected at time (t+Δt), is the displacement vector at time t, Δt is the corresponding time increment, and at time (t+Δt), the particle x k Reaction force to impact object for:

[0173]

[0174] In the formula, For mass x k The velocity vector before repositioning at time (t+Δt), ρ k and V k are density and volume respectively;

[0175] The reaction force F received by the impact object at the time (t+Δt) is obtained by summing the reaction forces received by all particles in the impact object. k for:

[0176]

[0177] in,

[0178] In addition, to prevent target material points from penetrating each other, a short-range repulsion force is added:

[0179]

[0180] In the formula, c sh =1.5c, c is the micromodulus of the material; d is the distance between material points i and j, expressed as:

[0181] d=min(0.9|x j -x i |,1.35Δx)

[0182] Where Δx is the near field radius.

[0183] The basic equation in peridynamic theory is the equation of motion, which is applicable to damage problems in many situations, including impact. The deformation of the impacted object is controlled by the equation of motion of peridynamic theory. Figure 7 It can be seen that there is mutual penetration between the impactor and the impacted object, but in physics, this mutual penetration does not exist, so the model needs to be rebuilt so that the particles that penetrate into the impactor will be squeezed to a new position outside the impactor.

[0184] Furthermore, the dynamic increase factor (DIF), which is the ratio of dynamic strength to static strength, proposed in the CEB-FIP model specification is added to the failure criterion to take into account the strain rate effect.

[0185] The modified impact crack growth model describes the fracture mechanism of the microscopic interaction force inside the material through the bond breaking model;

[0186] Wherein, the bond breaking model is:

[0187]

[0188] In the formula, and are the dynamic critical tensile and compressive elongations of the bond, and are the compression and extension rates of the bond, respectively; and are the quasi-static tensile strain rate and compressive strain rate, α, γ, δ, η are material constants, and f cu is the unconfined compressive strength of the cubic concrete specimen, E cd and E td are the dynamic compression and tension elastic moduli, respectively, c is the compressive strength of concrete, f t is the tensile strength of concrete.

[0189] The impact crack growth model is the core part of the entire macroscopic model. It predicts the destructive behavior of the material by analyzing the crack formation and expansion of the material under impact load. The bond breaking model is the microscopic part of the impact crack growth model, which is mainly used to describe the fracture mechanism of the microscopic interaction force inside the material. The bonds between each material point will gradually accumulate damage when impacted, eventually leading to fracture. When these microscopic bonds break, it will manifest as crack expansion on a macro scale. The bond breaking model is the basis for constructing the impact crack growth model. It simulates the destruction of the entire material by modeling the fracture process of a single bond. Compared with the ordinary static crack growth model, the modified impact crack growth model provided in this embodiment is more suitable for material destruction analysis under high strain rate conditions such as ECC, and can more accurately reflect its mechanical behavior under high-speed impact.

[0190] Particle relocation and dynamic increase factor (DIF) through explicit dynamic simulation algorithms are common practices in material modeling under impact loading, especially when considering strain rate effects. The DIF in the CEB-FIP specification is based on experimental and numerical fitting results and is usually used for dynamic strength modeling of brittle materials such as concrete. The crack propagation simulation of engineering cementitious composites under impact loading can be achieved through explicit time integration algorithms and peridynamic theory. Under impact loading, the strain rate effect failure criterion is combined in the model to correct the crack propagation model. This can more accurately describe the mechanical response of the material at different strain rates and enhance the practical applicability of the model. The dynamic propagation of impact cracks is simulated by explicit time integration algorithms, combined with the correction of the ratio of dynamic strength to static strength, which can more accurately reflect the failure behavior of engineering cementitious materials under high-speed impact conditions.

[0191] In order to more clearly express the technical solution of the present invention, the following specific embodiments are provided to introduce the solution:

[0192] like Figure 8 As shown, this embodiment takes a rigid cube impacting an ECC plate with prefabricated cracks as an example, and uses the method of the present invention to perform peridynamic modeling and analysis; Fig. 9The ECC thin plate shown in the figure has a length of L = 200 mm, a width of W = 50 mm, and a prefabricated crack of length L = 15 mm. The upper middle part of the sample is a rigid cube with a mass of m = 30 kg and a speed of V = 2 m / s. The elastic modulus of the cement matrix is ​​22.35 Gpa, and the fracture toughness is 0.287 Mpa m 1 / 2 , density is 2380kg / m 3 ; The tensile strength of PVA fiber is 1620Mpa; diameter d f =39μm, length l f =12mm, elastic modulus E f =42.8Gpa, elongation is 6%; PVA fiber volume interface bonding modulus k = 2.0*10 10 N / m, fiber interface debonding strength τ max =2.0MPa, initial friction force of fiber interface τ f =2.0MPa; In this example, the time iteration step is Δ t =2×10 -7 s, the peridynamic discretization schemes of fiber and matrix are both δ = 2 mm, Δ x =0.5mm, Poisson's ratio is 1 / 3. The distance between the prefabricated crack and the mid-span is b = 30mm, no other boundary conditions; fiber content V f =2%.

[0193] The specific implementation includes the following steps:

[0194] S1: The cement matrix and fiber to be simulated are discretized into a series of spatial material points respectively. Specifically, the discretized fiber is first placed on the background composed of the matrix discrete points, and then the adjacency relationship between the fiber and the matrix is ​​considered respectively. If the distance between two discrete points is less than or equal to the near-field radius δ, it is considered that there is an adjacency relationship between them. For matrix points, adjacency relationships can be established within the near-field range of the matrix points, including matrix points and fiber points; for fiber points, fiber points can only establish adjacency relationships with matrix points within their near-field range and other points belonging to the same fiber unit. Specifically: For the ECC plate model, uniform gridless particle division is performed, and the near-field dynamics discretization schemes of the fiber and the matrix are both near-field radius δ = 2mm, and the grid size Δ x =0.5mm, according to the initial position coordinates of the material point and the near-field range radius, the control equation for point association is determined as follows:

[0195]

[0196] Where ρ represents density, is the acceleration, f is the interaction force between material points, V pThe volume of any material point in the near field, is the external force on the material point, is the displacement vector of the neighboring material point P at time step n, x P is the initial spatial coordinate of the neighboring material point P, x i is the initial space coordinate of material point i.

[0197] S2: Input discretization file and command file, initialize material model and damage model according to input parameters. In this example, the time iteration step is Δ t =2×10 -7 s, loop over all fiber points and matrix points and determine their near-field domains and the points within them.

[0198] S3: Input the initial conditions. In this example, the elastic modulus of the cement matrix is ​​22.35 Gpa and the fracture toughness is 0.287 Mpa·m 1 / 2 , density is 2380kg / m 3 ; The tensile strength of PVA fiber is 1620Mpa; diameter d f =39μm, length l f =12mm, elastic modulus E f =42.8Gpa, elongation is 6%; PVA fiber volume interface bonding modulus k = 2.0*10 10 N / m, fiber interface debonding strength τ max =2.0MPa, initial friction force of fiber interface τ f =2.0MPa; loop all fiber elements and calculate the direction vector.

[0199] S4: Calculate the velocity, acceleration, displacement and position of each point. This example uses the Verlet explicit time integration algorithm for dynamic calculations, and updates the physical and mechanical information such as the position, velocity, acceleration, etc. of the material point in real time. Specifically:

[0200]

[0201] In the formula, u, They represent the velocity and acceleration of the material point respectively, and Δt is the uniform discrete time step.

[0202] S5: Loop all fiber units to determine whether they need interface force correction, loop all fiber points and calculate their pull-out force and pair force. Specifically, based on the embedding depth L of the fiber during pull-out, e The interface micro-force f is corrected by the change of * for:

[0203]

[0204] Among them, L e is the initial embedding depth of the fiber, Δ is the scalar value of the pull-out displacement. For the inclined fiber, Δ is taken as the corresponding imaginary horizontal fiber pull-out displacement as shown.

[0205] S6: Determine whether all fiber points are looped, loop all matrix points and calculate the paired forces and damage values ​​between matrix points in their neighborhood, end the loop of all points and update all forces, and calculate the required variables.

[0206] S7: Output the crack extension diagram and strain energy density diagram at different times. Fig.10 The crack propagation path diagram of the ECC plate under impact load at 0μs, 55μs, 95μs, and 160μs respectively. Fig.11 Strain energy density diagram of ECC plate at 0μs, 55μs, 95μs and 160μs respectively.

[0207] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A modeling method for engineering cement-based composite materials under impact load based on peridynamics, characterized in that: include: Constructing a fully discrete model of an engineering cement-based composite material, and discretizing the cement matrix and the fibers in the fully discrete model of the engineering cement-based composite material into a plurality of spatial material points respectively; By using the plurality of spatial material points, an impact crack propagation model is constructed based on peri-field dynamics; The impact crack growth model is modified by combining the failure criterion of the model strain rate effect to obtain a modified impact crack growth model; The modified impact crack growth model is used to analyze engineering cement-based composite materials under impact load.

2. The modeling method of engineering cement-based composite materials under impact load based on peridynamics according to claim 1, characterized in that: Constructing the fully discrete model of the engineering cement-based composite material includes: matrix modeling, fiber modeling and fiber-matrix interface modeling; The process of matrix modeling includes: Considering the softening behavior of the material and the damage caused by compression deformation, the damage correction factor λ of the bond is introduced to correct the point force function f in the PMB model to obtain the corrected constitutive force function, and the stress-strain response during the crack propagation process is obtained based on the corrected constitutive force function; Among them, the value range of the damage correction factor λ of the bond is 0 to 1, and the modified constitutive force function is: F=(1-λ)f F is the modified constitutive force function.

3. The modeling method of engineering cement-based composite materials under impact load based on peridynamics according to claim 2, characterized in that: The fiber modeling process includes: The fiber is modeled as a one-dimensional peridynamic rod, neglecting the effects of bending and rotation, showing the strengthening effect of the fiber during crack propagation, including the micromodulus of the fiber bond; Among them, the micro modulus of the fiber bond c f for: In the formula, E f is the elastic modulus of the fiber before failure, δ is the near field range of the fiber point, A f is the cross-sectional area of ​​a fiber unit; Critical tensile strain S of fiber bond c The fiber tensile strength σ ft Decide: If the elongation of the fiber bond exceeds the critical elongation S cr , the bond force is irreversibly set to zero, indicating that the bond has failed.

4. The modeling method of engineering cement-based composite materials under impact load based on peridynamics according to claim 3, characterized in that: The process of fiber-matrix interface modeling includes: Determine the relationship between the interfacial pair force f and the interfacial shear stress τ between the fiber and the matrix, calculate the fiber pull-out displacement, obtain the key mechanism of the interaction between the fiber and the matrix, and obtain the interfacial micro-force; The relationship between the interfacial pairing force f and the interfacial shear stress τ between the fiber and the matrix is: Where τ is the shear stress scalar value, d f is the fiber diameter, t is the interface thickness between the fiber and the matrix; The fiber pull-out displacement is calculated as follows: Where Δ is the displacement vector, x f ,y f are the fiber points on the reference configuration, y m 、x m are the base points on the reference configuration, n f is the direction vector of the fiber element.

5. The modeling method of engineering cement-based composite materials under impact load based on peridynamics according to claim 1, characterized in that: The process of constructing a fully discrete model of engineered cementitious composites also includes taking into account the fiber friction effect and modifying the interfacial forces between the fiber and the matrix according to the fiber orientation, specifically: Consider a fiber unit that is inclined relative to the crack surface. The angle between the fiber direction vector and the crack surface normal vector is θ. Let the bridging force contributed by the fiber be P θ , considering the friction effect of the fiber, the bridging force contributed by the fiber is: Where g is the friction coefficient, P θ＝0 is the bridging force contributed by the fiber when θ = 0, and e is the natural logarithm; Considering the fiber friction effect, when the fiber intersects the matrix crack, the interfacial force between the fiber and the matrix is ​​corrected according to the fiber direction. The corrected interfacial shear stress τ θ for: Based on the embedment depth L of the fiber during extraction e The change of the interface micro-force f int After correction, the actual interface micro-force f int * for: Among them, L e is the initial embedding depth of the fiber, and Δ is the scalar value of the pull-out displacement.

6. The modeling method of engineering cement-based composite materials under impact load based on peridynamics according to claim 1, characterized in that: The cement matrix and the fiber in the fully discrete model of the engineering cement-based composite material are discretized into a number of spatial material points, including: The cement matrix and the fiber are uniformly discretized into a number of material points with a discretization size of Δx; wherein the material points within the near-field domain of each material point satisfy the peridynamic motion equation, and the integral form in the peridynamic motion equation is converted into a summation form, specifically: In the formula, ρ represents density, is the acceleration, f is the interaction force between material points, V p The volume of any material point in the near field, is the external force on the material point, P is the neighboring material point, is the displacement vector of the neighboring material point P at time step n, x P is the initial spatial coordinate of the neighboring material point P, x i is the initial space coordinate of material point i.

7. The modeling method of engineering cement-based composite materials under impact load based on peridynamics according to claim 6, characterized in that: Through the several spatial material points, an impact crack propagation model is constructed based on peri-field dynamics, including: Using the explicit time integration algorithm, the rigid body moves at a preset speed. The particles in the impact object are squeezed to a new position outside the impact object, forming a contact surface between the impact object and the particles. k At the next time step (t+Δt), the particle x is relocated to a new position. k The speed v k for: In the formula, is the displacement vector corrected at time (t+Δt), is the displacement vector at time t, Δt is the corresponding time increment, and at time (t+Δt), the particle x k Reaction force to impact object for: In the formula, For mass x k The velocity vector before repositioning at time (t+Δt), ρ k and V k are density and volume respectively; The reaction force F received by the impact object at the time (t+Δt) is obtained by summing the reaction forces received by all particles in the impact object. k for: in, 8. The modeling method of engineering cement-based composite materials under impact load based on peridynamics according to claim 1, characterized in that: The modified impact crack growth model describes the fracture mechanism of the microscopic interaction force inside the material through a bond breaking model; Wherein, the bond breaking model is: In the formula, and are the dynamic critical tensile and compressive elongations of the bond, and are the compression and extension rates of the bond, respectively; and are the quasi-static tensile strain rate and compressive strain rate, α, γ, δ, η are material constants, and f cu is the unconfined compressive strength of the cubic concrete specimen, E cd and E td are the dynamic compression and tension elastic moduli, respectively, c is the compressive strength of concrete, f t is the tensile strength of concrete.

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