Method for analyzing mechanical properties of high-hardness and quasi-brittle material structural member

Abstract

The invention provides a mechanical property analysis method for a high-hardness and quasi-brittle material structural member. The method comprises the following steps: S1, establishing a key-type near-field dynamic model of the structural member; s2, inputting material parameters and applying boundary conditions; s3, solving a control equation set of the key-type near-field dynamic model; s4, judging the tension and compression conditions of the key; s5, according to the yield state of the key, a used model is selected to describe the relation between key extension and key force; s6, judging whether the key is fractured or not according to the elongation of the key and the fracture criterion of the key; if the keys are broken, deleting rigidity values contributed by the corresponding keys in the rigidity matrix; and S7, updating the time step, and after each time of updating the time step, circulating the steps S2 to S6 until the solution is completed. The method can simulate the whole-process mechanical response of special materials such as rocks and concrete from deformation to damage under the conditions of high strain rate and high pressure, and has great engineering application value.

Description

Technical Field

[0001] The present invention mainly relates to the technical field related to material mechanical analysis, and specifically is a method for analyzing the mechanical properties of high-hardness, quasi-brittle material structural parts. Background Art

[0002] Quasi-brittle materials with high hardness, such as rock and concrete, are widely used in various engineering fields. In addition to standard design loads, these materials are often subjected to strong dynamic loads in engineering structures, such as impact, earthquake, explosion, etc. A large number of studies have shown that as the dynamic load of the material increases, the material gradually begins to fail, microcracks initiate, expand, and fuse inside the material, eventually leading to the appearance of macrocracks. Therefore, studying the deformation and failure mechanism of common building materials such as rock and concrete is of great significance to protecting people's lives and property.

[0003] The classic Holmquist-Johnson-Cook (HJC) constitutive model can describe the mechanical behavior of materials under high strain rate and high pressure conditions, so it is often used to describe the mechanical response of materials such as concrete and rock. The bond-type peridynamics model is often used to describe the failure of materials and the fracture behavior of structures, but due to the particularity of special materials such as rock and concrete, the several commonly used constitutive models in bond-type peridynamics cannot accurately describe their mechanical response. Summary of the invention

[0004] In order to solve the shortcomings of current technology, the present invention combines the existing technology and, based on practical applications, provides a method for analyzing the mechanical properties of high-hardness, quasi-brittle material structures. This method is highly targeted and can simulate the full process mechanical response of special materials such as rocks and concrete from deformation to destruction under high strain rate and high pressure conditions, and has great engineering application value.

[0005] The technical solution of the present invention is as follows:

[0006] A method for analyzing mechanical properties of high-hardness, quasi-brittle material structural parts, characterized by comprising the following steps:

[0007] S1. Establish a bond-type peridynamic model of the structural component;

[0008] S2, input material parameters and apply boundary conditions;

[0009] S3, solving the control equations of the bond-type peridynamic model to obtain the displacement field, strain field and stress field of the structural component;

[0010] S4, judging the tension and compression conditions of the bond. If the bond is in tension, the established bond-type peridynamic model is used to describe the relationship between the bond elongation and the bond force. If the bond is in compression, judging whether the bond is currently in a yield state;

[0011] S5. If the bond is not in a yield state, the established bond-type peridynamic model is continued to be used to describe the relationship between bond elongation and bond force. If the bond is in a yield state, the PD-HJC constitutive model with rate-enhanced effect is used to describe the relationship between bond elongation and bond force.

[0012] S6. judging whether the bond is broken according to the bond elongation and the bond fracture criterion; if the bond is broken, deleting the stiffness value contributed by the corresponding bond in the stiffness matrix;

[0013] S7, update the time step, and loop through steps S2 to S6 each time the time step is updated until the solution is completed.

[0014] Furthermore, based on the peridynamics theory, the region Ω is considered to be a continuum consisting of a series of material points x. The spherical area with point x as the center and radius δ is called the neighborhood of point x. The motion state of x is affected by H δ The influence of all material points x' in (x), H δ The relative position vector ξ=x′-x between the points x and x′ in (x) is called the bond, and the relative displacement vector between x and x′ is expressed as η=u(x′)-u(x), where u(x′) and u(x) are the displacement vectors corresponding to the positions of points x′ and x, respectively. Therefore, the bond-type peridynamic model established in step S1 has the following governing equations:

[0015]

[0016] Where ρ is the density of the object, u represents the displacement, dH represents the integrated area, b is the body density, and f(x)<x'-x> represents the bond force acting directly from point x' to point x in bond-type peridynamics, f(x)<x'-x> The expression is as follows:

[0017] f(x)<x'-x> =C[x](ξ)·η

[0018] C[x](ξ) is the micromodulus tensor, expressed as follows:

[0019]

[0020] Where c[x](|ξ|) is a parameter related to material properties and is the micromodulus coefficient.

[0021] Further, in step S4, the volume strain at point x and point x' is calculated according to the displacement field to obtain the hydrostatic pressure related terms and the hydrostatic pressure independent terms, and then the yield strength f is obtained. Y Used to determine whether the key is currently in the yielded state.

[0022] Furthermore, the volume strain μ at point x and point x' satisfies μ<μ c , the hydrostatic pressure p is calculated as follows:

[0023] p=K e μ

[0024] Where K e is the bulk modulus of elasticity, μ c is the elastic limit volume strain;

[0025] If μ is satisfied c <μ<μ l , the hydrostatic pressure p is calculated as follows:

[0026]

[0027] Among them, p c represents the pore collapse pressure, K t is the bulk modulus in the transition stage, p max is the maximum pressure reached before the load is unloaded, μ max is the maximum volume strain reached before unloading, F is the compression coefficient, and K1 is the material constant;

[0028] K t Calculate as follows:

[0029]

[0030] Among them, p l and μ l is the hydrostatic pressure and volumetric strain when the hole completely collapses;

[0031] F is calculated as follows:

[0032]

[0033] p max Calculate as follows:

[0034] p max =p c +K t (μ max -μ c )

[0035] When the material is in the compaction stage, that is, p ≥ p l When , the hydrostatic pressure p is calculated as follows:

[0036]

[0037] K1, K2, and K3 are material constants. In order to make them equivalent to the relevant parameters of non-porous materials, the modified volume strain is used. ρg is the density of the material without pores, ρ0 is the initial density of the material;

[0038] After obtaining the hydrostatic pressure p, calculate the hydrostatic pressure related terms and hydrostatic pressure independent terms, and finally obtain the yield strength f Y .

[0039] Furthermore, the hydrostatic pressure-independent term f1 is calculated as follows:

[0040]

[0041] Among them, c 0 represents the micromodulus coefficient, ε r represents the elastic equivalent strain value, C is the strain rate coefficient, is the bond ξ elongation change rate,

[0042] The calculation is as follows:

[0043]

[0044] The water inlet pressure related term f2 is calculated as follows:

[0045] f2=β H f1

[0046] β H is the pressure-independent / dependent intensity ratio, calculated as follows:

[0047]

[0048] σ i (x) is the hydrostatic pressure related term of the yield stress at point x, σ i (x') is the hydrostatic pressure related term of the yield stress at point x', σ r is the hydrostatic pressure independent term of the yield stress, σ i (x) is calculated as follows:

[0049]

[0050] Among them, f c is the unconfined compressive strength, R is the normalized pressure hardening coefficient, and p(x) is the hydrostatic pressure at point x. The yield strength of the peridynamic bond is calculated as follows:

[0051] f Y =(1-W ξ )f1+f2

[0052] W ξ is the accumulated plastic damage of the bond, calculated as follows:

[0053]

[0054] Among them, Δ|η p | is the plastic strain increment of the bond, and Represents the equivalent crushing plastic strain under hydrostatic pressure

[0055] and equivalent crushing volume strain;

[0056]

[0057] D1 and D2 are material parameters, T * =T / f c is the normalized maximum hydrostatic tensile stress, where T is the maximum hydrostatic tensile stress, p * =p / f c is the normalized hydrostatic pressure;

[0058] If the bond force f(x)≤f Y , then the bond is not in a yielded state, if f(x)>f Y , the key is in yield state.

[0059] Further, in step S5, the PD-HJC constitutive model is used to describe the relationship between bond elongation and bond force, and the expression is as follows:

[0060] f(x)<x'-x> =C[x](ξ)·η=c 0 (|ξ|)(ξ·η)ξ≈c 0 (|ξ|)ε r |ξ| 3 .

[0061] Further, in step S6, the bond breaking criterion is:

[0062]

[0063] where ||·|| represents the length of the calculation vector, s is the elongation of the bond ξ, and s crit is the critical elongation of the bond, t represents the current time step, t' is any time step before the tth time step, s(t',ξ) represents the elongation of the bond ξ at the t'th time step, and μ(t,ξ) = 0 indicates that the bond ξ is broken.

[0064] Beneficial effects of the present invention:

[0065] 1. The analysis method of the present invention can accurately describe the mechanical properties of high-hardness quasi-brittle materials and obtain corresponding calculation results. Based on these calculation results, the load change trend, peak load, crack initiation position, crack propagation path, fracture mode and degree of structural damage of the structure under high strain rate and high pressure loading conditions can be understood. Based on this knowledge, engineers can optimize the design scheme with high-hardness quasi-brittle materials such as concrete as the main structure, which is helpful to build a more reliable and stable structure.

[0066] 2. The analysis method of the present invention is based on the HJC constitutive model in classical continuum mechanics, reconstructs the bond-type peridynamic model, and proposes a PD-HJC constitutive model analysis method for simulating the mechanical response of high-hardness, quasi-brittle materials such as concrete. Compared with the classical continuum mechanics model, the present invention can simulate the initiation and cracking process of cracks; compared with conventional peridynamic models, the present invention can describe the mechanical response of special properties materials such as concrete under high strain rate and high pressure loads based on a relatively simple bond-type peridynamic model. Compared with the unconventional state-type peridynamic models commonly used to develop various constitutive models, the bond-type peridynamic model used in the present invention has a small amount of calculation and saves calculation time; compared with conventional bond-type peridynamic models, the present invention improves the accuracy of simulation of materials such as concrete. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 is a flow chart of the method of the present invention;

[0068] Figure 2 The geometric dimensions and external load conditions of the concrete structure and charge in the embodiment;

[0069] Figure 3 The failure modes of the concrete structure at different times in the embodiment (side section view);

[0070] Figure 4 The failure modes of the concrete structure at different times in the embodiment (overall view). DETAILED DESCRIPTION

[0071] The present invention will be further described with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art may make various changes or modifications to the present invention, and these equivalent forms also fall within the scope limited by the application.

[0072] Peridynamics theory is a new type of continuous medium theory proposed. It reformulates the classical solid mechanics theory and replaces the traditional partial differential equations with integral equations, which provides a solution to the unification problem of continuity and discontinuity. This formulation eliminates the dependence of the equation on spatial derivatives and unifies the mathematical representation of continuous and discontinuous field variables. Peridynamics theory assumes that material points interact with all points within their near-field radius, and the relative position between two points is called a bond. The critical value of bond stretching is used to determine whether the bond is broken. When the bond breaks, it is considered that the crack begins to nucleate. With the accumulation of broken bonds, macroscopic cracks gradually appear. Unlike other non-local continuous fracture models, peridynamics introduces the concept of material point damage based on the bond. The breaking of the bond at the microscopic level will be reflected as the damage of the point at the macroscopic level. In a certain sense, this forms the evolution of discrete crack surfaces and can describe the initiation, extension or bifurcation of cracks.

[0073] The analysis method provided by the embodiment of the present invention can reconstruct the bond-type peridynamic model based on the HJC constitutive model of classical continuum mechanics, that is, it can describe the mechanical response of high-hardness, quasi-brittle materials under high strain rate and high pressure loads within the framework of peridynamic (PD) theory. This embodiment uses concrete materials as a reference to study the special properties of concrete. Concrete often exhibits plastic behavior when under compression, but only brittle fracture occurs when under tension. Therefore, in order to characterize the typical characteristics of concrete materials, the peridynamic elastic-brittle constitutive model is referenced in the tension stage, and the HJC plastic constitutive model is referenced in the compression stage. The peridynamic model is reconstructed to obtain a mechanical properties analysis method for high-hardness, quasi-brittle material structural parts based on the PD-HJC constitutive model. The specific scheme is as follows.

[0074] Step 1: Establish a bond-type peridynamic model for high-hardness, quasi-brittle material structures. Based on peridynamic theory, the region Ω is considered to be a continuum consisting of a series of material points x. The spherical area with point x as the center and radius δ is called the neighborhood of point x. The motion state of x is affected by H δ The influence of all material points x' in (x), H δ The relative position vector ξ = x′-x between points x and x′ in (x) is called the bond, and the relative displacement vector between x and x′ is expressed as η = u(x′)-u(x), where u(x′) and u(x) are the displacement vectors corresponding to the positions of points x′ and x, respectively. The bond-type peridynamic model is expressed as follows:

[0075]

[0076] Where ρ is the density of the object, u represents the displacement, b is the body density, and f(x)<x'-x> represents the bond force acting directly from x' to x in bond-type peridynamics and is defined as:

[0077] f(x)<x'-x> =C[x](ξ)·η

[0078] C[x](ξ) is called the micromodulus tensor and is defined as

[0079]

[0080] where c[x](|ξ|) is a parameter related to the material properties and is called the micromodulus coefficient.

[0081] Step 2: Define material parameters and apply boundary conditions.

[0082] Step 3: Solve the control equations shown in step 1 to obtain the displacement field, strain field and stress field of the structural member.

[0083] Step 4: Determine whether the bond is under tension or compression. If the bond is under tension, use the bond-type peridynamic constitutive model in step 1 to describe the relationship between bond elongation and bond force.

[0084] If the bond is compressed, the volume strain μ at points x and x' is calculated based on the displacement field. If μ<μ c , at this time:

[0085] p=K e μ

[0086] Where K e is the bulk modulus of elasticity, μ c is the elastic limit volume strain. When the material is in the transition stage, μ c <μ<μ l , the pores in the material gradually collapse and finally become completely compacted. The relationship between the hydrostatic pressure and volume strain in this stage is:

[0087]

[0088] p max =p c +K t (μ max -μ c )

[0089] Among them, K t is the bulk modulus in the transition stage, p l and μ l is the hydrostatic pressure and volume strain when the hole collapses completely, p max is the maximum pressure reached before the load is unloaded, μ max is the maximum volume strain reached before unloading, and F is the compression coefficient. When the material is in the compaction stage, that is, p ≥ p lWhen the material is in the fully compacted stage, the relationship between its hydrostatic pressure and volume can be expressed as:

[0090]

[0091] K1, K2, and K3 are material constants. In order to make them equivalent to the relevant parameters of non-porous materials, the modified volume strain is used. ρ g is the density of the non-porous material. After obtaining the hydrostatic pressure p, calculate σ i (x), which is the hydrostatic pressure-dependent term for the yield stress at point x.

[0092]

[0093] get:

[0094]

[0095] Now continue to calculate the hydrostatic pressure-independent terms in the peridynamic bond forces:

[0096]

[0097] in is the bond ξ elongation change rate, defined as:

[0098]

[0099] The hydrostatic pressure related terms are calculated:

[0100] f2=β H f1

[0101] The yield strength of the peridynamic bond is then obtained as:

[0102] f Y =(1-W ξ )f1+f2

[0103] W ξ is the accumulated plastic damage of the bond, defined as:

[0104]

[0105] where Δ|η p | is the plastic strain increment of the bond, and Represents the equivalent crushing plastic strain and equivalent crushing volume strain under hydrostatic pressure:

[0106]

[0107] At this time, the bond force of the peridynamic bond is recalculated:

[0108] f(x)<x'-x> =C[x](ξ)·η=c 0 (|ξ|)(ξ·η)ξ≈c 0 (|ξ|)ε r |ξ| 3 .

[0109] Step 5: If f(x)≤f Y , the bond is not in a yield state, and the original bond-type peridynamic constitutive model is used to describe the relationship between bond elongation and bond force; if f(x)>f Y , the bond is in a yield state, and the PD-HJC constitutive model with rate-enhanced effect is used to describe the relationship between bond elongation and bond force. At this time,

[0110]

[0111] The relationship between bond elongation and bond force described in the above constitutive model is obtained under the assumption of small deformation and by considering the rate strengthening effect corresponding to the rate of change of bond elongation.

[0112] Step 6: Determine whether the bond breaks according to the bond elongation and the bond fracture criterion; if the bond breaks, delete the stiffness value contributed by the corresponding bond in the stiffness matrix; the bond failure criterion can be defined as:

[0113]

[0114] where ||·|| represents the length of the calculation vector, s is the elongation of the bond ξ, and s crit is the critical elongation of the bond, t represents the current time step, t' is any time step before the tth time step, s(t',ξ) represents the elongation of the bond ξ at the t'th time step, and μ(t,ξ) = 0 indicates that the bond ξ is broken.

[0115] Step 7: Update the time step. After each time step is updated, repeat steps 2 to 6 until the solution is completed.

[0116] Example:

[0117] In this embodiment, the concrete structure is modeled using the analysis method proposed in the present invention to study the mechanical response of the concrete under the blast load of the built-in explosive. Figure 2 As shown, the strength of the concrete structure is set to C30, and the Poisson's ratio ν = 1 / 3. The depth of the hole in the upper part is h D Set to 215mm, the height of the TNT column h TThe thickness is set to 30 mm, the explosive charge is 96 g, and the detonation point is set at the center of the bottom of the explosive column. The concrete structure is discretized into 14559 hexahedral units, and a total of 1411265 near-field units are generated. The total calculation time is 150 μs, the time step is 0.5 μs, and a total of 3000 time steps are calculated. In order to facilitate the observation of the calculation results, the TNT explosives are hidden and only the destruction form of the concrete structure is observed.

[0118] Figure 2 The failure modes of the concrete structure at different times (side section view): (a) 5μs, (b) 12.5μs, (c) 25μs, (d) 50μs, (e) 100μs, and (f) 150μs; Figure 3 The damage morphology of the concrete structure at different times (overall view): (a) 5μs, (b) 12.5μs, (c) 25μs, (d) 50μs, (e) 100μs, (f) 150μs. Analysis shows that the TNT explosive exploded after ignition and began to squeeze the concrete structure. At 5μs, a local crushing zone was formed in the area where the concrete and the TNT body were in direct contact. The fracture of the bond caused the stiffness of the structure to begin to degrade, and the center of the concrete began to deform and formed a crater center with a diameter of 70mm. However, no phenomenon was observed on the surface of the concrete at this time. At 12.5μs, cracks appeared on the surface of the concrete before the inside of the soil. This was caused by the overlap of the stress wave reflected from the boundary and the new stress wave, resulting in layer cracking damage. The surface cracks were mainly formed at the center of each face of the cube, which was also the first position where the stress wave arrived. At 25μs, a small number of cracks appeared inside the soil, distributed on four main paths. The number of cracks on the soil surface has increased significantly, but these cracks are not irregular. From 50μs to 100μs, it can be observed that the cracks on the soil surface are interconnected to form a vertical and two horizontal main cracks. The vertical main cracks and horizontal main cracks passing through the center of the face are caused by the direct pressure of the explosion of the explosives, while the upper horizontal cracks are formed by layer cracking damage. The cracks on the four main paths have been interconnected and have also penetrated the center of the blast pit. The diameter of the center of the blast pit has increased to 96.6mm. At 150μs, the unit detachment in the center of the concrete has been very serious, and the radius of the center of the blast pit has increased to 107.7mm. The horizontal width of the concrete cube has also increased from 400mm to 441.8mm, which means that the concrete structure has undergone serious deformation. The fracture and shedding of units caused the overall stiffness of the concrete to deteriorate rapidly, exacerbating the cracking of the concrete. The through-type main cracks eventually divided the concrete structure into multiple fragments. The degree of damage in the upper half with holes was significantly stronger than that in the lower half without holes. The diameter of the crater and the maximum horizontal width of the structure increased by 115.4% and 10.45% respectively.

[0119] The analysis method provided in this embodiment models the concrete structure and simulates the service cycle of the structure from deformation to crack initiation, expansion and complete destruction under the action of high pressure and high strain rate explosion load, demonstrating the effectiveness and practicality of the method. The method will have broad application prospects.

Claims

1. A method for analyzing mechanical properties of high-hardness, quasi-brittle material structures, characterized in that: The steps include: S1. Establish a bond-type peridynamic model of the structural component; S2, input material parameters and apply boundary conditions; S3, solving the control equations of the bond-type peridynamic model to obtain the displacement field, strain field and stress field of the structural component; S4, judging the tension and compression conditions of the bond. If the bond is in tension, the established bond-type peridynamic model is used to describe the relationship between the bond elongation and the bond force. If the bond is in compression, judging whether the bond is currently in a yield state; S5. If the bond is not in a yield state, the established bond-type peridynamic model is continued to be used to describe the relationship between bond elongation and bond force. If the bond is in a yield state, the PD-HJC constitutive model with rate-enhanced effect is used to describe the relationship between bond elongation and bond force. S6. judging whether the bond is broken according to the bond elongation and the bond breaking criterion; If a bond breaks, the stiffness value contributed by the corresponding bond is deleted from the stiffness matrix; S7, update the time step, and loop through steps S2 to S6 each time the time step is updated until the solution is completed.

2. The method for analyzing mechanical properties of high-hardness, quasi-brittle material structures according to claim 1, characterized in that: Based on peridynamics theory, the region Ω is considered to be a continuum consisting of a series of material points x. The spherical area with point x as the center and radius δ is called the neighborhood of point x. The motion state of x is affected by H δ The influence of all material points x' in (x), H δ The relative position vector ξ=x′-x between the points x and x′ in (x) is called the bond, and the relative displacement vector between x and x′ is expressed as η=u(x′)-u(x), where u(x′) and u(x) are the displacement vectors corresponding to the positions of points x′ and x, respectively. Therefore, the bond-type peridynamic model established in step S1 has the following governing equations: Where ρ is the density of the object, u represents the displacement, dH represents the integrated area, b is the body density, and f(x)<x'-x> represents the bond force acting directly from point x' to point x in bond-type peridynamics, f(x)<x'-x> The expression is as follows: f(x)<x′-x> =C[x](ξ)·η C[x](ξ)is the micromodulus tensor, which is expressed as follows: Where c[x](|ξ|) is a parameter related to material properties and is the micromodulus coefficient.

3. The method for analyzing mechanical properties of high-hardness, quasi-brittle material structures according to claim 2, characterized in that: In step S4, the volume strain at point x and point x' is calculated according to the displacement field to obtain the hydrostatic pressure related terms and the hydrostatic pressure independent terms, and then the yield strength f is obtained. Y Used to determine whether the key is currently in the yielded state.

4. The method for analyzing mechanical properties of high-hardness, quasi-brittle material structures according to claim 3 is characterized in that: The volume strain μ at point x and point x' is if μ<μ c , the hydrostatic pressure p is calculated as follows: p=K e m Where K e is the bulk modulus of elasticity, μ c is the elastic limit volume strain; If μ is satisfied c <μ<μ l , the hydrostatic pressure p is calculated as follows: Among them, p c represents the pore collapse pressure, K t is the bulk modulus in the transition stage, p max is the maximum pressure reached before the load is unloaded, μ max is the maximum volumetric strain reached before unloading, F is the compression coefficient, and K1 is the material constant; K t Calculate as follows: Among them, p l and μl are the hydrostatic pressure and volume strain when the pores completely collapse; F is calculated as follows: p max Calculate as follows: p max =p c +K t (m max -m c ) When the material is in the compaction stage, that is, p ≥ p l When , the hydrostatic pressure p is calculated as follows: Among them, K1, K2, and K3 are material constants. In order to make them equivalent to the relevant parameters of non-porous materials, the modified volume strain is used. ρ g is the density of the material without pores, ρ0 is the initial density of the material; After obtaining the hydrostatic pressure p, calculate the hydrostatic pressure related terms and hydrostatic pressure independent terms, and finally obtain the yield strength f Y .

5. The method for analyzing mechanical properties of high-hardness, quasi-brittle material structures according to claim 4, characterized in that: The hydrostatic pressure independent term f1 is calculated as follows: Among them, c 0 represents the micromodulus coefficient, ε r represents the elastic equivalent strain value, C is the strain rate coefficient, is the bond ξ elongation change rate, The calculation is as follows: The water inlet pressure related term f2 is calculated as follows: f2=β H f1 β H is the pressure-independent / dependent intensity ratio, calculated as follows: σ i (x) is the hydrostatic pressure related term of the yield stress at point x, σ i (x') is the hydrostatic pressure related term of the yield stress at point x', σ r is the hydrostatic pressure independent term of the yield stress, σ i (x) is calculated as follows: Among them, f c is the unconfined compressive strength, R is the normalized pressure hardening coefficient, and p(x) is the hydrostatic pressure at point x; The yield strength of the peridynamic bond is calculated as follows: f Y =(1-W ξ )f1+f2 W ξ is the accumulated plastic damage of the bond, calculated as follows: Among them, Δ|η p | is the plastic strain increment of the bond, and represents the equivalent crushing plastic strain and equivalent crushing volume strain under hydrostatic pressure; D1 and D2 are material parameters, T * =T / f c is the normalized maximum hydrostatic tensile stress, where T is the maximum hydrostatic tensile stress, p * =p / f c is the normalized hydrostatic pressure; If the bond force f(x)≤f Y , then the bond is not in a yielded state, if f(x)>f Y , the key is in yield state.

6. The method for analyzing mechanical properties of high-hardness, quasi-brittle material structures according to claim 5, characterized in that: In step S5, the PD-HJC constitutive model is used to describe the relationship between bond elongation and bond force, and the expression is as follows: f(x)<x'-x> =C[x](ξ)·η=c 0 (|ξ|)(ξ·η)ξ≈c 0 (|ξ|)e r |ξ| 3 。 7. The method for analyzing mechanical properties of high-hardness, quasi-brittle material structures according to claim 2, characterized in that: In step S6, the bond breaking criterion is: where ||·|| represents the length of the calculation vector, s is the elongation of the bond ξ, and s crit is the critical elongation of the bond, t represents the current time step, t' is any time step before the tth time step, s(t',ξ) represents the elongation of the bond ξ at the t'th time step, and μ(t,ξ) = 0 indicates that the bond ξ is broken.

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