A method, system, device and medium for predicting the mechanical behavior of unidirectional fiber reinforced composite materials

Abstract

The present application discloses a method, system, device, and medium for predicting the mechanical behavior of unidirectional fiber-reinforced composite materials, relating to the field of mechanical constitutive research of fiber-reinforced composite materials. The method comprises: preparing fiber composite specimens with different layup angles and conducting quasi-static compression and shear tests; determining the anisotropic elastic modulus rotation formula based on the basic equations of continuum mechanics and the mechanical properties of the specimens; using the method of solving operator properties in genetic elasticity theory to consider time-related effects, deriving an explicit operator for the genetic elastic modulus, introducing the relationship between the fractional-exponential function and the Heaviside unit step function, deriving a constitutive equation with a fractional-exponential operator, further determining the shear constitutive equation under the influence of strain rate, and predicting the shear stress-strain relationship. The constitutive equation constructed in the present application is applicable to all reinforced fiber composite materials and can accurately predict the shear stress-strain relationship of unidirectional fiber-reinforced composite materials.

Description

Technical Field

[0001] The present application relates to the field of mechanical constitutive research of fiber-reinforced composite materials, and in particular to a method, system, equipment and medium for predicting the mechanical behavior of unidirectional fiber-reinforced composite materials taking into account time effects. Background Art

[0002] Fiber-reinforced composites, as commonly used multifunctional materials, have the advantages of being lightweight, high-strength, corrosion-resistant, and highly designable. They have been widely used in important applications such as aerospace, transportation, and precision instruments. Therefore, accurately understanding the mechanical properties of fiber-reinforced composites can provide accurate and reasonable performance predictions for engineering applications in various situations, avoiding the huge losses caused by material failure. The mechanical constitutive model of fiber-reinforced composites is a mathematical model that describes the mechanical behavior of fiber-reinforced composites. It can be used to construct numerical calculation methods and develop finite element prediction models to meet practical needs such as engineering structure design and mechanical property optimization of fiber-reinforced composites.

[0003] However, due to factors such as preparation process, fiber orientation, interface strength, and material nonlinearity, the mechanical behavior of fiber-reinforced composites is not uniform, which leads to poor prediction results of previous constitutive equations and a complex system of accurate constitutive equations. For example, Chinese invention patent application number CN202010366881.4, titled "A method for testing the axial compression properties of carbon fiber composite materials and a constitutive model", and CN201911268610.9, titled "A method for calculating the compressive mechanics constitutive model of forged carbon fiber composite materials", proposed corresponding phenomenological composite material constitutive models, but the terms in their mathematical models have no specific physical meaning, which makes this method only applicable to one type of material and has poor prediction results, and has limitations and uncertainties.

[0004] Current constitutive equations are usually designed for specific material systems and are difficult to apply to fiber composites of different types or compositions. This limits their transformation and application in different application fields. A more general and accurate model is needed to solve this problem. Summary of the Invention

[0005] The purpose of this application is to provide a method, system, equipment and medium for predicting the mechanical behavior of unidirectional fiber reinforced composite materials. The constructed constitutive equation is applicable to all reinforced fiber composite materials and can accurately predict the shear stress-strain relationship of unidirectional fiber reinforced composite materials.

[0006] To achieve the above objectives, this application provides the following solutions:

[0007] In a first aspect, the present application provides a method for predicting the mechanical behavior of unidirectional fiber reinforced composite materials, comprising:

[0008] Preparation of fiber composite specimens with different ply angles;

[0009] Performing a quasi-static compression test and a quasi-static shear test on the fiber composite material specimen to determine the mechanical properties of the fiber composite material specimen;

[0010] Based on the basic equations of continuum mechanics and the mechanical properties of the fiber composite material specimen, a rotation formula of the anisotropic elastic modulus is determined;

[0011] Based on the anisotropic elastic modulus rotation formula, the method of solving operator properties in genetic elasticity theory is adopted to consider time-related effects and derive an explicit operator for the genetic elastic modulus;

[0012] Based on the explicit operator of the genetic elastic modulus, the relationship between the fractional-exponential function and the Heaviside unit step function is introduced, and the constitutive equation with the fractional-exponential operator is derived;

[0013] Determine the shear constitutive equation of the unidirectional fiber reinforced composite material under the influence of strain rate based on the anisotropic elastic modulus rotation formula and the constitutive equation with the fractional-exponential operator;

[0014] Based on the shear constitutive equation, the shear stress-strain relationship of unidirectional fiber reinforced composite materials is predicted.

[0015] Optionally, preparing fiber composite material specimens with different ply angles specifically includes: preparing fiber composite material specimens with ply angles of 90° and 45°.

[0016] Optionally, performing a quasi-static compression test and a quasi-static shear test on the fiber composite material specimen to determine the mechanical properties of the fiber composite material specimen specifically includes:

[0017] performing a quasi-static shear test on the fiber composite material specimen to obtain the elastic modulus of the fiber composite material specimen on different planes and obtain a phenomenological shear stress-strain curve;

[0018] performing a quasi-static compression test on the fiber composite material specimen to obtain the shear modulus of the fiber composite material specimen in different directions and obtain a phenomenological compression stress-strain curve;

[0019] The mechanical properties of the fiber composite material specimen are determined according to the shear stress-strain curve and the compressive stress-strain curve.

[0020] Optionally, based on the basic equations of continuum mechanics and the mechanical properties of the fiber composite material specimen, a rotation formula of the anisotropic elastic modulus is determined, specifically including:

[0021] Based on the basic equations of continuum mechanics, the material constitutive equation is determined:

[0022] σ θ =E θ ·ε θ ;

[0023] Among them, σ θ is the stress at the ply angle θ, ε θ is the strain at the ply angle θ, E θ is the elastic modulus at the ply angle θ;

[0024] Based on the material constitutive equation and the mechanical properties of the fiber composite material specimen, the anisotropic elastic modulus rotation formula is determined:

[0025]

[0026] Among them, E1 is the elastic modulus along the fiber direction, E2 is the elastic modulus perpendicular to the fiber direction, G 12 is the shear modulus of the fiber composite material, v 12 is the Poisson's ratio of the fiber composite material, m and n both represent the directions of the orthotropic principal axes, m is the cosine trigonometric function value of the ply angle, n is the sine trigonometric function value of the ply angle, m = cosθ, n = sinθ.

[0027] Optionally, based on the anisotropic elastic modulus rotation formula, a method for solving operator properties in genetic elasticity theory is adopted to consider time-related effects and derive an explicit operator of the genetic elastic modulus, specifically including:

[0028] The genetic modulus operator of the anisotropic elastic modulus rotation formula is determined using the following formula:

[0029]

[0030] in, is the genetic modulus at ply angle θ, is the instantaneous shear modulus of the fiber composite material, is the instantaneous elastic modulus perpendicular to the fiber direction, is the genetic operator in the horizontal direction, is the genetic operator of shear direction;

[0031] The expression for determining the elastic modulus according to the genetic modulus operator is:

[0032]

[0033] in, is a genetic operator, including and A θ and B θ All are intermediate amounts, k 12 is the coefficient in the shear direction, k2 is the material parameter;

[0034] The explicit operator of the genetic elastic modulus is determined according to the expression of the elastic modulus:

[0035]

[0036] in, is the initial modulus of the material in the transverse direction, k θ is the intermediate parameter, is the Rabotnov fractional-exponential operator.

[0037] Alternatively, the constitutive equation with the fractional-exponential operator is:

[0038]

[0039] Optionally, based on the anisotropic elastic modulus rotation formula and the constitutive equation with the fractional-exponential operator, determining the shear constitutive equation of the unidirectional fiber reinforced composite material under the influence of strain rate specifically includes:

[0040] Based on the anisotropic elastic modulus rotation formula and the constitutive equation with the fractional-exponential operator, the constitutive equation of the stress-strain curve under the influence of strain rate is determined:

[0041]

[0042] in, is the quasi-static strain rate, α is the singularity parameter;

[0043] Based on the constitutive equation of the stress-strain curve under the influence of strain rate, the shear constitutive equation of the unidirectional fiber reinforced composite material under the influence of strain rate is determined:

[0044]

[0045] Among them, τ 12 is the shear stress of unidirectional fiber reinforced composite materials, a and b are constants, H is the Heaviside equation, Ψ b (t) is the time-dependent coefficient equation, t b is the time coefficient, is the shear strain rate, Ψ1(t) is the time-dependent coefficient at the first time step, Ψ0(t * ) is the coefficient corresponding to one time step at the initial point, t is the time, t * is the time step.

[0046] In a second aspect, the present application provides a system for predicting the mechanical behavior of unidirectional fiber-reinforced composite materials, comprising:

[0047] Specimen preparation module, used to prepare fiber composite specimens with different layup angles;

[0048] A test module, used to perform a quasi-static compression test and a quasi-static shear test on the fiber composite material specimen to determine the mechanical properties of the fiber composite material specimen;

[0049] an elastic modulus rotation formula determination module, for determining an anisotropic elastic modulus rotation formula based on the basic equations of continuum mechanics and the mechanical properties of the fiber composite material specimen;

[0050] An explicit operator determination module is used to derive an explicit operator of the genetic elastic modulus based on the anisotropic elastic modulus rotation formula and by taking into account time-related effects using a method for solving operator properties in genetic elasticity theory;

[0051] An operator constitutive equation determination module is used to introduce the action relationship of the fractional-exponential function on the Heaviside unit step function based on the explicit operator of the genetic elastic modulus, and derive the constitutive equation with the fractional-exponential operator;

[0052] a shear constitutive equation determination module, configured to determine the shear constitutive equation of the unidirectional fiber reinforced composite material under the influence of strain rate based on the anisotropic elastic modulus rotation formula and the constitutive equation with the fractional-exponential operator;

[0053] The stress-strain relationship prediction module is used to predict the shear stress-strain relationship of the unidirectional fiber reinforced composite material based on the shear constitutive equation.

[0054] In a third aspect, the present application provides a computer device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-mentioned method for predicting the mechanical behavior of unidirectional fiber-reinforced composite materials.

[0055] In a fourth aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned method for predicting the mechanical behavior of unidirectional fiber-reinforced composite materials.

[0056] According to the specific embodiments provided in this application, this application has the following technical effects:

[0057] The present application provides a method, system, equipment and medium for predicting the mechanical behavior of unidirectional fiber-reinforced composite materials, which fully considers the influence of strain rate on the performance of fiber composite materials. By introducing genetic elasticity theory and considering the influence of shear and compression loads, a constitutive equation related to time effect is established, which reveals the generation mechanism of mechanical behavior from the perspective of physical essence. It can be applied to all reinforced fiber composite materials and has stronger universality. The shear constitutive equation proposed in this application can accurately describe the stress-strain relationship of unidirectional fiber-reinforced composite materials under different strain rate conditions, and thus accurately predict the shear stress-strain relationship of unidirectional fiber-reinforced composite materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0059] Figure 1 A schematic flow chart of a method for predicting the mechanical behavior of a unidirectional fiber-reinforced composite material provided in one embodiment of the present application;

[0060] Figure 2 A comparison diagram of the shear stress-shear strain relationship obtained by calculation and experiment in an embodiment of the present application;

[0061] Figure 3 A schematic diagram of the functional modules of a mechanical behavior prediction system for unidirectional fiber-reinforced composite materials provided in one embodiment of the present application. DETAILED DESCRIPTION

[0062] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0063] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0064] In an exemplary embodiment, Figure 1As shown, a method for predicting the mechanical behavior of a unidirectional fiber reinforced composite material is provided. The method is executed by a computer device, specifically, a computer device such as a terminal or a server, or a terminal and a server. In the embodiment of the present application, the method for predicting the mechanical behavior of a unidirectional fiber reinforced composite material includes the following steps 101 to 107. Among them:

[0065] Step 101: Prepare fiber composite material specimens with different layup angles.

[0066] In an exemplary embodiment, fiber composite material specimens with ply angles of 90° and 45° are prepared by cutting the fiber composite material specimens.

[0067] Step 102: Perform a quasi-static compression test and a quasi-static shear test on the fiber composite material specimen to determine the mechanical properties of the fiber composite material specimen.

[0068] In an exemplary embodiment, step 102 includes the following steps (21) to (23):

[0069] (21) A quasi-static shear test is performed on the fiber composite material specimen to obtain the elastic modulus of the fiber composite material specimen on different planes and obtain a phenomenological shear stress-strain curve.

[0070] (22) A quasi-static compression test is performed on the fiber composite material specimen to obtain the shear modulus of the fiber composite material specimen in different directions and obtain a phenomenological compression stress-strain curve.

[0071] (23) Determine the mechanical properties of the fiber composite material specimen based on the shear stress-strain curve and the compressive stress-strain curve.

[0072] Specifically, unidirectional fiber-reinforced composite specimens were prepared, with ply angles of 90° and 45° based on the loading direction, respectively. The elastic modulus of the material was determined through a quasi-static compression test, and the shear modulus of the material was obtained through a quasi-static shear test. The Poisson's ratio of the fiber composite material was calculated by combining the elastic modulus and shear modulus.

[0073] Step 103: Determine the rotation formula of the anisotropic elastic modulus based on the basic equations of continuum mechanics and the mechanical properties of the fiber composite material specimen.

[0074] In an exemplary embodiment, step 103 includes the following steps (31) to (32):

[0075] (31) Based on the basic equations of continuum mechanics, the material constitutive equation is determined:

[0076] σ θ =E θ·ε θ (1)

[0077] Among them, σ θ is the stress at the ply angle θ, ε θ is the strain at the ply angle θ, E θ is the elastic modulus at the ply angle θ.

[0078] Specifically, based on the basic constitutive equation of material mechanics, the material constitutive equation with a ply angle of θ can be obtained.

[0079] (32) Based on the material constitutive equation and the mechanical properties of the fiber composite material specimen, the anisotropic elastic modulus rotation formula is determined:

[0080]

[0081] Among them, E1 is the elastic modulus along the fiber direction, E2 is the elastic modulus perpendicular to the fiber direction, G 12 is the shear modulus of the fiber composite material, v 12 is the Poisson's ratio of the fiber composite material, m and n both represent the directions of the orthotropic principal axes, m is the cosine trigonometric function value of the ply angle, n is the sine trigonometric function value of the ply angle, m = cosθ, n = sinθ.

[0082] Step 104 : Based on the anisotropic elastic modulus rotation formula, the method of solving operator properties in the genetic elasticity theory is adopted to consider time-related effects and derive an explicit operator of the genetic elastic modulus.

[0083] In an exemplary embodiment, a constitutive equation that takes into account the material ply angle is derived based on the basic constitutive equation. That is, the genetic elasticity theory is introduced and the influence of time-related effects is considered to derive an explicit operator expression for the genetic elastic modulus. Step 104 includes the following steps (41) to (43):

[0084] (41) According to the Volterra principle, the operator of the elastic modulus is expressed as:

[0085]

[0086] Among them, E * is the genetic modulus, K * is the genetic operator, E 0 is the instantaneous elastic modulus. In the absence of time effect, E 0 The value of is determined by the constitutive relation under quasi-static load, and λ is a constant coefficient.

[0087] Assuming that the genetic elastic properties are affected by shear and compression loads perpendicular to the direction of the reinforcement fibers, and the influence of the time effect in the direction of the reinforcement fibers can be considered to be small enough to be negligible, the genetic modulus operator of formula (1) can be written as:

[0088]

[0089] in, is the genetic modulus at ply angle θ, is the instantaneous shear modulus of the fiber composite material, is the instantaneous elastic modulus perpendicular to the fiber direction, is the genetic operator in the horizontal direction, is the genetic operator for the shear direction.

[0090] (42) Select the operator with Abel in formula (4) as the genetic operator It determines the time-dependent properties of the material, so the genetic operator can be expressed as:

[0091]

[0092] Where α is the singularity parameter, -1<α<0, f refers to the possible equation, Г refers to the Gamma equation, and t is time.

[0093] Therefore, the expression for the elastic modulus is:

[0094]

[0095] in, is a genetic operator, including and That is, the genetic modulus operator, A θ and B θ All are intermediate amounts, k 12 is the coefficient in the shear direction, and k2 is the material parameter.

[0096] Since formula (6) belongs to the category of analyzable operations, it can be expressed as:

[0097]

[0098] in, is the Rabotnov fractional-exponential operator used to solve the genetic operator k θ is the intermediate parameter,

[0099] (43) From formula (7), we can obtain the explicit operator of the genetic elastic modulus:

[0100]

[0101] in, is the initial modulus (instantaneous modulus) of the material in the transverse direction, Formula (18) represents the explicit operator expression of the genetic elastic modulus.

[0102] Step 105 : Based on the explicit operator of the genetic elastic modulus, the action relationship of the fractional-exponential function on the Heaviside unit step function is introduced to derive the constitutive equation with the fractional-exponential operator.

[0103] In an exemplary embodiment, the effect of the fractional-exponential function on the Heaviside unit step function is introduced:

[0104]

[0105] Where β > 0, Γ[1+(1+α)(1+n')] is the Gamma equation, which represents the action of the fractional-exponential function on the Heaviside unit step function. n' is the independent variable in the summation operation and is used as a superscript to denote the exponent.

[0106] The core of the fractional-exponential operator is:

[0107]

[0108] When the material layup angle is 90°, the following relationship can be obtained by combining formula (4):

[0109]

[0110] in, is the instantaneous elastic modulus perpendicular to the fiber direction, which is expressed here as the initial modulus of the material in the transverse direction.

[0111] Combining formula (7) and formula (11), we can get the following relationship:

[0112]

[0113] Then the constitutive equation with the fractional-exponential operator is:

[0114] Step 106 : determining a shear constitutive equation of the unidirectional fiber reinforced composite material under the influence of strain rate based on the anisotropic elastic modulus rotation formula and the constitutive equation with the fractional-exponential operator.

[0115] In an exemplary embodiment, step 106 includes the following steps (61) to (63):

[0116] (61) Based on the anisotropic elastic modulus rotation formula and the constitutive equation with the fractional-exponential operator, the constitutive equation of the stress-strain curve under the influence of strain rate is determined.

[0117] Combining formula (8), formula (11) and formula (12), we can obtain the constitutive equation of the stress-strain curve under the influence of strain rate:

[0118]

[0119] in, is the quasi-static strain rate.

[0120] In order to determine the remaining parameters of the constitutive equation and k 12 , characterizing the rheological properties of unidirectional composite materials, the constitutive equation when θ = 90° can be written as:

[0121]

[0122] The constitutive equation when θ = 45° can be written as:

[0123]

[0124] (62) Based on the constitutive equation of the stress-strain curve under the influence of strain rate, the shear constitutive equation of unidirectional fiber reinforced composite materials under the influence of strain rate is determined.

[0125] In order to characterize the rheological properties of unidirectional composite materials, consider the shear condition and assume The instantaneous deformation curve expression is:

[0126]

[0127] Among them, τ 12 is the shear stress of the material.

[0128] Inverse formula (16) to obtain:

[0129]

[0130] The Heaviside step-by-step equation is used to represent the curve:

[0131]

[0132] Among them, H(γ 12 -γ * ) is the Heaviside equation, γ * is the critical value of shear strain, after which nonlinear deformation begins; a and b are constants.

[0133] make The nonlinear strain can be written as:

[0134]

[0135] It can be considered that quasi-static stress is just a special case of dynamic stress at a fixed strain rate. Using formula (19), the shear constitutive equation of unidirectional fiber reinforced composite materials under the influence of strain rate is obtained:

[0136]

[0137] Among them, v 12 is the shear stress of unidirectional fiber reinforced composite materials, a and b are constants, H is the Heaviside equation, Ψ b (t) is the time-dependent coefficient equation, t b is the time coefficient, is the shear strain rate, Ψ1(t) is the time-dependent coefficient at the first time step, Ψ0(t * ) is the coefficient corresponding to one time step at the initial point, t is the time, t * The time step is,

[0138] Step 107 : predicting the shear stress-strain relationship of the unidirectional fiber reinforced composite material based on the shear constitutive equation.

[0139] In an exemplary embodiment, based on the shear constitutive equation and the material parameters obtained from the experiment, the stress-strain analysis results of the unidirectional fiber reinforced composite material are obtained, and the shear stress-strain relationship is accurately predicted, thereby more accurately predicting the mechanical behavior of the material.

[0140] This application fully considers the influence of strain rate on material properties. By introducing the theory of genetic elasticity and considering the influence of shear and compression loads, a constitutive equation related to time effect is established. This reveals the generation mechanism of mechanical behavior from the perspective of physical essence. It can be applied to all reinforced fiber composite materials and has stronger universality. The shear constitutive equation proposed in this application can accurately describe the stress-strain relationship of unidirectional fiber reinforced composite materials under different strain rate conditions, providing an effective theoretical basis for practical engineering applications and providing a reference for the theoretical prediction of the stress-strain curve relationship of unidirectional fiber composite materials and multilayer composite materials under the influence of strain rate.

[0141] This application also provides a specific embodiment: First, prepare AS4 / 3501-6 test samples with ply angles of 90° and 45°, where the single-layer unidirectional material is composed of AS4 fiber and 3501-6 epoxy resin. Through quasi-static compression test, the elastic modulus is measured to be Through the quasi-static shear test, the shear modulus is Combining the elastic modulus and shear modulus, the Poisson's ratio v of the fiber composite material can be obtained 12 =0.65.

[0142] Fitted material parameters: k2 = 0.2018s -(1+α) ; k 45 =0.2564s -(1+α) ;k 12 =0.3015s -(1+α) ;α=-0.9;γ * =0.75%; a=3; b=0.8.

[0143] Substituting the material parameters into formulas (17)-(18), the shear stress-strain relationship is obtained as follows: Figure 2 As shown in the figure, the predicted results of the constitutive equation are almost consistent with the experimental data, and can describe the shear mechanical properties of the composite material. This proves that the constitutive equation and prediction method established in this application can well predict the mechanical behavior of the composite material.

[0144] Based on the same inventive concept, the present application also provides a unidirectional fiber-reinforced composite material mechanical behavior prediction system for implementing the aforementioned method for predicting the mechanical behavior of unidirectional fiber-reinforced composite materials. The solution provided by this system is similar to the solution described in the aforementioned method. Therefore, the specific limitations of one or more of the following embodiments of the unidirectional fiber-reinforced composite material mechanical behavior prediction system can be found in the above-mentioned limitations of the method for predicting the mechanical behavior of unidirectional fiber-reinforced composite materials, and will not be repeated here.

[0145] In an exemplary embodiment, Figure 3 As shown, a unidirectional fiber reinforced composite material mechanical behavior prediction system is provided, including: a specimen preparation module 301, a test module 302, an elastic modulus rotation formula determination module 303, an explicit operator determination module 304, an operator constitutive equation determination module 305, a shear constitutive equation determination module 306 and a stress-strain relationship prediction module 307.

[0146] The specimen preparation module 301 is used to prepare fiber composite material specimens with different layup angles.

[0147] The test module 302 is used to perform a quasi-static compression test and a quasi-static shear test on the fiber composite material specimen to determine the mechanical properties of the fiber composite material specimen.

[0148] The elastic modulus rotation formula determination module 303 is used to determine the anisotropic elastic modulus rotation formula based on the basic equations of continuum mechanics and the mechanical properties of the fiber composite material specimen.

[0149] The explicit operator determination module 304 is used to derive the explicit operator of the genetic elastic modulus based on the anisotropic elastic modulus rotation formula and by taking into account the time-related effect by adopting the method of solving operator properties in the genetic elasticity theory.

[0150] The operator constitutive equation determination module 305 is used to introduce the action relationship of the fractional-exponential function on the Heaviside unit step function based on the explicit operator of the genetic elastic modulus, and derive the constitutive equation with the fractional-exponential operator.

[0151] The shear constitutive equation determination module 306 is used to determine the shear constitutive equation of the unidirectional fiber reinforced composite material under the influence of strain rate based on the anisotropic elastic modulus rotation formula and the constitutive equation with the fractional-exponential operator.

[0152] The stress-strain relationship prediction module 307 is used to predict the shear stress-strain relationship of the unidirectional fiber reinforced composite material based on the shear constitutive equation.

[0153] In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps in the above method embodiments when executing the computer program.

[0154] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0155] In an exemplary embodiment, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0156] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0157] In this application, all actions to obtain signals, information or data are carried out in compliance with the relevant data protection laws and policies of the country where they are located and with the authorization given by the owner of the corresponding device.

[0158] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, database or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0159] The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may include, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units based on quantum computing, and the like.

[0160] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0161] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A method for predicting the mechanical behavior of unidirectional fiber reinforced composite materials, characterized in that: The method for predicting the mechanical behavior of unidirectional fiber reinforced composite materials includes: Preparation of fiber composite specimens with different ply angles; Performing a quasi-static compression test and a quasi-static shear test on the fiber composite material specimen to determine the mechanical properties of the fiber composite material specimen; Based on the basic equations of continuum mechanics and the mechanical properties of the fiber composite material specimen, a rotation formula of the anisotropic elastic modulus is determined; Based on the anisotropic elastic modulus rotation formula, the method of solving operator properties in genetic elasticity theory is adopted to consider time-related effects and derive an explicit operator for the genetic elastic modulus; Based on the explicit operator of the genetic elastic modulus, the relationship between the fractional-exponential function and the Heaviside unit step function is introduced, and the constitutive equation with the fractional-exponential operator is derived; Based on the anisotropic elastic modulus rotation formula and the constitutive equation with the fractional-exponential operator, the shear constitutive equation of the unidirectional fiber reinforced composite material under the influence of strain rate is determined, specifically including: Based on the anisotropic elastic modulus rotation formula and the constitutive equation with the fractional-exponential operator, the constitutive equation of the stress-strain curve under the influence of strain rate is determined: in, is the quasi-static strain rate, α is the singularity parameter, σ θ is the stress at the ply angle θ, is the initial modulus of the material in the transverse direction, k θ is the intermediate parameter, ε θ is the strain at the ply angle θ; Based on the constitutive equation of the stress-strain curve under the influence of strain rate, the shear constitutive equation of the unidirectional fiber reinforced composite material under the influence of strain rate is determined: Among them, τ 12 is the shear stress of unidirectional fiber reinforced composite materials, is the instantaneous shear modulus of the fiber composite material, a and b are constants, H is the Heaviside equation, k 12 is the coefficient in the shear direction, Ψ b (t) is the time-dependent coefficient equation, t b is the time coefficient, is the shear strain rate, Ψ1(t) is the time-dependent coefficient at the first time step, Ψ0(t * ) is the coefficient corresponding to one time step at the initial point, t is the time, t * is the time step; Based on the shear constitutive equation, the shear stress-strain relationship of unidirectional fiber reinforced composite materials is predicted.

2. The method for predicting the mechanical behavior of unidirectional fiber reinforced composite materials according to claim 1, characterized in that: Preparation of fiber composite test pieces with different ply angles, specifically including: Fiber composite specimens with ply angles of 90° and 45° were prepared.

3. The method for predicting the mechanical behavior of unidirectional fiber reinforced composite materials according to claim 1, characterized in that: The fiber composite material specimen is subjected to a quasi-static compression test and a quasi-static shear test to determine the mechanical properties of the fiber composite material specimen, specifically including: performing a quasi-static shear test on the fiber composite material specimen to obtain the elastic modulus of the fiber composite material specimen on different planes and obtain a phenomenological shear stress-strain curve; performing a quasi-static compression test on the fiber composite material specimen to obtain the shear modulus of the fiber composite material specimen in different directions and obtain a phenomenological compression stress-strain curve; The mechanical properties of the fiber composite material specimen are determined according to the shear stress-strain curve and the compressive stress-strain curve.

4. The method for predicting the mechanical behavior of unidirectional fiber reinforced composite materials according to claim 1, characterized in that: Based on the basic equations of continuum mechanics and the mechanical properties of the fiber composite material specimen, the anisotropic elastic modulus rotation formula is determined, specifically including: Based on the basic equations of continuum mechanics, the material constitutive equation is determined: s θ =E θ ·e θ ; Among them, E θ is the elastic modulus at the ply angle θ; Based on the material constitutive equation and the mechanical properties of the fiber composite material specimen, the anisotropic elastic modulus rotation formula is determined: Among them, E1 is the elastic modulus along the fiber direction, E2 is the elastic modulus perpendicular to the fiber direction, G 12 is the shear modulus of the fiber composite material, v 12 is the Poisson's ratio of the fiber composite material, m and n both represent the directions of the orthotropic principal axes, m is the cosine trigonometric function value of the ply angle, and n is the sine trigonometric function value of the ply angle, m = cosθ, n = sinθ.

5. The method for predicting the mechanical behavior of unidirectional fiber reinforced composite materials according to claim 4, characterized in that: Based on the anisotropic elastic modulus rotation formula, the method of solving operator properties in genetic elasticity theory is adopted to consider time-related effects and derive the explicit operator of the genetic elastic modulus, which specifically includes: The genetic modulus operator of the anisotropic elastic modulus rotation formula is determined using the following formula: in, is the genetic modulus at ply angle θ, is the instantaneous elastic modulus perpendicular to the fiber direction, is the genetic operator in the horizontal direction, is the genetic operator of shear direction; The expression for determining the elastic modulus according to the genetic modulus operator is: in, is a genetic operator, including and A θ and B θ All are intermediate amounts, k2 is the material parameter; The explicit operator of the genetic elastic modulus is determined according to the expression of the elastic modulus: in, is the Rabotnov fractional-exponential operator.

6. The method for predicting the mechanical behavior of unidirectional fiber reinforced composite materials according to claim 5, characterized in that: The constitutive equation with the fractional-exponential operator is:

7. A system for predicting the mechanical behavior of unidirectional fiber reinforced composite materials, applied to the method for predicting the mechanical behavior of unidirectional fiber reinforced composite materials according to any one of claims 1 to 6, characterized in that: The unidirectional fiber reinforced composite material mechanical behavior prediction system includes: Specimen preparation module, used to prepare fiber composite specimens with different layup angles; a test module, configured to perform a quasi-static compression test and a quasi-static shear test on the fiber composite material specimen to determine the mechanical properties of the fiber composite material specimen; an elastic modulus rotation formula determination module, for determining an anisotropic elastic modulus rotation formula based on the basic equations of continuum mechanics and the mechanical properties of the fiber composite material specimen; An explicit operator determination module is used to derive an explicit operator of the genetic elastic modulus based on the anisotropic elastic modulus rotation formula and by taking into account time-related effects using a method for solving operator properties in genetic elasticity theory; An operator constitutive equation determination module is used to introduce the action relationship of the fractional-exponential function on the Heaviside unit step function based on the explicit operator of the genetic elastic modulus, and derive the constitutive equation with the fractional-exponential operator; a shear constitutive equation determination module, configured to determine the shear constitutive equation of the unidirectional fiber reinforced composite material under the influence of strain rate based on the anisotropic elastic modulus rotation formula and the constitutive equation with the fractional-exponential operator; The stress-strain relationship prediction module is used to predict the shear stress-strain relationship of the unidirectional fiber reinforced composite material based on the shear constitutive equation.

8. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method for predicting the mechanical behavior of a unidirectional fiber-reinforced composite material according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for predicting the mechanical behavior of a unidirectional fiber reinforced composite material according to any one of claims 1 to 6 is implemented.

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