A method for preparing an nc-ecc functionally graded material based on strain compatibility

Abstract

The application relates to an NC-ECC function gradient material design method based on strain coordination, which comprises the following steps: regarding the NC-ECC function gradient material as being composed of multiple layers of NC-ECC composite materials with different ECC volume fractions, the elastic modulus of the NC-ECC composite material presents nonlinear change in the form of an exponential function E ( v ) with the increase of the ECC volume fraction; listing an elastic modulus linear function E ( z ) along the thickness direction, so that the interlayer strain of the NC-ECC function gradient material tends to be coordinated when the NC-ECC function gradient material is stressed; carrying out layered design on the NC-ECC function gradient material, obtaining E ( k , n ) by substituting the position coordinates into the elastic modulus linear function, calculating the volume fractions corresponding to different gradient sublayers by equating the exponential function E ( v ); and carrying out one-dimensional theoretical description on the NC-ECC function gradient material, obtaining the value of the shape coefficient N by equating the volume fraction design values obtained by each layer and the one-dimensional description theory. The NC-ECC function gradient material designed by the method has good mechanical properties, crack control ability and low cost.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of civil engineering materials, and particularly relates to a design method of NC-ECC functional gradient material based on strain coordination. BACKGROUND

[0002] Normal concrete (NC) is widely used in various infrastructure constructions due to its high compressive strength, rich raw materials, low price, simple process and other advantages. However, it has the disadvantages of large brittleness, poor toughness, small tensile strength and difficult control of crack width after cracking, and is accompanied by a series of problems such as carbonation reaction, alkali-aggregate reaction and corrosion damage to the component under the action of the harsh natural environment, resulting in huge detection and maintenance costs. Therefore, it is imperative to develop a new material with crack control ability.

[0003] In order to solve such problems, engineered cementitious composites (ECC) emerge as the times require. The fiber volume fraction of the cement-based material is not greater than 2%, and the cement-based material has good mechanical properties and can produce multiple cracking effect when subjected to tension. However, the price of ECC is much higher than that of concrete, and the use of ECC for the entire component is too low in cost performance. Therefore, the concept of functional gradient is introduced into the cement-based material, and NC-ECC functional gradient material is obtained by combining NC and ECC, so as to fully utilize the material while reducing the cost.

[0004] Functional gradient material is a concept formed by human beings through inspiration from the gradient structure (bamboo stem, tooth, bone, etc.) in nature. Compared with homogeneous materials and simple composite materials, the superiority of functional gradient material mainly lies in the structure composition. The principle is to gradually change the structure of two or more materials with different properties. The composition of the composite material changes uniformly, there is no obvious interface in the interior, and the performance of the material changes slowly with the change of the composition and structure of the material, so as to show the effect of gradient function. In the field of aerospace, the concept of functional gradient is introduced to combine metal and ceramic materials, so that the surface of the material has the heat insulation performance of ceramic, the interior has the strength and toughness of metal, and the material can achieve thermal stress relaxation under the action of large temperature difference.

[0005] However, the application of the concept of functional gradient in cement-based materials is still rare, and the related experimental research is not mature enough, lacking design principles and theoretical guidance. Many of them are only designed by simply changing the volume percentage of the composition from top to bottom (or from inside to outside). SUMMARY

[0006] The application aims to provide a strain coordination-based NC-ECC functional gradient material design method, which has good mechanical properties and crack control ability and low cost.

[0007] To achieve the above-mentioned purpose, the technical scheme adopted by the application is as follows: a strain coordination-based NC-ECC functional gradient material design method, comprising the following steps:

[0008] Step S1: regarding the NC-ECC functional gradient material as being composed of multiple layers of NC-ECC composite materials with different ECC volume fractions, the elastic modulus of the NC-ECC composite material presents nonlinear change in the form of an exponential function E(v) with the increase of the ECC volume fraction;

[0009] Step S2: taking the thickness direction z as the independent variable, listing the function E(z) of the linear change of the elastic modulus along the thickness direction, so that the interlayer strain of the NC-ECC functional gradient material tends to be coordinated when the material is stressed;

[0010] Step S3: performing layered design on the NC-ECC functional gradient material, taking the barycentric coordinates of each layer to represent the position of each layer, substituting the position coordinates into the linear function of the elastic modulus to obtain E(k,n), and calculating the volume fraction corresponding to different gradient sublayers by equating the exponential function E(v);

[0011] Step S4: performing one-dimensional theoretical description on the NC-ECC functional gradient material, wherein the shape coefficient N is used to describe the gradual change of the volume fraction of the NC-ECC functional gradient material from one position to another, and the value of the shape coefficient N is obtained by equating the volume fraction design value obtained by each layer with the one-dimensional description theory.

[0012] Further, the NC-ECC composite material is a mixture of NC and ECC with different volume fractions, the volume fraction of NC is V N , the volume fraction of ECC is V E , and V N +V E =1.

[0013] Further, the elastic modulus model of the NC-ECC composite material is a function E(v) of the volume fraction of ECC, wherein the exponential function is used to correct and fit the elastic modulus model of the NC-ECC composite material;

[0014] E(v) = y0 + A1 exp(-v / t1) + A2 exp(-v / t2) (1)

[0015] Further, the position of each layer is represented by the z-axis barycentric coordinates of the layer, and the relationship between the layering and the position of each layer is integrated to obtain the regular formula between the layering and the position of each layer of the NC-ECC functionally graded material:

[0016]

[0017] wherein k is the kth layer of the functionally graded specimen after layering, n is the number of layers of the functionally graded material, n>2, z represents the z-axis coordinate position of the kth layer, and d-dm represents the thickness of the gradient sublayer.

[0018] Further, the elastic modulus between layers presents linear variation, so as to ensure that the strain generated by each gradient sublayer of the material during the stress process will not have a jump mutation, avoid stress concentration, and make the interlayer strain coordinated with each other. The linear variation function of the elastic modulus is as follows:

[0019]

[0020] The z of formula (2) is substituted into E(z) to obtain:

[0021]

[0022] Further, in order to obtain the volume fraction that each gradient sublayer of the NC-ECC functionally graded material should reach, formula (1) and formula (4) are equal, and then:

[0023] E(v)=E(k,n) (5)

[0024]

[0025] wherein n is the number of layers, k represents the kth layer of the functionally graded specimen after layering, y0, A1, A2, t1, and t2 are fitting parameters, and are all known quantities.

[0026] Further, the one-dimensional theory of the NC-ECC functionally graded material is described by using the distribution coefficient N, and the gradual change of the ECC volume fraction from one position to another position is explained:

[0027]

[0028] wherein N is the distribution coefficient for describing the volume fraction of each layer of the functionally graded specimen; N=1 represents that the volume fraction of each layer is linearly changed; N>1 and N<1 both represent that the volume fraction of each layer is nonlinearly changed; d and dm divide the functionally graded material into different regions, (-dm,dm) is a gradually changed functionally graded layer, (-dm,-d) and (dm,d) respectively represent the NC and ECC base phase material layers.

[0029] Further, the one-dimensional theoretical description formula, i.e., formula (7) is equal to the volume fraction function, i.e., formula (6), is substituted into the known parameters, and the value of the distribution coefficient N is solved by logarithmic solution:

[0030]

[0031] Further, the distribution coefficient of the one-dimensional theoretical description is different when different materials are used for functional gradient.

[0032] Compared with the prior art, the present application has the following beneficial effects: a NC-ECC functional gradient material design method based on strain coordination is provided, which, in view of the problems of expensive ECC material cost and the interface damage problem easily occurring in ordinary laminated materials, takes NC and ECC as the basic phase, takes the linear change of the elastic modulus as the design principle, and performs layered design on the NC and ECC through the functional gradient method, so that the interface weak area can be eliminated and the interlayer strain can be coordinated while the NC-ECC composite material with different volume fractions is layered and combined, the NC-ECC functional gradient material still has the high ductility and crack control ability of ECC, has low cost, makes full use of the material, avoids resource waste, saves a large amount of cost, has a wide application prospect in engineering construction, and the like. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 is a method implementation flowchart of the embodiment of the present application;

[0034] Figure 2 is a functional gradient test piece and shape parameter in the embodiment of the present application;

[0035] Figure 3 is a relationship diagram between the thickness and the elastic modulus of the functional gradient test piece in the embodiment of the present application;

[0036] Figure 4 is a linear function of the elastic modulus about the z-axis coordinate position in the embodiment of the present application;

[0037] Figure 5 is a three-point bending load-displacement curve diagram in the embodiment of the present application;

[0038] Figure 6 is a compression load-displacement curve diagram in the embodiment of the present application. DETAILED DESCRIPTION

[0039] The present application will be further described below in combination with the drawings and embodiments.

[0040] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0041] It is to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, steps, operations, elements, components, and / or groups thereof, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof.

[0042] As shown in Figure 1 The present embodiment provides a design method of NC-ECC functionally graded material based on strain coordination, comprising:

[0043] Step S1, the NC-ECC functionally graded material is regarded as being composed of multiple layers of NC-ECC composite materials with different ECC volume fractions, the elastic modulus of the NC-ECC composite material presents nonlinear change in the form of exponential function E(v) with the increase of the ECC volume fraction, and the exponential function E(v) is used to describe the nonlinear change.

[0044] Step S2, taking the elastic modulus E(v) of the NC-ECC composite material as the starting point and taking the thickness direction z as the independent variable, the function E(z) of the linear change of the elastic modulus along the thickness direction is listed, so that the interlayer strain of the NC-ECC functionally graded material tends to be coordinated when stressed.

[0045] Step S3, the NC-ECC functionally graded material is designed in layers, the volume fraction of each layer is designed, the position of each layer is represented by the barycentric coordinates of each layer, the position coordinates are substituted into the linear function of the elastic modulus to obtain E(k, n), and the volume fractions corresponding to different gradient sub-layers are calculated by equating the exponential function E(v).

[0046] Step S4, the NC-ECC functionally graded material is described in one dimension, the shape coefficient N is used to describe the gradual change of the volume fraction of the NC-ECC functionally graded material from one position to another, the volume fraction design value obtained by each layer is equated with the one-dimensional description theory, and the value of the shape coefficient N is obtained.

[0047] Wherein, the NC-ECC composite material is a mixture of NC and ECC with different volume fractions, the volume fraction of NC is V N , the volume fraction of ECC is V E , and V N +VE =1.

[0048] The elastic modulus model of NC-ECC composites is a function of the compressive elastic modulus E(v) with respect to the volume fraction of ECC. It is typically fitted using an exponential function.

[0049] E(v)=y0+A1 exp(-v / t1)+A2 exp(-v / t2) (1)

[0050] Where y0, A1, A2, t1, and t2 are fitting parameters, which can be obtained through Origin nonlinear fitting, v is the ECC volume fraction, and E is the elastic modulus.

[0051] Treating functionally graded layers as composed of multiple sublayers, and using the shape parameter N to explain the functionally graded system composed of different components, a one-dimensional theoretical description of NC-ECC functionally graded materials is provided (Equation 3). This description can explain the gradual change in their volume fraction from one location to another. Figure 2 As shown.

[0052] V N (z)+V E (z)=1,|z|≤d (2)

[0053]

[0054] Where z is the coordinate of the functionally graded specimen along the thickness direction; N is the distribution coefficient describing the volume fraction of each layer of the functionally graded specimen; N=1 indicates that the volume fraction of each layer changes linearly; N>1 and N<1 both indicate that the volume fraction of each layer changes non-linearly; d and dm divide the functionally graded material into different regions, (-dm,dm) is a gradually changing functionally graded layer, and (-dm,-d) and (dm,d) represent the NC and ECC base phase material layers, respectively.

[0055] V E (z)=1,V N (z)=0, -d≤z≤-d m (4)

[0056] V E (z)=0,V N (z)=1,d m ≤z≤d (5)

[0057] Using the z-axis centroid coordinate of each layer to represent its position, and combining the relationship between layering and the position of each layer, the following pattern can be obtained:

[0058]

[0059] where k is the kth layer of the functionally graded specimen, n is the number of layers of the functionally graded material (n > 2), z k z represents the z-axis coordinate position of the kth layer. d-dm represents the thickness of the gradient sublayer.

[0060] For the functionally graded cement-based material, the main research is its performance under static load, so the elastic modulus is the starting point of the design of functionally graded material. When the functionally graded cement-based material is prepared by the layered pouring method, by designing the functionally graded layer, the static elastic modulus is ensured to change linearly between the two base layers, so that the functionally graded cement-based material specimen does not have a sudden change in elastic modulus at a certain position, and the purpose of interlayer strain coordination is achieved, so that the interface damage does not occur.

[0061] Figure 3 The horizontal axis is the thickness of the functionally graded specimen, and the vertical axis is the elastic modulus. (a) is a simple two-phase laminated specimen. Because the elastic modulus of the two phases is quite different, and the elastic modulus changes sharply at the interface position, it is easy to cause interface damage under static load. (b) is a functionally graded specimen. The transition from base phase 1 to base phase 2 uses a functionally graded layer, so that the elastic modulus changes linearly and gradually, and there is no obvious interface weak zone inside, and the material performance is fully utilized.

[0062] Therefore, the design principle of NC-ECC functionally graded material is that the elastic modulus is a linear function of the z-axis coordinate position, as shown in Figure 4 , which can be represented by the following function:

[0063]

[0064] Substituting equation (6) into equation (7) can obtain the relationship between the elastic modulus and the position of each gradient sublayer.

[0065]

[0066] where E2 is the elastic modulus of NC, E1 is the elastic modulus of ECC, n is the number of layers, and k represents the kth layer of the functionally graded specimen after layering.

[0067] In order to obtain the volume fraction that each gradient sublayer of NC-ECC functionally graded material should be designed to achieve, equation (1) and equation (8) are equal, then:

[0068] E(v) = E(k, n) (9)

[0069] By calculating the inverse function of this equation, the design value v(k, n) of the volume fraction of each gradient sublayer ECC can be obtained:

[0070]

[0071] Wherein, n is the number of layers, k represents the kth layer after the functional gradient specimen is layered, y0, A1, A2, t1, t2 are fitting parameters, all are known quantities, and E(k, n) can be obtained by substituting k and n, and then v(k, n) can be obtained.

[0072] In order to obtain the distribution coefficient N of the one-dimensional theoretical description of the NC-ECC functional gradient material, the one-dimensional theoretical description formula (formula (3)) and the inverse function (formula (10)) are taken as equal, as shown in the following formula (11), and the known parameters are substituted, and the value of the distribution coefficient N can be obtained by logarithmic solution (formula (14)). Different materials are used for functional gradient, and the distribution coefficient of the one-dimensional theoretical description is different.

[0073]

[0074] Taking the 5-layer NC-ECC functional gradient material as an example, according to the content, the NC-ECC functional gradient material is prepared, and by combining the above-mentioned design principle based on the linear change of elastic modulus, the volume fraction required by each layer of the NC-ECC functional gradient material can be known by calculating the following functions.

[0075]

[0076] It should be noted that one difference between functional gradient materials and ordinary laminated materials is the number of layers, and ordinary laminated materials usually have only two layers, while the number of layers of functional gradient materials is n≥3. NC and ECC are base phases, and the intermediate is a transition layer of NC-ECC composite material with different volume fractions. By substituting the number of layers n and the specified layer k, the specific ECC volume fraction of each layer can be obtained by calculation. Table 1 shows the design value of the volume fraction of each layer of the 5-layer NC-ECC functional gradient material.

[0077] Table 1: Design value of volume fraction of each layer

[0078]

[0079] Wherein, n is the number of layers, k represents the kth layer after the functional gradient specimen is layered.

[0080] It should be noted that theoretically, the more the number of gradient layers is subdivided, the smoother the performance gradient is, and the better the functional gradient effect is. However, the NC-ECC functional gradient material studied in the present application is essentially a fiber cement-based material, and considering the influence of the thickness of each layer, it cannot be subdivided into too many layers like metal ceramics, so the 5-layer NC-ECC functional gradient material is taken as an example for calculation.

[0081] Meanwhile, the number of layers n = 5, the corresponding position coordinates z of each layer and the corresponding ECC volume fraction v are known, and the distribution coefficient N of the NC-ECC functional gradient material can be obtained by substituting the known parameters into the following formula and calculating the pair of logarithmic functions, that is, N = -0.28.

[0082]

[0083] Therefore, the complete one-dimensional theoretical description of the NC-ECC functional gradient material is as follows:

[0084]

[0085] Example 1

[0086] In order to verify the effectiveness of the above functional gradient design theory based on strain coordination, the volume fraction of each sub-layer is calculated according to the theoretical calculation, and a five-layer NC-ECC functional gradient material is prepared. The three-point bending test is carried out on the NC-ECC functional gradient prism specimen with a size of 100mmx100mmx400mm. The same size of ordinary laminated material and ECC material are used as comparative examples to compare with the present application. From the load-displacement curve and the ductility, the superiority of the NC-ECC functional gradient material design method based on strain coordination is demonstrated.

[0087] From Figure 5 It can be seen from the above table that the bending resistance of the ordinary laminated specimen is 30.08KN, while the bending resistance of the specimen with functional gradient layered design is improved to 37.12KN, and has a clear yield stage as the ECC material.

[0088] Table 2 Ductility parameters

[0089]

[0090] Table 2 lists the bending ductility parameters of Example 1 and Comparative Examples 1 and 2. By comparing the overall volume of the specimen as 1, it can be found that the fiber volume fraction of the present example is 1.18%, which is almost half of Comparative Example 1 (ECC material), and has little difference with Comparative Example 2 (ordinary laminated material).

[0091] The displacement ductility coefficient of the ordinary laminated material is 1.571, which is lower than that of the ECC material. When the gradient layered design is adopted, the ductility will be greatly improved. The displacement ductility coefficient of the material designed according to the functional gradient design theory is 1.992, which is increased by 26.79% compared with the ordinary laminated material. This also proves that the material designed based on the functional gradient design theory of elastic modulus has better bending ductility.

[0092] Example 2

[0093] Similarly, five-layer NC-ECC functionally graded material prism specimens with dimensions of 100mm×100mm×300mm were prepared and subjected to prism compressive strength tests. Ordinary laminated materials and ECC materials of the same size were used as Comparative Examples 1 and 2 for comparison with Example 2. The superiority of the strain-coordinated NC-ECC functionally graded material design method was demonstrated from the perspective of load-displacement curves and ductility. Table 3 lists the comparison of compressive ductility parameters between Example 2 and Comparative Examples 1 and 2.

[0094] Table 3. Pressure Performance Parameters

[0095]

[0096] Depend on Figure 6 It can be seen that the compressive strength of NC-ECC functionally graded materials is not significantly different from that of ordinary laminates, at 50.04 MPa, which is 1.42 times that of ECC materials. Furthermore, the peak displacement of NC-ECC functionally graded materials is 1.1 mm, similar to that of ECC materials, while the peak displacement of ordinary laminates is only 0.63 mm. Calculations show that the ductility of NC-ECC functionally graded materials is 1.597, very close to that of ECC materials. Compared to ordinary laminates, the ductility of NC-ECC functionally graded materials is improved by 25.85%.

[0097] Research has shown that while conventional laminates reduce the amount of fiber material used, their mechanical properties, such as ductility and crack control, are significantly compromised. However, materials prepared using the strain-coordination-based NC-ECC functional graded material design method of this invention can reduce the amount of fiber material used while maintaining the excellent properties of the original ECC material.

[0098] In summary, compared with existing ECC materials and ordinary laminated materials, the NC-ECC functionally graded materials prepared based on strain-coordinated functionally graded design method inherit the advantages of good compressive strength of ordinary concrete and high ductility of ECC materials. They have better mechanical properties required in engineering. In addition, they can make full use of materials, avoid resource waste, and save a lot of costs.

[0099] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0100] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks. Figure 1 one or more flow or blocks.

[0101] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart block or blocks. Figure 1 one or more flow or blocks. Figure 1 one or more flow or blocks.

[0102] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks. Figure 1 one or more flow or blocks.

[0103] The above description is only preferred embodiments of the present application, not intended to limit other forms of the application. Any person familiar with the art can make changes or modifications to the above-mentioned technical content of the disclosure, or equivalent embodiments with equivalent changes. However, any simple modification, equivalent change and modification of the above-mentioned embodiments without departing from the technical solution of the present application, according to the technical essence of the present application, still belongs to the protection scope of the technical solution of the present application.

Claims

1. A method for preparing strain-coordinated NC-ECC functionally graded materials, characterized in that, include: Step S1: The NC-ECC functionally graded material is regarded as being composed of multiple layers of NC-ECC composite materials with different ECC volume fractions. The elastic modulus of the NC-ECC composite material changes nonlinearly with the increase of ECC volume fraction as an exponential function E(v). Step S2: Using the thickness direction z as the independent variable, list the function E(z) that the elastic modulus changes linearly along the thickness direction, so that the interlaminar strain of the NC-ECC functional graded material tends to be coordinated when under stress. Step S3: Perform layered design on the NC-ECC functionally graded material. Use the centroid coordinates of each layer to represent the position of each layer. Substitute the position coordinates into the linear function of elastic modulus to obtain E(k,n). By taking the same value as the exponential function E(v), calculate the volume fraction corresponding to different gradient sublayers. Step S4: Perform a one-dimensional theoretical description of the NC-ECC functionally graded material, where the shape factor N is used to describe the gradual change of the volume fraction of the NC-ECC functionally graded material from one location to another. The design value of the volume fraction obtained by each layer is equal to the one-dimensional description theory to obtain the value of the distribution factor N. The NC-ECC composite material is a mixture of NC and ECC in different volume fractions, where the volume fraction of NC is V. N The volume fraction of ECC is V. E Satisfying V N +V E =1; The elastic modulus model of the NC-ECC composite material is an exponential function E(v) of the compressive elastic modulus with respect to the volume fraction of ECC, wherein the exponential function is used to correct and fit the elastic modulus model of the NC-ECC composite material. E(v)=y0+A1exp(-v / t1)+A2exp(-v / t2) (1) Where v is the ECC volume fraction; Using the z-axis centroid coordinate of each layer to represent the position of that sublayer, and combining the relationship between layering and the positions of each layer, we obtain the formula governing the relationship between layering and the positions of each layer in NC-ECC functionally graded materials: Where k is the k-th layer after the functionally graded specimen is decomposed, n is the number of functionally graded material layers, n>2, z represents the z-axis coordinate position of the k-th layer, and dd m Indicates the gradient sublayer thickness; The elastic modulus varies linearly between layers, ensuring that the strain generated in each gradient sublayer does not jump abruptly during the material's stress process, thus avoiding stress concentration and ensuring that the interlayer strain is coordinated. The linear variation function of the elastic modulus is shown below: Substituting z into E(z) from equation (2), we get: Where E2 is the elastic modulus of NC and E1 is the elastic modulus of ECC; To determine the volume fraction that each gradient sublayer of the NC-ECC functionally graded material should achieve, and to make equations (1) and (4) equal, we have: E(v)=E(k,n) (5) Where y0, A1, A2, t1, and t2 are fitting parameters, all of which are known quantities; A one-dimensional theoretical description of NC-ECC functionally graded materials is provided using the distribution coefficient N to explain the gradual change in ECC volume fraction from one location to another: Where N is the distribution coefficient describing the volume fraction of each layer in the functionally graded sample; N = 1 indicates that the volume fraction of each layer changes linearly; N > 1 and N < 1 both indicate that the volume fraction of each layer changes non-linearly; d and d m Functionally graded materials are divided into different regions (-d m ,d m ) is a gradually changing function gradient layer, (-d m , -d) and (d m ,d) represent the NC and ECC base phase material layers, respectively; Equalizing the one-dimensional theoretical description formula, i.e., equation (7), with the volume fraction function, i.e., equation (6), and substituting the known parameters, we can then perform a logarithmic solution to obtain the value of the distribution coefficient N:

2. The method for preparing NC-ECC functionally graded materials based on strain coordination according to claim 1, characterized in that, When different materials are used for functional gradation, the distribution coefficients described by the one-dimensional theory are also different.

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