Reconstituted bamboo compression creep strain prediction method based on improved Maxwell model

Abstract

The invention discloses a reconstituted bamboo compression creep strain prediction method based on an improved Maxwell model, and the method comprises the steps: firstly carrying out the creep test of a reconstituted bamboo under two different stress levels, and employing a new Maxwell viscoelastic mechanical constitutive relation model defined based on a Captou fractional order theory of variable order to carry out the analysis of the reconstituted bamboo; obtaining viscosity coefficients and orders of the model under the two stress levels; secondly, fitting the stress level-order relation and the stress level-viscosity coefficient relation by adopting an exponential function and a power function respectively to obtain numerical values of the two parameters under any other specified stress level; and finally, on the basis of the parameter values obtained in the previous step and a Maxwell model, the compression creep of the recombined bamboo under other stress levels is predicted. Research results show that based on the method, the defect that the recombined bamboo is high in mechanical property dispersity can be effectively overcome, the compression creep strain of multiple recombined bamboo test pieces can be accurately predicted, and the method has good engineering applicability.

Description

Technical Field

[0001] The invention relates to the technical field of reconstituted bamboo material compression creep strain prediction, in particular to a reconstituted bamboo material compression creep strain prediction method based on an improved Maxwell model. Background Art

[0002] Reconstructed bamboo is a new type of bamboo material with high strength, large specifications and natural structure, which is made by loosening bamboo bundles of a certain length, maintaining the original arrangement of fibers and cross-linking each other, and then drying, gluing, and hot pressing them along the grain. This product has been developed and applied to outdoor floors, wall panels, and building structural materials, and has become the fastest growing and most in-demand product among bamboo products.

[0003] At present, when predicting the compressive creep strain of reconstructed bamboo, due to the strong dispersion of the mechanical properties of reconstructed bamboo itself, it is impossible to accurately predict the compressive creep strain of the reconstructed bamboo specimens, and the prediction effect is poor. Summary of the invention

[0004] The purpose of this section is to summarize some aspects of the embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the specification abstract and invention title of this application to avoid blurring the purpose of this section, specification abstract and invention title, and such simplifications or omissions cannot be used to limit the scope of the present invention.

[0005] Therefore, the purpose of the present invention is to provide a method for predicting the compressive creep strain of reconstructed bamboo based on the improved Maxwell model, which can effectively overcome the defect of strong dispersion of mechanical properties of reconstructed bamboo itself and accurately predict the compressive creep strain of multiple reconstructed bamboo specimens.

[0006] To solve the above technical problems, according to one aspect of the present invention, the present invention provides the following technical solutions:

[0007] A method for predicting the compressive creep strain of reconstructed bamboo based on the improved Maxwell model, the steps are as follows:

[0008] S1. Conduct creep tests on reconstructed bamboo compression creep specimens at two different stress levels and record the compression creep strain growth process during the test;

[0009] S2. Use the Maxwell model based on the variable-order Captou fractional definition to fit and analyze the compressive creep strains under the two stress levels and determine the main parameter values ​​of the model;

[0010] S3, fitting the stress level-order and stress level-viscosity coefficient relationships to obtain the values ​​of these two relationship parameters at any other specified stress level;

[0011] S4. Substitute the derived model parameters into the Maxwell model with the same Captou fractional order definition to predict the compressive creep strain of the reconstructed bamboo specimen at a specified stress level.

[0012] As a preferred embodiment of the method for predicting the compressive creep strain of reconstituted bamboo based on the improved Maxwell model described in the present invention, in step S2, the Maxwell model is composed of an elastic unit and a viscous unit connected in series, wherein the stress-strain relationship of the elastic unit and the viscous unit is respectively:

[0013] σ1=σ2=σ0 (1)

[0014] σ1=E0ε1(t) (2)

[0015]

[0016] Where σ0 is the total stress of the model, σ1 and σ2 are the stresses of the elastic unit and the viscous unit respectively, ε1 and ε2 are the strains of the elastic unit and the viscous unit respectively, E0 is the elastic modulus, α is the order of the fractional derivative, and η0 is the viscosity coefficient.

[0017] As a preferred embodiment of the method for predicting the compressive creep strain of reconstituted bamboo based on the improved Maxwell model described in the present invention, in step S2, the Captou fractional order model is specifically defined as:

[0018]

[0019] In the formula, α is the order of the fractional order.

[0020] As a preferred solution of the method for predicting the compression creep strain of reconstituted bamboo based on the improved Maxwell model described in the present invention, in step S2, the variable order fractional order is defined as follows:

[0021]

[0022] Based on this model, the stress-strain relationship of the viscous unit can be fitted, and the result is:

[0023]

[0024] In the formula, α(t i+1 ) and η(t i+1 ) are the values ​​of order and viscosity coefficient in the i-th time step, respectively. The corresponding stress-strain relationship is:

[0025]

[0026] Where t = (k + 1) μ, where μ is the time step length and t is the total time.

[0027] As a preferred embodiment of the method for predicting the compressive creep strain of reconstituted bamboo based on the improved Maxwell model described in the present invention, in step S3, an exponential function and a power function are used to fit the stress level-order and stress level-viscosity coefficient relationships.

[0028] As a preferred embodiment of the method for predicting the compressive creep strain of reconstituted bamboo based on the improved Maxwell model described in the present invention, in step S3, the stress level-order and stress level-viscosity coefficient relationships are fitted to obtain the values ​​of these two relationship parameters at any other specified stress level. The specific steps are as follows:

[0029] The exponential function is used to fit the stress level-order relationship, and the influence of the stress level on the relationship parameters is quantitatively determined. On this basis, the specific value of the parameter at any other specified stress level is determined.

[0030] The power function is used to fit the relationship between stress level and viscosity coefficient, and the influence of stress level on the parameter is quantitatively determined. On this basis, the specific value of the parameter at any other specified stress level is determined.

[0031] Compared with the prior art, the present invention has the following beneficial effects: the Maxwell viscoelastic mechanics constitutive relationship model defined based on the variable-order Captou fractional theory can effectively overcome the defect of strong dispersion of the mechanical properties of reconstructed bamboo itself, accurately predict the compressive creep strain of a variety of reconstructed bamboo specimens, and has good engineering applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below in combination with the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:

[0033] Figure 1 This is a flow chart of a method for predicting compression creep strain of reconstituted bamboo based on an improved Maxwell model of the present invention;

[0034] Figure 2 A schematic diagram of the Maxwell model structure provided by the present invention;

[0035] Figure 3 This is a schematic diagram of the fitting results of specimen 1 in the embodiment provided by the present invention;

[0036] Figure 4 This is a schematic diagram of the fitting results of specimen 2 in the embodiment provided by the present invention;

[0037] Figure 5 This is a schematic diagram of the fitting results of specimen 3 in the embodiment provided by the present invention;

[0038] Figure 6 A schematic diagram of the prediction results of specimen 1 in the embodiment provided by the present invention;

[0039] Figure 7 This is a schematic diagram of the prediction results of specimen 2 in the embodiment provided by the present invention;

[0040] Figure 8 This is a schematic diagram of the prediction results of specimen 3 in the embodiment provided by the present invention. DETAILED DESCRIPTION

[0041] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0042] Secondly, the present invention is described in detail with reference to schematic diagrams. When describing the embodiments of the present invention in detail, for the sake of convenience, the cross-sectional diagrams showing the device structure will not be partially enlarged according to the general scale, and the schematic diagrams are only examples, which should not limit the scope of protection of the present invention. In addition, in actual production, the three-dimensional dimensions of length, width and depth should be included.

[0043] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0044] The present invention provides a method for predicting the compressive creep strain of reconstructed bamboo based on an improved Maxwell model, which can effectively overcome the defect of strong dispersion of mechanical properties of reconstructed bamboo itself and accurately predict the compressive creep strain of multiple reconstructed bamboo specimens.

[0045] The compression creep strain prediction method of reconstructed bamboo based on the improved Maxwell model specifically includes the following two parts: (1) model definition and (2) model prediction.

[0046] (1) Model definition

[0047] like Figure 2 As shown in the figure, the model is a Maxwell model, which is composed of an elastic unit and a viscous unit in series. The stress-strain relationship between the elastic unit and the viscous unit is:

[0048] σ1=σ2=σ0 (1)

[0049] σ1=E0ε1(t) (2)

[0050]

[0051] In the formula, σ0 is the total stress of the model, σ1 and σ2 are the stresses of the elastic unit and the viscous unit respectively, ε1 and ε2 are the strains of the elastic unit and the viscous unit respectively, E0 is the elastic modulus, α is the order of the fractional derivative, and η0 is the viscosity coefficient. The fractional model used in this method is the Captou fractional model, which is defined as:

[0052]

[0053] This method is applied to study the compressive creep properties of reconstructed bamboo under various stress levels. Previous studies have shown that when the creep properties of reconstructed bamboo are studied based on fractional order theory, the order of the fractional order is related to the stress level. Therefore, this paper uses variable order fractional order theory to analyze it, and its definition form is:

[0054]

[0055] Based on this model, the stress-strain relationship of the viscous unit can be fitted, and the result is:

[0056]

[0057] In the formula, α(t i+1 ) and η(t i+1 ) are the values ​​of the order and viscosity coefficient in the i-th time step, respectively. When the stress level in the time step remains unchanged, it can be assumed that the values ​​of these two parameters remain unchanged. Based on this assumption, the corresponding stress-strain relationship is:

[0058]

[0059] In the formula, t = (k + 1) μ, where μ is the time step length and t is the total time. Based on this equation, the corresponding viscous unit and the stress-strain relationship of the Maxwell model can be derived.

[0060] (2) Model prediction

[0061] For natural fiber reinforced composite materials such as reconstituted bamboo, their mechanical properties often have a large dispersion. Even if the same batch of reconstituted bamboo specimens are made with the same raw materials and processes, the relative error of some mechanical property parameters (tensile strength, compressive strength, etc.) will exceed 10%. In view of this feature, such as Figure 1 As shown, the present invention proposes a method for predicting the compression creep strain of reconstituted bamboo based on the Maxwell model defined by the Captou fractional order theory, and the specific steps are as follows:

[0062] Step 1: Select a certain reconstructed bamboo compression creep specimen, conduct compression creep tests on it under two stress levels, and record the compression creep strain growth process during the test;

[0063] Step 2: Use the Maxwell model defined by the Captou fractional order to fit and analyze the compressive creep strains under the two stress levels, and determine the main parameter values ​​of the model (order, viscosity coefficient);

[0064] Step 3: Use exponential function and power function to fit the two sets of relationships between stress level and order and stress level and viscosity coefficient, quantitatively determine the influence of stress level on these two model parameters, and on this basis determine the specific values ​​of these two model parameters at any other specified stress level;

[0065] Step 4: Substitute the derived model parameters into the Maxwell model with the same Captou fractional order definition to predict the compressive creep strain of the reconstructed bamboo specimen at a specified stress level.

[0066] In order to further verify the universality of this method, three groups of specimens were used for prediction research. According to step one, the three groups of specimens were first subjected to compression creep tests at two stress levels (30% and 40% compressive strength), and the compression creep strain growth process during the test was recorded. Then, according to step two, the Maxwell model defined by the Captou fractional order theory mentioned above was used to fit and analyze the compression creep strain of the three groups of specimens at different stress levels. The results are shown in Figure 2. Figures 3 to 5 shown.

[0067] like Figures 3 to 5 As shown in the figure, it can be seen that when the Maxwell model defined by Captou fractional order theory is used to fit the compressive creep strain of the three groups of specimens at different stress levels, the fitting results are basically consistent with the original test data, indicating that the model has good applicability in analyzing the compressive creep characteristics of reconstructed bamboo at these two stress levels. The corresponding model order and viscosity coefficient fitting results of different specimens are shown in Table 1:

[0068] Table 1 Maxwell model parameter fitting results

[0069]

[0070] As shown in Table 1, it can be seen that for the same specimen, the stress level has a significant effect on the model parameters. At the same time, even at the same stress level, there are large differences between the model parameter values ​​of different specimens, which is caused by the large dispersion of the mechanical properties of the reconstructed bamboo itself. Based on the fitting results in Table 1, the exponential function and power function are used to analyze the two sets of relationships between stress level-order and stress level-viscosity coefficient, and the values ​​of these two model parameters of different specimens at 10% and 20% stress levels are calculated. The results are shown in Table 2:

[0071] Table 2 Parameter estimation results of Maxwell model

[0072]

[0073] The model parameter values ​​obtained from the analysis in Table 2 are combined with the Maxwell model defined by the Captou fractional-order theory mentioned above to predict the compressive creep strain of the three groups of specimens at these stress levels. The results are as follows: Figures 6 to 8 As shown in the figure, it can be seen that when the compression creep strain of reconstructed bamboo is predicted based on this method, the prediction results are basically consistent with the actual test results, and the relative error of each time node does not exceed 2%. This shows that this method can effectively overcome the dispersion of the mechanical properties of the material itself and has good universality.

[0074] Although the present invention has been described above with reference to the embodiments, various modifications may be made thereto and parts thereof may be replaced by equivalents without departing from the scope of the present invention. In particular, as long as there is no structural conflict, the various features in the embodiments disclosed in the present invention may be used in combination with each other in any manner, and the fact that these combinations are not exhaustively described in this specification is only for the sake of omitting space and saving resources. Therefore, the present invention is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A method for predicting the compressive creep strain of reconstructed bamboo based on an improved Maxwell model, characterized in that: Here are the steps: S1. Conduct creep tests on reconstructed bamboo compression creep specimens at two different stress levels and record the compression creep strain growth process during the test; S2. Use the Maxwell model based on the variable-order Captou fractional definition to fit and analyze the compressive creep strains under the two stress levels and determine the main parameter values ​​of the model; S3, fitting the stress level-order and stress level-viscosity coefficient relationships to obtain the values ​​of these two relationship parameters at any other specified stress level; S4. Substitute the derived model parameters into the Maxwell model with the same Captou fractional order definition to predict the compressive creep strain of the reconstructed bamboo specimen at a specified stress level.

2. The method for predicting the compressive creep strain of reconstituted bamboo based on the improved Maxwell model according to claim 1, characterized in that: In step S2, the Maxwell model is composed of an elastic unit and a viscous unit connected in series, where the stress-strain relationship of the elastic unit and the viscous unit is: σ1=σ2=σ0 (1) σ1=E0ε1(t) (2) Where σ0 is the total stress of the model, σ1 and σ2 are the stresses of the elastic unit and the viscous unit respectively, ε1 and ε2 are the strains of the elastic unit and the viscous unit respectively, E0 is the elastic modulus, α is the order of the fractional derivative, and η0 is the viscosity coefficient.

3. The method for predicting the compressive creep strain of reconstituted bamboo based on the improved Maxwell model according to claim 1, characterized in that: In step S2, the Captou fractional order model is specifically defined as: In the formula, α is the order of the fractional order.

4. The method for predicting the compressive creep strain of reconstituted bamboo based on the improved Maxwell model according to claim 1, characterized in that: In step S2, the variable order fractional order is defined as: Based on this model, the stress-strain relationship of the viscous unit can be fitted, and the result is: In the formula, α(t i+1 ) and η(t i+1 ) are the values ​​of order and viscosity coefficient in the i-th time step, respectively. The corresponding stress-strain relationship is: Where t = (k + 1) μ, where μ is the time step length and t is the total time.

5. The method for predicting the compression creep strain of reconstituted bamboo based on the improved Maxwell model according to claim 1, characterized in that: In step S3, exponential function and power function are used to fit the stress level-order and stress level-viscosity coefficient relationships.

6. The method for predicting the compressive creep strain of reconstituted bamboo based on the improved Maxwell model according to claim 1, characterized in that: In step S3, the stress level-order and stress level-viscosity coefficient relationships are fitted to obtain the values ​​of these two relationship parameters at any other specified stress level. The specific steps are as follows: The exponential function is used to fit the stress level-order relationship, and the influence of the stress level on the relationship parameters is quantitatively determined. On this basis, the specific value of the parameter at any other specified stress level is determined. The power function is used to fit the relationship between stress level and viscosity coefficient, and the influence of stress level on the parameter is quantitatively determined. On this basis, the specific value of the parameter at any other specified stress level is determined.

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