A method for predicting compression creep strain of restructured bamboo based on improved Kelvin-Voight model

Abstract

The present invention discloses a method for predicting the compression creep strain of reconstructed bamboo based on an improved Kelvin-Voight model. The method firstly performs creep tests on reconstructed bamboo under two different stress levels, and adopts a new Kelvin-Voight viscoelastic mechanical constitutive relationship model defined based on variable-order R-L fractional theory to analyze the reconstructed bamboo, and obtains the main parameter values ​​of the model under the two stress levels; secondly, exponential functions and power functions are respectively adopted to fit the relationship between stress and main model parameters, and the values ​​of these model parameters under other arbitrary specified stress levels are obtained; finally, based on the parameter values ​​obtained in the previous step and the Kelvin-Voight model, the compression creep of reconstructed bamboo under other stress levels is predicted. The research results show that the method can effectively overcome the defect of strong dispersion of mechanical properties of reconstructed bamboo itself, accurately predict the compression creep strain of multiple reconstructed bamboo specimens, and has good engineering applicability.

Description

Technical Field

[0001] The present invention relates to the technical field of predicting the compressive creep strain of recombinant bamboo, and specifically provides a method for predicting the compressive creep strain of recombinant bamboo based on an improved Kelvin-Voight model. Background Art

[0002] Recombinant bamboo is a new type of bamboo material with high strength, large specifications, and natural structure. It is made by loosening bamboo into bamboo bundles of a certain length, maintaining the original arrangement of fibers and cross-linking them, and then drying, sizing, and hot-pressing the billets in the longitudinal direction. This product has been developed and applied to outdoor floors, wall panels, and building structural materials, and is popular among people in countries such as Europe, America, and Australia. It has also become the fastest-growing and most-demanded product among bamboo products.

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

[0004] The purpose of this part is to outline some aspects of the embodiments of the present invention and briefly introduce some preferred embodiments. Simplifications or omissions may be made in this part, as well as in the abstract and title of the present application, to avoid obscuring the purpose of this part, the abstract, and the title. However, such simplifications or omissions shall not 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 recombinant bamboo based on an improved Kelvin-Voight model, which can effectively overcome the defect of strong dispersion of the mechanical properties of recombinant bamboo itself and accurately predict the compressive creep strain of multiple recombinant bamboo specimens.

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

[0007] A method for predicting the compressive creep strain of recombinant bamboo based on an improved Kelvin-Voight model, which includes:

[0008] S1. Conduct creep tests on recombinant bamboo under two different stress levels, and record the growth process of compressive creep strain during the test;

[0009] S2. Use the Kelvin-Voight model defined by the variable-order R-L fractional-order theory to fit and analyze the compressive creep strain under two stress levels, and determine the main parameter values of the model;

[0010] S3. Fit the relationship between stress and the main parameters of the model to obtain the values of these model parameters at any other specified stress levels;

[0011] S4. Substitute the derived model parameters into the Kelvin-Voight model defined by the same R-L fractional order to predict the compressive creep of the laminated bamboo at other stress levels.

[0012] As a preferred embodiment of the method for predicting the compressive creep strain of laminated bamboo based on the improved Kelvin-Voight model according to the present invention, in step S2, the Kelvin-Voight model is composed of an elastic element E 1 connected in series with a Kelvin element, where the Kelvin element is composed of an elastic element E 3 and a viscous element η 2 connected in parallel. The stress-strain relationship of this model in the time domain is:

[0013] σ 1 = σ 2 + σ 3 = σ 0 (1)

[0014] σ 1 (t) = E 1 ε 1 (t) (2)

[0015] σ 3 (t) = E 3 ε 3 (t) (3)

[0016] ε 3 (t) = ε 2 (t) (4)

[0017] In the formula, σ 0 is the total stress value of the model, and σ 1 , σ 2 and σ 3 are the stress values of the elastic element E 1 , the viscous element, and the elastic element E 3 respectively. ε 1 , ε 2 and ε 3 are the strain values of the same elements respectively.

[0018] As a preferred embodiment of the method for predicting the compressive creep strain of laminated bamboo based on the improved Kelvin-Voight model according to the present invention, in step S2, the time-domain stress-strain relationship of the viscous element is studied using the fractional order theory, and the corresponding definition is:

[0019]

[0020] In the formula, α is the order of the fractional order.

[0021] As a preferred scheme of a method for predicting the compression creep strain of recombinant bamboo based on an improved Kelvin-Voight model according to the present invention, wherein, in step S2,

[0022] The fractional order model adopted is the R-L fractional order model, and its definition is:

[0023]

[0024] The variable order fractional order theory is used for analysis, and the definition form is:

[0025]

[0026] In the formula, the subscript i represents the i-th time step. Based on this model, the stress-strain relationship of the viscous element can be fitted, and the result is:

[0027]

[0028] In the formula, α(t i+1 ) and η(t i+1 ) are respectively the values of the order and the viscous coefficient in the i-th time step. When the stress level remains unchanged within this time step, it can be considered that the numerical values of these two parameters also remain unchanged. Based on this assumption, the corresponding stress-strain relationship is:

[0029]

[0030] As a preferred scheme of a method for predicting the compression creep strain of recombinant bamboo based on an improved Kelvin-Voight model according to the present invention, wherein, in step S3, an exponential function and a power function are used to fit the relationship between the stress and the main parameters of the model.

[0031] As a preferred scheme of a method for predicting the compression creep strain of recombinant bamboo based on an improved Kelvin-Voight model according to the present invention, wherein, in step S3, the fitting of the relationship between the stress and the main parameters of the model is specifically as follows:

[0032] An exponential function is used to fit the two groups of relationships of stress level - order and stress level - elastic modulus, quantitatively determine the influence law of the stress level on the parameters of these two groups of relationships, and on this basis, determine the specific values of these two model parameters at any other specified stress level;

[0033] The power function is adopted to fit the relationship between the stress level and the viscosity coefficient, quantitatively determine the influence law of the stress level on this parameter, and on this basis, determine the specific value of this parameter at any other specified stress level.

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows: Based on the Kelvin-Voight model defined by the R-L fractional order theory, the present invention can effectively overcome the defect of strong dispersion in the mechanical properties of laminated bamboo, accurately predict the compressive creep strain of multiple laminated bamboo specimens, and has good engineering applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] 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 with reference to the drawings and specific embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts. Among them:

[0036] Figure 1 is a flowchart of a method for predicting the compressive creep strain of laminated bamboo based on an improved Kelvin-Voight model of the present invention;

[0037] Figure 2 is a schematic structural diagram of the Kelvin-Voight model provided by the present invention;

[0038] Figure 3 is a schematic diagram of the fitting result at a 30% stress level provided by the present invention;

[0039] Figure 4 is a schematic diagram of the fitting result at a 40% stress level provided by the present invention;

[0040] Figure 5 is a schematic diagram of the prediction result at a 10% stress level provided by the present invention;

[0041] Figure 6 is a schematic diagram of the prediction result at a 20% stress level provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0042] In order to make the above objects, features, and advantages of the present invention more obvious and understandable, the following detailed description of the specific embodiments of the present invention will be made with reference to the drawings.

[0043] Secondly, the present invention will be described in detail with reference to the schematic diagrams. When describing the embodiments of the present invention in detail, for the convenience of explanation, the cross-sectional views showing the device structure will be enlarged locally out of the general scale, and the schematic diagrams are only examples and should not limit the scope of protection of the present invention herein. In addition, in actual production, three-dimensional spatial dimensions including length, width, and depth should be included.

[0044] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0045] The present invention provides a method for predicting the compressive creep strain of recombined bamboo based on an improved Kelvin-Voight model, which can effectively overcome the defect of strong dispersion in the mechanical properties of recombined bamboo itself and accurately predict the compressive creep strain of multiple recombined bamboo specimens.

[0046] The method for predicting the compressive creep strain of recombined bamboo based on the improved Kelvin-Voight model specifically includes the following two parts: (1) model definition, (2) model prediction.

[0047] (1) Model definition

[0048] As Figure 2 shown, this model is a Kelvin-Voight model, which is composed of an elastic element E 1 in series with a Kelvin element, where the Kelvin element is composed of an elastic element E 3 and a viscous element η 2 in parallel. The stress-strain relationship of this model in the time domain is:

[0049] σ 1 = σ 2 + σ 3 = σ 0 (1)

[0050] σ 1 (t) = E 1 ε 1 (t) (2)

[0051] σ 3 (t) = E 3 ε 3 (t) (3)

[0052] ε 3 (t) = ε 2 (t) (4)

[0053] In the formula, σ 0 is the total stress value of the model, σ 1 , σ 2 and σ 3are the elastic unit E 1 , the stress values of the viscous unit and the elastic unit E 3 , ε 1 , ε 2 and ε 3 are the strain values of the same units respectively

[0054] Among them, the time-domain stress-strain relationship of the viscous unit is studied using the fractional-order theory, and the corresponding definition is:

[0055]

[0056] In the formula, α is the order of the fractional order.

[0057] Among them, the fractional-order model adopted is the R-L (Riemann–Liouville) fractional-order model, and its definition is:

[0058]

[0059] This method is applied to study the compression creep performance of recombinant bamboo under various stress levels. Previous studies have shown that when studying the creep performance of recombinant bamboo based on the fractional-order theory, the order of the fractional order is related to the stress level. Therefore, the variable-order fractional-order theory is adopted in this invention for analysis, and its definition form is:

[0060]

[0061] In the formula, the subscript i represents the i-th time step. Based on this model, the stress-strain relationship of the viscous unit can be fitted, and the result is:

[0062]

[0063] In the formula, α(t i+1 ) and η(t i+1 ) are the values of the order and the viscous coefficient in the i-th time step respectively. When the stress level remains unchanged within this time step, it can be considered that the values of these two parameters also remain unchanged. Based on this assumption, the corresponding stress-strain relationship is:

[0064]

[0065] Based on this equation, the stress-strain relationships of the corresponding viscous unit and the Kelvin-Voight model in the time domain can be deduced.

[0066] (2) Model prediction

[0067] Based on the Kelvin-Voight model defined by the above R-L fractional-order theory, the compression creep strain of recombinant bamboo can be predicted, such asFigure 1 As shown below, the specific steps are as follows:

[0068] Step 1: Select a certain type of recombinant bamboo compression creep specimen, and conduct compression creep tests on it under two stress levels successively, and record the growth process of compression creep strain during the test;

[0069] Step 2: Use the Kelvin-Voight model defined by the above R-L fractional order to fit and analyze the compression creep strain under these two stress levels, and determine the main parameter values of the model (model order, viscosity coefficient, and elastic modulus);

[0070] Step 3: Use the exponential function to fit the two sets of relationships of stress level - order and stress level - elastic modulus, quantitatively determine the influence law of stress level on these two model parameters, and on this basis, determine the specific values of these two model parameters under any other specified stress level;

[0071] Step 4: Use the power function to fit the relationship of stress level - viscosity coefficient, quantitatively determine the influence law of stress level on this parameter, and on this basis, determine the specific value of this parameter under any other specified stress level;

[0072] Step 5: Substitute the derived model parameters into the same Kelvin-Voight model defined by the R-L fractional order, and the compression creep strain of this recombinant bamboo specimen under the specified stress level can be predicted.

[0073] To further verify the universality of this method, three groups of specimens were used for prediction research. According to Step 1, first conduct compression creep tests on these three groups of specimens under two stress levels successively (30% and 40% of the compressive strength), and record the growth process of compression creep strain during the test. Then according to Step 2, use the Kelvin-Voight model defined by the R-L fractional order theory described above to fit and analyze the compression creep strain of these three groups of specimens under different stress levels, and the results are as Figures 3 to 4 shown:

[0074] As Figures 3 to 4 shown, it can be seen that when using the Kelvin-Voight model defined by the R-L fractional order theory to fit and analyze the compression creep strain of these three groups of specimens under different stress levels, the fitting results are basically consistent with the original test data, indicating that this model has good applicability in analyzing the compression creep characteristics of recombinant bamboo under these two stress levels. The fitting results of the model order and viscosity coefficient of the corresponding different specimens are shown in Table 1.

[0075] Table 1 Fitting results of Kelvin-Voight model parameters

[0076]

[0077] Taking the fitting results in Table 1 as the benchmark, the exponential function and the power function are respectively used to analyze the two groups of relationships between the stress level - order and the stress level - viscosity coefficient, and the numerical values of these two model parameters for different specimens at 10% and 20% stress levels are calculated. The results are shown in Table 2:

[0078] Table 2 Calculation results of Kelvin - Voight model parameters

[0079]

[0080] Using the model parameter values obtained from the analysis in Table 2 and combining with the Kelvin - Voight model defined by the R - L fractional - order theory described above, the compression creep strains of these three groups of specimens at these stress levels are predicted and analyzed. The results are as Figures 5 to 6 shown. It can be seen that when predicting the compression creep strain of laminated bamboo based on this method, the prediction results are basically consistent with the actual test results, and the relative error at each time node does not exceed 3%. This shows that this method can effectively overcome the dispersion of the mechanical properties of the material itself and has good universality.

[0081] Although the present invention has been described with reference to the embodiments above, various improvements can be made to it and components therein can be replaced with 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 disclosed embodiments of the present invention can be combined with each other in any way. The exhaustive description of these combinations is not given in this specification only for the sake of saving space and resources. Therefore, the present invention is not limited to the specific embodiments disclosed in the text, 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 Kelvin-Voight model, characterized in that: include: S1. Conduct creep tests on reconstructed bamboo at two different stress levels and record the compressive creep strain growth process during the test; S2. The Kelvin-Voight model defined based on the variable-order RL fractional theory is used to fit and analyze the compressive creep strains under two stress levels to determine the main parameter values ​​of the model; S3, fitting the relationship between stress and main parameters of the model to obtain the values ​​of these model parameters at any other specified stress level; S4, substituting the derived model parameters into the Kelvin-Voight model with the same RL fractional definition to predict the compression creep of reconstructed bamboo at other stress levels; In step S2, the Kelvin-Voight model is composed of an elastic unit E1 and a Kelvin unit in series, wherein the Kelvin unit is composed of an elastic unit E3 and a viscous unit η2 in parallel. The stress-strain relationship of the model in the time domain is: σ1=σ2+σ3=σ0 (1) σ1(t)=E1ε1(t) (2) σ3(t)=E3ε3(t) (3) ε3(t)=ε2(t) (4) Where σ0 is the total stress value of the model, σ1, σ2 and σ3 are the stress values ​​of the elastic unit E1, the viscous unit and the elastic unit E3 respectively, and ε1, ε2 and ε3 are the strain values ​​of the same unit respectively; The time-domain stress-strain relationship of the viscous element is studied using the fractional-order theory, and the corresponding definition is: Where α is the order of the fractional order; in step S2, The fractional-order model used is the RL fractional-order model, which is defined as: The variable-order fractional-order theory is used for analysis, and the definition form is: In the formula, the subscript i represents the i-th time step. 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. 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:

2. The method for predicting the compressive creep strain of reconstructed bamboo based on the improved Kelvin-Voight model according to claim 1, characterized in that: In step S3, exponential function and power function are used to fit the relationship between stress and main parameters of the model.

3. The method for predicting the compressive creep strain of reconstituted bamboo based on the improved Kelvin-Voight model according to claim 1, characterized in that: In step S3, the relationship between stress and main parameters of the model is fitted as follows: The exponential function is used to fit the two sets of relationships between stress level and order and stress level and elastic modulus, and the influence of stress level on the two sets of relationship parameters is quantitatively determined. On this basis, the specific values ​​of the two model parameters at any other specified stress level are 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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