A method for constructing mechanical constitutive model based on Matlab

Abstract

This invention discloses a method for constructing a mechanical constitutive model based on Matlab. Based on mechanical experimental data, the model is constructed using the Matlab platform. This method exhibits excellent compatibility and portability, adapting to material mechanical data processing under diverse working conditions. Furthermore, the method provides high throughput and rapid computational response, maximizing the accuracy and efficiency of calculating material properties and enhancing computational stability. This method is beneficial to the development of mechanical research and possesses significant scientific significance and engineering application value.

Description

Technical Field

[0001] The present invention belongs to the technical field of material mechanics, and particularly relates to the design of a mechanical constitutive model construction method based on Matlab. Background Art

[0002] When studying the mechanical properties of materials, the mechanical constitutive model is one of the most researched directions. The most direct and easy-to-think-of method is to deduce the functional relationship satisfied by these data through classical theoretical analysis, but it is also a very difficult thing. Based on this, the data fitting processing method has been favored by people. In order to better construct the mechanical constitutive model of the material, it is necessary to fit the experimental data after obtaining the experimental data to obtain a functional relationship that conforms to the data, and then have a deeper understanding of the various parameters of the experiment, and be able to analyze the influence of each parameter on the experimental results. However, the selection of the fitting method usually requires consideration of many factors, which increases the difficulty of fitting. The existing fitting methods for the mechanical constitutive model of materials have the problems of large amount of calculation and long calculation time, which makes it difficult to achieve rapid processing of large amounts of data. Summary of the Invention

[0003] The purpose of this invention is to propose a mechanical constitutive model construction method based on Matlab, which can realize the rapid establishment of mechanical constitutive model, greatly save the amount of calculation and calculation time, and obtain more accurate material mechanical constitutive relationship.

[0004] The technical solution of the present invention is: a method for constructing a mechanical constitutive model based on Matlab, comprising the following steps:

[0005] S1. Set the material strain rate column vector.

[0006] S2. Read the stress-strain data at different strain rates in the Excel table through Matlab.

[0007] S3. Divide the stress-strain data into elastic and plastic regions.

[0008] S4. Use Matlab fitting function to fit the stress-strain curve of the elastic region.

[0009] S5. Use Matlab fitting function to fit the stress-strain curve of the plastic zone.

[0010] S6. According to the stress-strain curve in the elastic region, the relationship between the elastic modulus and the strain rate was determined using the Matlab fitting function.

[0011] S7. According to the stress-strain curve in the plastic zone, the material parameters in the constitutive model are determined using the Matlab fitting function.

[0012] S8. Calculate the R-square of the plastic zone at different strain rates.

[0013] S9. Determine whether R-squared is greater than 0.95. If so, proceed to step S10; otherwise, return to step S5.

[0014] S10. Construct a mechanical constitutive model of the material.

[0015] Furthermore, step S3 is specifically as follows: using the plot(x,y) function to draw a scatter plot of stress-strain data at the same strain rate, and dividing the stress-strain data into an elastic zone and a plastic zone by observing the scatter plot, where x is the overall strain data and y is the overall stress data.

[0016] Furthermore, the relationship between the elastic modulus and the strain rate determined in step S6 is:

[0017]

[0018] Where E represents the elastic modulus, and S=log s represents the logarithm of the strain rate s with base 10.

[0019] Furthermore, the constitutive model in step S7 is:

[0020] σ=A×e B×ε

[0021] Where σ represents the true stress of the material, ε represents the strain of the material, and A and B are material parameters.

[0022] Furthermore, the material parameters of the constitutive model determined in step S7 are:

[0023]

[0024]

[0025] Where S=lgs represents the logarithm of the strain rate s with base 10.

[0026] Furthermore, the calculation formula of R square of the plastic zone in step S8 is:

[0027]

[0028] where R 2 represents the R-square of the plastic zone, sum[·] represents the sum function, mean(·) represents the mean function, y represents the true value of the stress in the plastic zone, and y1 represents the predicted value of the stress in the plastic zone.

[0029] Furthermore, the calculation formula of the predicted value y1 is:

[0030] y1=F(f1(S),f2(S),...,fn (S), strain)

[0031] Where F(·) is the constitutive model function, S=lgs represents the logarithm of the strain rate s with the base 10, strain represents the strain data, and f i (S) represents the function of the i-th parameter in the constitutive model with respect to S, i = 1, 2, ..., n, and n represents the number of parameters in the constitutive model.

[0032] Furthermore, the mechanical constitutive model of the material constructed in step S10 is:

[0033]

[0034] where exp[·] represents an exponential function with the natural constant e as its base.

[0035] The beneficial effects of the present invention are:

[0036] (1) The present invention designs a data fitting processing method for the mechanical constitutive model based on the Matlab platform, which solves the problem of rapid calculation and processing of massive experimental data.

[0037] (2) Based on mechanical experimental data, the present invention uses the Matlab platform to construct a mechanical constitutive model, which has good compatibility and portability and can adapt to the material mechanical data processing of different working conditions.

[0038] (3) The mechanical constitutive model construction method provided by the present invention has high throughput and fast computational response capabilities, which maximizes the accuracy and efficiency of calculating material properties, enhances the stability of the calculation, is conducive to the development of mechanical research, and has important scientific significance and engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 The figure shows a flow chart of a method for constructing a mechanical constitutive model based on Matlab provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0040] The exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the accompanying drawings are merely exemplary and are intended to illustrate the principles and spirit of the present invention, rather than to limit the scope of the present invention.

[0041] The embodiment of the present invention provides a method for constructing a mechanical constitutive model based on Matlab, such as Figure 1 As shown, the following steps S1 to S10 are included:

[0042] S1. Set the material strain rate column vector.

[0043] In the embodiment of the present invention, taking the strain rates of 0.0025, 0.00025, 0.000025 as an example, the strain rate column vector of the material is s=[0.0025, 0.00025, 0.000025].

[0044] S2. Read the stress-strain data at different strain rates in the Excel table through Matlab.

[0045] In the embodiment of the present invention, the Matlab function xlsread(filename,sheet,xlRange) is used to read the stress-strain data at different strain rates in the Excel table, and they are named strain_f and stress_f, respectively, where filename represents the file name, sheet represents the worksheet name, xlRange represents the specified range in the worksheet, and f represents the decimal part of the original strain rate. For example, when the strain rate is 0.0025, the stress-strain data are named strain_0025 and stress_0025.

[0046] S3. Divide the stress-strain data into elastic and plastic regions.

[0047] In the embodiment of the present invention, the plot(x,y) function is used to draw a scatter plot of stress-strain data at the same strain rate. By observing the scatter plot, the stress-strain data is divided into the elastic region and the plastic region, where x is the overall strain data and y is the overall stress data. The elastic region strain data, elastic region stress data, plastic region strain data, and plastic region stress data are named s_tr,ai_n,f, respectively, for example, s_tr0a0i2n5,es_.

[0048] S4. Use Matlab fitting function to fit the stress-strain curve of the elastic region.

[0049] In the embodiment of the present invention, the fitting function used in step S4 is newtype=fittype('e*x e '); fit(x e ,y e ,newtype), where x e is the strain data in the elastic region, y e The stress data of the elastic region, parameter e, is stored in the elastic modulus column vector E.

[0050] S5. Use Matlab fitting function to fit the stress-strain curve of the plastic zone.

[0051] In the embodiment of the present invention, the fitting function used in step S5 is newtype=fittype('F(x p )'); fit(x p,y p ,newtype), where x p is the strain data in the plastic zone, y p is the stress data in the plastic zone, F(·) is the custom function, that is, the constitutive model function that needs to be determined, and the parameters a1, a2, a3... of the custom function F(·) are stored in the column vectors A1, A2, A3... respectively.

[0052] In the embodiment of the present invention, the stress-strain curve of the plastic zone may also be fitted using a Matlab fitting toolbox.

[0053] S6. According to the stress-strain curve in the elastic region, the relationship between the elastic modulus and the strain rate was determined using the Matlab fitting function.

[0054] In the embodiment of the present invention, the fitting function used in step S6 is newtype=fittype('type'); fit(X, Y, newtype), where type is a user-defined function, X is the logarithm S of the strain rate s with base 10, and Y is a parameter column vector.

[0055] In the embodiment of the present invention, the relationship between the elastic modulus and the strain rate is determined as follows:

[0056]

[0057] Where E represents the elastic modulus, and S=lgs represents the logarithm of the strain rate s with base 10.

[0058] S7. According to the stress-strain curve in the plastic zone, the material parameters in the constitutive model are determined using the Matlab fitting function. In the embodiment of the present invention, the fitting function used in step S7 is the same as the fitting function in step S6, and the constitutive model is:

[0059] σ=A×e B×ε

[0060] Where σ represents the true stress of the material, ε represents the strain of the material, and A and B are both material parameters, which are finally determined as:

[0061]

[0062]

[0063] S8. Calculate the R-square of the plastic zone at different strain rates.

[0064] The calculation formula for R square is:

[0065]

[0066] where R 2represents the R-square of the plastic zone, sum[·] represents the sum function, mean(·) represents the mean function, y represents the true value of the stress in the plastic zone, and y1 represents the predicted value of the stress in the plastic zone. The calculation formula is:

[0067] y1=F(f1(S),f2(S),...,f n (S), strain)

[0068] Where F(·) is the constitutive model function, S=lgs represents the logarithm of the strain rate s with the base 10, strain represents the strain data, and f i (S) represents the function of the i-th parameter in the constitutive model with respect to S, i = 1, 2, ..., n, and n represents the number of parameters in the constitutive model.

[0069] S9. Determine whether R-squared is greater than 0.95. If so, it is considered that the fitting effect is good and go to step S10. Otherwise, return to step S5.

[0070] S10. Construct a mechanical constitutive model of the material.

[0071] In the embodiment of the present invention, the mechanical constitutive model of the material is constructed as follows:

[0072]

[0073] where exp[·] represents an exponential function with the natural constant e as its base. The above mechanical constitutive model is a strain rate-dependent constitutive model for TiAl alloy manufactured by electron beam additive manufacturing at 1050°C.

[0074] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A method for constructing a mechanical constitutive model based on Matlab, characterized in that: The following steps are involved: S1, set the strain rate column vector of the material; S2. Read the stress-strain data at different strain rates in the Excel table through Matlab; S3, dividing the stress-strain data into elastic and plastic regions; S4, use Matlab fitting function to fit the stress-strain curve of the elastic region; S5. Use Matlab fitting function to fit the stress-strain curve of the plastic zone; S6. Based on the stress-strain curve in the elastic region, the relationship between the elastic modulus and the strain rate was determined using the Matlab fitting function. S7. According to the stress-strain curve in the plastic zone, the material parameters in the constitutive model are determined using the Matlab fitting function; S8. Calculate the R-square of the plastic zone at different strain rates; S9, determine whether R-squared is greater than 0.95, if so, proceed to step S10, otherwise return to step S5; S10, constructing a mechanical constitutive model of the material; The constitutive model in step S7 is: ； in represents the true stress of the material, represents the strain of the material, 、 All are material parameters; The material parameters of the constitutive model determined in step S7 are: ； ； in It represents the logarithm of strain rate s to base 10; The calculation formula of the R square of the plastic zone in step S8 is: ； in represents the R-square of the plastic zone, represents the summation function, represents the mean function, represents the true value of stress in the plastic zone, Indicates the predicted value of stress in the plastic zone; The mechanical constitutive model is a strain rate-dependent constitutive model of TiAl alloy manufactured by electron beam additive manufacturing at 1050°C.

2. The method for constructing a mechanical constitutive model according to claim 1, wherein: The step S3 is specifically as follows: The function draws a scatter plot of stress-strain data at the same strain rate. By observing the scatter plot, the stress-strain data can be divided into elastic and plastic regions, where x is the overall strain data and y is the overall stress data.

3. The method for constructing a mechanical constitutive model according to claim 1, wherein: The relationship between the elastic modulus and the strain rate determined in step S6 is: ； in represents the elastic modulus, It represents the logarithm of the strain rate s to the base 10.

4. The method for constructing a mechanical constitutive model according to claim 1, wherein: The predicted value The calculation formula is: ； in is the constitutive model function, represents the logarithm of the strain rate s to the base 10, represents strain data, Indicates the constitutive model Parameters about function, , represents the number of parameters in the constitutive model.

Images