TW202236138A - Stress-strain curve simulation method - Google Patents

Abstract

A stress-strain curve simulation method, adapted for calculating a simulated stress-strain curve of an object clamped between a mass block and a testing platform, the method comprises: obtaining a first acceleration curve and a second acceleration curve, wherein the first acceleration curve is associated a plurality of pieces of acceleration data of the mass block and the second acceleration curve is associated a plurality of pieces of acceleration data of the testing platform, extracting a part of the first acceleration curve within a period to obtain a first validated curve, and extracting a part of the second acceleration curve within the period to obtain a second validated curve, obtaining an object strain curve according to the first validated curve and the second validated curve, calculating an object stress curve based on the first validated curve and a contact area between the mass block and the object, and calculating the simulated stress-strain curve with an exponential equation based on the object stress curve and the object strain curve, wherein the simulated stress-strain curve is configured to continue to a tested stress-strain curve.

Description

Stress-strain curve simulation method

The invention relates to a stress-strain curve simulation method.

When simulating the drop test with computer-aided engineering software (Computer Aided Engineering, CAE), it is necessary to input the dynamic stress-strain curve of the complete material (for example, expanded polyethylene (EPE) foam) in the CAE simulation software, That is, in the strain range [0,1), the stress of the material changes with the strain. However, since the material properties tested by different manufacturers are different, and it is difficult to actually test the data of the strain being 1, it is difficult to use CAE simulation to obtain a result close to the actual situation.

In view of the above, the present invention provides a method for simulating stress-strain curves to meet the above requirements.

A stress-strain curve simulation method according to an embodiment of the present invention is used to calculate a simulated stress-strain curve of an object to be tested sandwiched between a mass block and a test platform, the method comprising: obtaining a first an acceleration curve and a second acceleration curve, wherein the first acceleration curve is associated with a plurality of acceleration data of the proof mass, and the second acceleration curve is associated with a plurality of acceleration data of the test platform; the first acceleration is retrieved part of the curve in a time period to obtain a first effective curve, and extract the part of the second acceleration curve in the time period to obtain a second effective curve; according to the first effective curve and the first effective curve Two effective curves obtain a strain curve of the test object; calculate a stress curve of the test object based on the first effective curve and a contact area between the mass block and the test object; and use an exponential equation based on the test object The simulated stress-strain curve is calculated from the object-strain curve and the measured object stress curve, wherein the simulated stress-strain curve is used to continue with a measured stress-strain curve.

In summary, according to the stress-strain curve simulation method shown in one or more embodiments of the present invention, more accurate stress-strain simulation results can be obtained by obtaining the acceleration data of the mass block and the test platform during the drop test, Therefore, when the computer-aided engineering software (Computer Aided Engineering, CAE) is used to simulate the drop test, the simulation results that are more accurate and closer to the actual situation can be obtained. In addition, it is difficult to obtain a strain value closer to 1 in the conventional stress-strain test process, but according to the stress-strain curve simulation method shown in one or more embodiments of the present invention, it can be obtained in the strain range [0,1) A strain value close to 1 can be obtained in the middle, and a larger and more complete stress-strain data can be used as the basis for simulation when computer-aided engineering software is used for simulation.

The above description of the disclosure and the following description of the implementation are used to demonstrate and explain the spirit and principle of the present invention, and provide a further explanation of the patent application scope of the present invention.

The detailed features and advantages of the present invention are described in detail below in the implementation mode, and its content is enough to make any person familiar with the related art understand the technical content of the present invention and implement it accordingly, and according to the content disclosed in this specification, the scope of the patent application and the drawings , anyone skilled in the art can easily understand the purpose and advantages of the present invention. The following examples are to further describe the concept of the present invention in detail, but not to limit the scope of the present invention in any way.

Please refer to FIG. 1 first. FIG. 1 is a schematic diagram of an experimental setup for obtaining acceleration data. The stress-strain curve simulation method shown in the present invention calculates the simulated stress-strain curve based on the acceleration data, and the schematic diagram of the experimental setup shown in FIG. 1 can be used to obtain the acceleration data suitable for the present invention. Specifically, the stress-strain curve simulation method shown in the present invention is used to calculate a simulated stress-strain curve of a test object O, wherein the test object O is sandwiched between a mass m and a test platform PLAT , and an accelerometer acc1 is attached to the mass block m, and an accelerometer acc2 is attached to the test platform PLAT, so that the mass block m, the object O to be tested and the test platform PLAT fall downward when simulating free fall. acc1 and acc2 can measure the acceleration data associated with the mass m and the test platform PLAT, and calculate a simulated stress-strain data based on the acceleration data of the mass m and the test platform PLAT. In addition, the test platform PLAT is along a predetermined path (as shown in FIG. 1 , the free-fall path defined by two flat tracks). In this embodiment, the quality of the mass block m is 26.8 kg, and the height of the test platform PLAT from the ground is 30 inches (inch), so that the maximum speed of the test platform PLAT after it falls is approximately the same as the speed when it freely falls on the ground However, the test platform PLAT can also be lifted up by a buffer external force when it lands near the end of the predetermined path; the object O to be tested is expanded polyethylene (EPE) foam, the thickness of the foam is 50mm, and the density is 1.7pcf, but the above-mentioned parameters are only examples, and the present invention does not limit the experimental setup and parameters.

Please refer to FIG. 2 and FIG. 3 together, wherein FIG. 2 is a flow chart of a stress-strain curve simulation method according to an embodiment of the present invention; FIG. 3 is an example diagram showing an acceleration curve and an effective curve.

Step S10: Obtain the first acceleration curve and the second acceleration curve.

Part (a) of Figure 3 is an example diagram of the first acceleration curve a1 obtained by the accelerometer acc1, and part (b) of Figure 3 is an example diagram of the second acceleration curve a2 obtained by the accelerometer acc2, in which the first acceleration The curve a1 is a plurality of acceleration data related to the mass m, and the second acceleration curve a2 is a plurality of acceleration data related to the test platform PLAT, wherein the first acceleration curve a1 and the second acceleration curve a1 are actual acceleration values and A plot of the ratio of the acceleration due to gravity versus time (s).

In other words, during the period from the mass m, the object under test O, and the test platform PLAT to the ground, the accelerometers acc1 and acc2 respectively obtain multiple actual acceleration values, and the first acceleration curve a1 is obtained by the accelerometer acc1 The actual acceleration at different time points is divided by the gravitational acceleration to form a curve; the second acceleration curve a2 is a curve obtained by dividing the actual acceleration at different time points obtained by the accelerometer acc2 by the gravitational acceleration.

Step S20 : Extracting the part of the first acceleration curve and the second acceleration curve in the same time period to obtain the first effective curve and the second effective curve.

The acceleration data used to calculate the simulated stress-strain curve is preferably the data between the time when the mass m is about to compress the object O to be measured and the compressed amount of the object O reaches the maximum value, and this period of data ( The starting point of the first effective curve a_v1) shown in part (c) of Figure 3 is the first data point P1 corresponding to the first acceleration curve a1 of Figure 3 (a) and is greater than zero, and its ending point is The second data point P2 corresponding to the peak value of the first acceleration curve a2. Since the first effective curve a_v1 corresponds to a time period PD, the part of the same time period PD extracted from the second acceleration curve a2 in (b) of FIG. 3 is the second effective curve a_v2 .

Step S30: Obtain the strain curve of the object under test according to the first effective curve and the second effective curve.

The implementation of step S30 includes performing an integration procedure on the two effective curves a_v1 and a_v2 to obtain a first displacement curve d1 of part (c) of FIG. 5 and a second displacement curve d2 of part (d) of FIG. 5 , and subtracting the two displacement curves d1 and d2 to obtain the strain curve of the object under test. For example, the implementation of step S30 includes performing an integration procedure on the first effective curve a_v1 and the second effective curve a_v2 to obtain the first displacement curve d1 and the second displacement curve d2, which can be obtained according to the strain formula (ɛ=d/t ) Calculate the strain curve of the object O by using the two displacement curves d1 and d2, and its detailed implementation will be described in detail in the embodiment of FIG. 4 .

Please refer to step S40 first: calculating the stress curve of the object under test based on the first effective curve and the contact area between the mass block and the object under test.

Before calculating the stress data, first calculate the reaction force curve (F=ma) of the object O acting on the mass m based on the first effective curve a_v1 and the mass of the mass m, and then further based on the reaction force curve and mass The contact area between the block m and the test object O is calculated by the stress formula (σ=F/S) to calculate the test object stress curve (not shown in the figure) of the test object O. In this embodiment, Since the contact area between the mass m and the object O is a surface area of the mass m shown in Figure 1, when calculating the stress curve of the object to be measured, the mass m can contact the object O The area of the surface is referred to as the contact area.

In addition, after the strain curve of the test object is obtained in step S30 and the stress curve of the test object is obtained in step S40, the strain curve of the test object and the stress curve of the test object can be combined to obtain the measured stress-strain curve EXP as shown in FIG. 7 . It should be noted that step S40 in FIG. 2 is shown as continuing after step S30, but step S40 may also be executed before step S30, or executed simultaneously with step S30. The present invention does not apply to step S30 and step S40. The order of execution is restricted.

Step S50 : Calculate the simulated stress-strain curve based on the strain curve of the test object and the stress curve of the test object by an exponential equation, wherein the simulated stress-strain curve is used to continue the measured stress-strain curve EXP.

The exponential equation is, for example, a third-order exponential equation or a seventh-order exponential equation, and the method for calculating the simulated stress-strain curve includes using a final data point on the measured stress-strain curve EXP as a previous data point Prev_P, and using the The previous data point Prev_P is substituted into the index equation to calculate a post data point Cal_P, and then the previous data point is updated with the post data point Cal_P, so that the updated previous data point is substituted into the index equation to calculate the next post The detailed implementation of the data points will be described below with reference to FIG. 7 .

For a more detailed description of obtaining the strain curve according to the two effective curves in step S30 of FIG. 2 , please refer to FIG. 4 , which is a detailed flow chart of step S30 in FIG. 2 .

Step S301: Integrate the first effective curve to obtain a first speed integration curve; Step S302: Integrate the second effective curve to obtain a second speed integration curve. Since the two effective curves a_v1 and a_v2 are data related to acceleration, integrating the two effective curves a_v1 and a_v2 can respectively obtain a first speed integral curve and a second speed integral curve (not shown in the figure).

Step S303: Subtract the first initial velocity of the mass from multiple data points on the first velocity integral curve to obtain the first relative velocity curve; Step S304: Subtract the second initial velocity of the test platform from the data points on the second velocity integral curve multiple data points to obtain a second relative velocity curve.

Step S303 is to subtract the first initial velocity of the mass m from a plurality of velocity data points on the first velocity integral curve to obtain the first relative velocity curve v1 as shown in part (a) of Figure 5; and step S304 is to subtract the data points of multiple speeds on the second speed integral curve from the second initial speed of the test platform PLAT to obtain the second relative speed curve v2 shown in part (b) of Figure 5, wherein the mass The first initial velocity of m is the maximum velocity of mass m in the direction of falling downward (z-axis direction), which is equal to the second initial velocity of the test platform PLAT, that is, the first initial velocity and the second initial velocity are numerically equal It is equal to the maximum value on the second speed integral curve.

Step S305: Integrate the first relative velocity curve to obtain a first displacement curve; Step S306: Integrate the second relative velocity curve to obtain a second displacement curve.

Step S305 is to integrate the first relative velocity curve v1 to obtain the first displacement curve d1 as shown in part (c) of Figure 5; and step S306 is to integrate the second relative velocity curve v2 to obtain the (d ) part of the second displacement curve d2 shown. Accordingly, the displacement-time curve (d1) of the mass m and the displacement-time curve (d2) of the test platform PLAT can be obtained.

Step S307: Subtracting the first displacement curve from the second displacement curve to obtain a strain curve of the object under test.

Please also refer to FIG. 6 . FIG. 6 is an example diagram showing a strain curve obtained according to the first displacement curve and the second displacement curve. Please refer to part (a) of Figure 6 first, the first displacement curve d1 and the second displacement curve d2 are obviously different data, so subtracting the first displacement curve d1 and the second displacement curve d2 can obtain the data as shown in Figure 6 (b) The strain curve Δd of the object to be measured (in this example, the first displacement curve d1 is subtracted from the second displacement curve d2 to obtain the strain curve Δd of the object to be measured, but the present invention is not limited thereto). In addition, part (a) of Figure 6 shows that the first displacement curve d1 and the second displacement curve d2 are drawn in the same graph for easy understanding. In actual operation, the drawing of the two displacement curves can be omitted steps in the same diagram.

Please refer to FIG. 7 . FIG. 7 is an example diagram showing a measured stress-strain curve and a simulated stress-strain curve. After obtaining the strain curve Δd of the object to be measured in step S30 and the stress curve of the object to be measured in step S40, the strain curve Δd of the object to be measured and the stress curve of the object to be measured can be combined, and the two curves can be combined into the graph shown in Figure 7 Measured stress-strain curve EXP. Step S50 is implemented by substituting the previous data point Prev_P into the exponential equation to calculate the rear data point Cal_P, and a simulated curve segment formed by the previous data point Prev_P and the calculated rear data point Cal_P can be used as the simulated stress-strain curve SIM Wherein, when the first post-data point Cal_P is to be calculated, the previous data point Prev_P is preferably the last stress-strain data on the measured stress-strain curve EXP. After calculating the post data point Cal_P, the post data point Cal_P can be used to update the previous data point Prev_P, and the post data point Cal_P can be used as the next previous data point to calculate the next post data point following the post data point Cal_P, and The simulated stress-strain curve SIM is formed by sequentially concatenating multiple simulated curve segments formed in this way. In addition, when calculating the rear data points, it is preferable to use a fixed strain interval Δɛ as the basis for calculating the rear data points (that is, the interval between the strain value of the previous data point and the strain value of the rear data point is Δɛ), In this example, the strain interval Δɛ is, for example, 0.1, but the present invention is not limited thereto.

－（1）

－（2） In more detail, the exponential equation can include the following formula (1) and formula (2)

-(1)

-(2)

為一後模擬應力數據（例如，後數據點Cal_P的應力值）；

為一前模擬應力數據（例如，前數據點Prev_P的應力值），且如前所述，在欲計算出第一個後模擬應力數據時，前模擬應力數據較佳是實測應力應變曲線EXP上的最後一個應力數據。 In formula (1),

is a post-simulation stress data (for example, the stress value of post-data point Cal_P);

It is a pre-simulation stress data (for example, the stress value of the previous data point Prev_P), and as mentioned above, when the first post-simulation stress data is to be calculated, the pre-simulation stress data is preferably on the measured stress-strain curve EXP The last stress data for .

為每一該些模擬曲線段的一終端應力數據點（例如，後數據點Cal_P的應力值）；

為該終端應力數據點的前一個應力數據點（例如，前數據點Prev_P的應力值）；

為一後模擬應變數據（例如，後數據點Cal_P的應變值）；

為每一該些模擬曲線段的一終端應變數據點（例如，後數據點Cal_P的應變值）；

為該終端應變數據點的前一個應變數據點（即

的前一個應變數據點）；

為該指數方程式在

處的偏微分數值，其中

，

，且

與

之間的間隔可以為如前述的應變間隔Δɛ。 In formula (2),

a terminal stress data point for each of the simulated curve segments (for example, the stress value of the last data point Cal_P);

is the previous stress data point of the terminal stress data point (for example, the stress value of the previous data point Prev_P);

is a post-simulation strain data (for example, the strain value of post-data point Cal_P);

is a terminal strain data point for each of the simulated curve segments (for example, the strain value of the last data point Cal_P);

is the previous strain data point of the terminal strain data point (ie

the previous strain data point);

for this index equation in

The partial differential value at , where

,

,and

and

The interval between can be the strain interval Δɛ as mentioned above.

與

雖然皆可為後數據點Cal_P的應力值，然因

係基於公式（1）所計算出的應力值，而

係用於公式（2）中以於公式（1）計算出

，故

與

可以彼此相同或不同；同理，

與

可以彼此相同或不同，本發明不以此為限。 In addition, it should be noted that,

and

Although both can be the stress value of the last data point Cal_P, but because

is the stress value calculated based on formula (1), while

is used in formula (2) to calculate in formula (1)

, so

and

can be the same or different from each other; similarly,

and

may be the same as or different from each other, and the present invention is not limited thereto.

As mentioned above, after obtaining the measured stress-strain curve EXP and calculating the simulated stress-strain curve SIM in step S50 based on the measured stress-strain curve EXP, the simulated stress-strain curve SIM calculated in step S50 can be used to continue the measured The stress-strain curve EXP is used to obtain a complete stress-strain curve as shown in FIG. 7 , and the strain value of the last data point of the complete stress-strain curve can approach 1.

In summary, according to the stress-strain curve simulation method shown in one or more embodiments of the present invention, more accurate stress-strain simulation results can be obtained by obtaining the acceleration data of the mass block and the test platform during the drop test, Therefore, when the computer-aided engineering software (Computer Aided Engineering, CAE) is used to simulate the drop test, the simulation results that are more accurate and closer to the actual situation can be obtained. In addition, it is difficult to obtain a strain value closer to 1 in the conventional stress-strain test process, but according to the stress-strain curve simulation method shown in one or more embodiments of the present invention, it can be obtained in the strain range [0,1) A strain value close to 1 can be obtained in the middle, and a larger and more complete stress-strain data can be used as the basis for simulation when computer-aided engineering software is used for simulation.

Although the present invention is disclosed by the aforementioned embodiments, they are not intended to limit the present invention. Without departing from the spirit and scope of the present invention, all changes and modifications are within the scope of patent protection of the present invention. For the scope of protection defined by the present invention, please refer to the appended scope of patent application.

m: Mass block O: analyte PLAT: test platform acc1, acc2: accelerometer a1: The first acceleration curve a2: Second acceleration curve a_v1: the first valid curve a_v2: the second valid curve PD: time period d1: the first displacement curve d2: second displacement curve Δd: strain curve of the object to be measured EXP: measured stress-strain curve SIM: simulated stress-strain curve Prev_P: previous data point Cal_P: post data point Δɛ: strain interval

Figure 1 is a schematic diagram of the experimental setup for obtaining acceleration data. FIG. 2 is a flowchart of a stress-strain curve simulation method according to an embodiment of the present invention. FIG. 3 is an example diagram showing an acceleration curve and an effective curve. FIG. 4 is a detailed flowchart of step S30 in FIG. 2 . FIG. 5 is an example diagram showing velocity curves and displacement curves. FIG. 6 is an example diagram illustrating a strain curve obtained according to the first displacement curve and the second displacement curve. FIG. 7 is an example diagram showing measured stress-strain curves and simulated stress-strain curves.

Claims (10)

A stress-strain curve simulation method for calculating a simulated stress-strain curve of an object to be tested sandwiched between a mass block and a test platform, the method comprising: obtaining a first acceleration curve and a second acceleration curve Curves, wherein the first acceleration curve is associated with a plurality of acceleration data of the proof mass, and the second acceleration curve is associated with a plurality of acceleration data of the test platform; the first acceleration curve in a period of time is extracted Part to obtain a first effective curve, and extract the part of the second acceleration curve in the time period to obtain a second effective curve; obtain a test target according to the first effective curve and the second effective curve an object strain curve; calculate an analyte stress curve based on the first effective curve and a contact area between the mass block and the analyte; and use an exponential equation based on the analyte strain curve and the analyte The simulated stress-strain curve is calculated from the physical stress curve, wherein the simulated stress-strain curve is used to continue a measured stress-strain curve. The method according to claim 1, wherein the starting point of the first effective curve is the point where the first acceleration curve is greater than zero, and the ending point of the first effective curve is the peak point of the first acceleration curve. The method according to claim 1, wherein obtaining the strain curve of the object under test according to the first effective curve and the second effective curve comprises: respectively performing an integration procedure on the first effective curve and the second effective curve to obtain a first displacement curve and a second displacement curve; and subtracting the first displacement curve from the second displacement curve to obtain the strain curve of the object under test. The method as described in claim 3, wherein performing the integration procedure on the first effective curve comprises: integrating the first effective curve to obtain a first velocity integral curve; subtracting the first initial velocity of the mass from the first initial velocity a plurality of data points on a velocity integration curve to obtain a first relative velocity curve; and integrating the first relative velocity curve to obtain the first displacement curve. The method as described in claim 3, wherein performing the integration program on the second effective curve includes: integrating the second effective curve to obtain a second velocity integral curve; subtracting the second initial velocity of the test platform from the first integrating multiple data points on the velocity curve to obtain a second relative velocity curve; and integrating the second relative velocity curve to obtain the second displacement curve. The method as described in claim 1, wherein calculating the simulated stress-strain curve includes: using a final data point on the measured stress-strain curve as a previous data point; substituting the previous data point into the exponential equation to calculate a a subsequent data point; and updating the previous data point with the latter data point. The method according to claim 6, wherein the exponential equation is a third-order exponential equation or a seventh-order exponential equation, and there is a strain interval between the strain value of the previous data point and the strain value of the rear data point. The method as described in claim item 1, wherein the simulated stress-strain curve is formed by concatenation of multiple simulated curve segments, and the exponential equation includes:

,and

,in

is the post-simulation stress data;

is a pre-simulation stress data;

is a terminal stress data point for each of the simulated curve segments;

is the previous stress data point of the terminal stress data point;

is the post-simulation strain data;

is a terminal strain data point for each of the simulated curve segments;

is the previous strain data point of the terminal strain data point;

for this index equation in

The partial differential value at , where there is a strain interval between the terminal strain data point and its previous strain data point, and

,

. The method as described in claim 1, further comprising: combining the strain curve of the test object and the stress curve of the test object to obtain the measured stress-strain curve; and connecting the simulated stress-strain curve to the measured stress-strain curve to obtain A complete stress-strain curve. The method according to claim 1, wherein the stress curve system of the analyte is calculated based on the first effective curve and the contact area between the mass and the analyte: based on the first effective curve and the mass calculating a reaction force curve based on the mass of the block; and calculating the stress curve of the object under test based on the reaction force curve and the contact area.

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