CN112557220B - High-speed impact special-shaped piece orthotropic elastic constant virtual field synchronous characterization method - Google Patents

High-speed impact special-shaped piece orthotropic elastic constant virtual field synchronous characterization method Download PDF

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CN112557220B
CN112557220B CN202011263568.4A CN202011263568A CN112557220B CN 112557220 B CN112557220 B CN 112557220B CN 202011263568 A CN202011263568 A CN 202011263568A CN 112557220 B CN112557220 B CN 112557220B
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付佳伟
齐乐华
聂祥樊
朱开宇
汤毓源
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Northwestern Polytechnical University
Air Force Engineering University of PLA
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Air Force Engineering University of PLA
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    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
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    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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Abstract

The invention relates to a virtual field synchronous characterization method of orthotropic elastic constant of a high-speed impact special-shaped piece, which is characterized in that a proper special-shaped piece high-speed impact loading configuration is designed, so that a test piece can generate balanced positive strain and shearing strain under a unidirectional impact condition, a dynamic virtual field identification algorithm of orthotropic elastic parameters is established, and all parameters of orthotropic elasticity are synchronously and accurately identified from a plurality of impact loading moments by adopting a least square global optimization method. Compared with the background technology, the invention is not limited by one-dimensional stress wave and uniform deformation state assumption conditions, can realize multi-parameter global characterization of orthotropic elasticity only by one-time direct impact of a bullet and acquisition of a high-speed deformation field of a test piece, can furthest reduce the experiment quantity, does not need a huge rod system in a Hopkinson rod method, and simplifies an experimental device.

Description

High-speed impact special-shaped piece orthotropic elastic constant virtual field synchronous characterization method
Technical Field
The invention belongs to a dynamic mechanical property characterization method of materials, relates to a virtual field synchronous characterization method of orthotropic elastic constants of a high-speed impact special-shaped piece, and particularly relates to a multi-parameter synchronous characterization method of orthotropic elastic properties of materials under high-speed impact based on a dynamic virtual field method.
Background
In the fields of aviation, aerospace, weapons and the like, equipment such as aircrafts, armored vehicles and the like are frequently subjected to high-speed impact of foreign objects such as flying birds, shrapnel, shock waves and the like, and the dynamic mechanical properties of structural materials under the high-speed impact condition are closely related to the behaviors such as deformation, failure and the like of the structure. The dynamic mechanical properties of the material are generally obviously different from those of the material under the quasi-static condition, and the service safety of equipment is directly affected. Meanwhile, advanced structural materials such as fiber reinforced composite materials, alloy plates and the like have remarkable mechanical property anisotropism due to the forming process and tissue structure characteristics, so that the dynamic deformation and failure behaviors of the material structure are more complex. For a long time, hopkinson pressure bar systems are mainly adopted at home and abroad to represent dynamic mechanical properties of materials under high-speed impact conditions. The hopkinson bar method also has certain limitations as the most widely used dynamic mechanical property test method at present. Firstly, the method is limited by preconditions of one-dimensional stress wave transmission and uniform stress strain state, multiple impact experiments need to be carried out along different material directions for characterization of anisotropic mechanical properties of materials, the process is complex and tedious, and under the preconditions, the Hopkinson bar method is also difficult to realize characterization of property parameters of complex effects such as anisotropic material tensile shear coupling, double tensile coupling and the like from a monotonic stress strain state. Secondly, the conventional Hopkinson bar method is difficult to be applied to low-impedance materials such as rubber, and the like, because the transmission speed of stress waves in the low-impedance materials is low, the time required for a test piece to reach an equilibrium state after being impacted by the Hopkinson bar influences the effective test time of a system, and the impedance difference between the low-impedance test piece and the high-impedance impact bar can also cause attenuation of acquired signals and increase of noise influence.
With the rapid development of ultra-high speed imaging technology and digital image related technology, it has become possible to extract dynamic mechanical properties of materials using richer full-field deformation data. The document "pieron F, et al Philosophical Transactions of the Royal Society A,2014,372 (2023), 20130195" devised a high-speed impact loading configuration and experiment of rectangular plate members, and based on a virtual field method in the form of dynamic conditions, the young's modulus and poisson's ratio of the material were reversely calculated from the data of the high-speed strain field and acceleration field under the inertial effect of the test piece when a bullet directly impacted the test piece. Although the method realizes accurate identification of the isotropic elastic constant under the dynamic condition, for the anisotropic elastic constant, the characterization accuracy is obviously affected by the stress strain state of the test piece, and the global accurate characterization of the anisotropic parameter is difficult to ensure by adopting the method of impact loading of the test piece with the uniform section.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides a high-speed impact abnormal-shaped piece orthotropic elastic constant virtual field synchronous characterization method.
Technical proposal
A high-speed impact abnormal part orthotropic elastic constant virtual field synchronous characterization method is characterized by comprising the following steps:
step 1, developing a high-speed impact experiment of the special-shaped test piece: spraying speckles on the surface of the special-shaped test piece; the air cannon is adopted to launch the bullet, and the bullet directly impacts one end of the special-shaped test piece at a high speed; shooting a digital image of an inertial acceleration stage of a test piece under high-speed impact; calculating a digital image by adopting digital image correlation to obtain a full-field deformation field of the test piece in an inertial acceleration stage under high-speed impact, and calculating the deformation field to obtain a strain field, a strain rate field, an acceleration field and acceleration a of each point;
step 2, constructing a virtual field constitutive parameter identification algorithm at any loading moment under a dynamic condition aiming at the orthotropic elastic parameter:
according to the equilibrium equation
Figure BDA0002775394280000021
Orthotropic elasticity, stress tensor sigma
Figure BDA0002775394280000031
Q xx ,Q yy ,Q xy And Q ss Anisotropic elastic parameters to be characterized; epsilon x ,ε y ,γ s Representing the strain field and the strain at each point;
wherein σ is the stress tensor, ρ is the material density, a is the acceleration vector, u * For a defined virtual displacement vector, a virtual strain tensor ε * From u * Deriving;
substituting the constitutive relation in equation 3 into equation 2, balance equation 2 is:
Figure BDA0002775394280000032
wherein S is the surface area of the test piece; selecting four independent virtual displacement fields u * Constructing a quaternary once equation set about four rigidity coefficients to be solved, and obtaining four rigidity coefficients corresponding to any loading moment by solving the equation set;
step 3, constructing a virtual field constitutive parameter optimization recognition algorithm with multiple loading moments under a dynamic condition aiming at the orthotropic elastic parameters:
defining the j-th loading moment, the 1 st group virtual field corresponds to the internal virtual work and the acceleration virtual work respectively as
Figure BDA0002775394280000033
And->
Figure BDA0002775394280000034
The internal virtual work and acceleration virtual work corresponding to the 2 nd group virtual field are +.>
Figure BDA0002775394280000035
And->
Figure BDA0002775394280000036
The internal virtual work and acceleration virtual work corresponding to the 3 rd group virtual field are respectively +.>
Figure BDA0002775394280000037
And->
Figure BDA0002775394280000038
The internal virtual work and acceleration virtual work corresponding to the 4 th group virtual field are respectively +.>
Figure BDA0002775394280000039
And->
Figure BDA00027753942800000310
On the basis of this, an objective function f is defined which is equal to the sum of the virtual work in the test piece and the acceleration virtual work at a plurality of loading moments, i.e.
Figure BDA00027753942800000311
Where k is the total number of selected loading moments;
and (3) as the sum of the virtual work in the test piece and the acceleration virtual work at any moment is zero, performing least square global optimization on the objective function f to obtain four dynamic orthotropic elastic parameters of the special-shaped plate under the high-speed impact condition.
For non-special-shaped plates, notches, corners or holes are designed on the plates with the uniform cross section to form the special-shaped plates.
Advantageous effects
The invention provides a virtual field synchronous characterization method for orthotropic elastic constants of a high-speed impact special-shaped piece, which is characterized in that a proper special-shaped piece high-speed impact loading configuration is designed, so that a test piece can generate balanced positive strain and shearing strain under a unidirectional impact condition, a dynamic virtual field identification algorithm for orthotropic elastic parameters is established, and all parameters of orthotropic elasticity are synchronously and accurately identified from a plurality of impact loading moments by adopting a least square global optimization method. Compared with the background technology, the invention is not limited by one-dimensional stress wave and uniform deformation state assumption conditions, can realize multi-parameter global characterization of orthotropic elasticity only by one-time direct impact of a bullet and acquisition of a high-speed deformation field of a test piece, can furthest reduce the experiment quantity, does not need a huge rod system in a Hopkinson rod method, and simplifies an experimental device.
The invention has the beneficial effects that:
1) Compared with the existing dynamic mechanical property testing method, the method has the advantages that by designing the proper test piece configuration, the test piece simultaneously generates rich positive strain and shear strain under simple unidirectional high-speed impact loading, so that four orthogonal anisotropic elastic parameters are obtained from one unidirectional impact loading experiment, the experiment number is reduced to the greatest extent, the test piece is in a wide strain rate level range, and the represented constitutive parameters can represent material properties in the wide strain rate range;
2) Compared with the traditional Hopkinson pressure bar method, the invention breaks through the condition limitation of one-dimensional stress wave transmission and uniform stress strain state of the traditional method, improves the flexibility of an experimental method, realizes the synchronous characterization of dynamic anisotropic properties which are difficult to be completed by the traditional method, and can be used for characterizing the property parameters of complex coupling effects such as composite material tensile shear coupling, double tensile coupling and the like which are difficult to be characterized by the traditional method;
3) Compared with the traditional Hopkinson pressure bar method, the experimental device required by the dynamic anisotropic mechanical property characterization method omits a huge Hopkinson bar system, and the required impact device only comprises an air cannon and an impact bullet, so that compared with the Hopkinson bar system experimental device, the space volume required by the device is greatly reduced, and the experimental system is simple and convenient to assemble.
Drawings
FIG. 1 is a high-speed impact loading configuration diagram of two special-shaped test pieces and one rectangular test piece designed according to the invention;
FIG. 2 is a cloud plot of the strain field at 10 microseconds under high-speed impact of three test pieces;
FIG. 3 is a cloud plot of strain rate fields at 10 microseconds under high-speed impact of three test pieces;
FIG. 4 is a cloud plot of acceleration fields at 10 microseconds under high-speed impact of three test pieces;
FIG. 5 is a graph showing stress state distribution of each point in the first 10 microseconds under high-speed impact of three test pieces;
reference numerals illustrate: in fig. 1 to 5, (a) shows the results of the M-type test piece, (b) shows the results of the double-sided notched test piece, and (c) shows the results of the rectangular test piece.
Detailed Description
The invention will now be further described with reference to examples, figures:
the invention comprises the following steps:
step one: designing a high-speed impact loading configuration of the special-shaped test piece;
removing part of materials on the rectangular plate to enable the test piece to obtain structural characteristics such as gaps, corners and the like, wherein the test piece can generate remarkable positive strain and shear strain at the same time under high-speed impact of bullets, and the strain rate distribution of the test piece can cover a wide horizontal range; machining a test piece according to the designed configuration;
step two: developing a high-speed impact experiment of the special-shaped test piece;
spraying speckles on the surface of the special-shaped test piece; the air cannon is adopted to launch the bullet, and the bullet directly impacts one end of the special-shaped test piece at a high speed; acquiring a digital image of the inertia acceleration stage of the test piece under high-speed impact by adopting an ultra-high-speed imaging system, acquiring a full-field deformation field of the inertia acceleration stage of the test piece under high-speed impact by digital image correlation operation, and calculating to obtain a corresponding strain field, strain of each point, a strain rate field, an acceleration field and acceleration a of each point;
step three: constructing a virtual field constitutive parameter identification algorithm at any loading moment under a dynamic condition aiming at the orthotropic elastic parameter;
for a homogeneous deformable solid test piece with a volume V and under the action of a load vector T on the boundary, according to the virtual work principle, the balance equation of the internal virtual work, the external virtual work and the acceleration virtual work is provided
Figure BDA0002775394280000051
Wherein σ is the stress tensor, ρ is the material density, a is the acceleration vector, u * For a defined virtual displacement vector, a virtual strain tensor ε * From u * Deriving; by selecting an appropriate virtual displacement field u * Thereby eliminating the contribution of the load vector T to the external virtual work, the following balance equation can be obtained
Figure BDA0002775394280000061
For orthotropic elasticity, the stress tensor σ can be expressed as
Figure BDA0002775394280000062
Wherein Q is xx ,Q yy ,Q xy And Q ss Anisotropic elastic parameters to be characterized;
Figure BDA0002775394280000063
representing the strain field and the strain at each point;
substituting constitutive relation in equation (3) into equation (2) can assume plane stress state for plane plate test piece, and thus, equilibrium equation (2) can be replaced with
Figure BDA0002775394280000064
Wherein S is the surface area of the test piece; selecting four independent virtual displacement fields u * A quaternary once equation set about four rigidity coefficients to be solved can be constructed, and the four rigidity coefficients corresponding to any loading moment can be obtained by solving the equation set;
step four: constructing a virtual field constitutive parameter optimization recognition algorithm at multiple loading moments under a dynamic condition aiming at the orthotropic elastic parameters;
defining the j-th loading moment, the 1 st group virtual field corresponds to the internal virtual work and the acceleration virtual work respectively as
Figure BDA0002775394280000065
And->
Figure BDA0002775394280000066
The internal virtual work and acceleration virtual work corresponding to the 2 nd group virtual field are +.>
Figure BDA0002775394280000067
And->
Figure BDA0002775394280000068
The internal virtual work and acceleration virtual work corresponding to the 3 rd group virtual field are respectively +.>
Figure BDA0002775394280000069
And->
Figure BDA00027753942800000610
The internal virtual work and acceleration virtual work corresponding to the 4 th group virtual field are respectively +.>
Figure BDA00027753942800000611
And->
Figure BDA00027753942800000612
On the basis of this, an objective function f is defined which is equal to the sum of the virtual work in the test piece and the acceleration virtual work at a plurality of loading moments, i.e.
Figure BDA0002775394280000071
Wherein k is the total number of the selected loading moments, and the sum of the virtual work in the test piece and the virtual work of the acceleration at any moment is zero, so that the global optimal solution of four orthotropic elastic parameters at multiple moments can be obtained by minimizing the objective function f; when solving, firstly inputting any initial value, starting an iterative loop until the operation converges;
substituting experimental data to represent the dynamic orthotropic elastic constant of the measured material under the high-speed impact condition;
substituting the strain field and the acceleration field at any moment obtained in the high-speed impact experiment in the second step into the orthotropic elastic parameter virtual field constitutive parameter identification algorithm at the single loading moment established in the third step, and solving to obtain the orthotropic elastic parameter corresponding to the moment;
substituting the strain fields and the acceleration fields at a plurality of moments obtained in the high-speed impact experiment in the second step into the virtual field constitutive parameter identification algorithm of the orthotropic elastic parameter at a plurality of loading moments established in the fourth step, and solving to obtain the global optimized orthotropic elastic parameter at a plurality of moments.
The following examples refer to fig. 1-5.
Example 1: numerical simulation of a high-speed impact experiment is carried out by adopting finite element software, a material constitutive model and model parameters are set, unidirectional high-speed impact loading of a test piece is simulated, simulation data of a strain field, a strain rate field and an acceleration field 10 microseconds before the test piece are derived, and the simulation data are substituted into a written anisotropic elastic constant dynamic virtual field
Figure BDA0002775394280000073
And the characterization program is used for identifying the orthotropic elastic constant based on the simulation data, comparing the parameter characterization result with the reference value of the input model, and verifying the accuracy of the method.
Step one: designing a high-speed impact loading configuration of a special-shaped test piece, and performing finite element software
Figure BDA0002775394280000074
Removing part of materials from the rectangular plate, so that the test piece obtains structural characteristics such as gaps, corners and the like, the test piece can generate remarkable positive strain and shear strain at the same time under the high-speed impact of bullets, and the strain rate distribution of the test piece can cover a wide horizontal range; the test piece impact loading configuration designed in the embodiment is shown in fig. 1, and comprises an M-shaped test piece impact loading configuration, a double-side notch test piece impact loading configuration and a rectangular test piece impact loading configuration for comparison;
step two: in finite element software
Figure BDA0002775394280000072
Performing high-speed impact finite element numerical simulation on three test piece configurations in the first step, wherein geometric parameters, material orthotropic model parameters and impact parameters of a finite element model are shown in an attached table 1, and strain field, strain rate field and acceleration field simulation data of each unit node of the three test pieces in the first 10 microseconds in the impact process are derived from the finite element numerical simulation results; FIG. 2 shows three impact loading finite element numerical simulations at 10 μsFig. 3 shows a strain rate field cloud for three impact loaded finite element numerical simulations at 10 microseconds, fig. 3 shows that M-type and double sided notched test pieces can cover a wider strain rate level, fig. 4 shows an acceleration field cloud for three impact loaded finite element numerical simulations at 10 microseconds (in M/s 2 ) FIG. 5 shows stress state distribution diagrams of each point in the first 10 microseconds under high-speed impact of three test pieces, and FIG. 5 shows that the M-shaped test pieces and the two-side notch test pieces can generate higher level of shear strain under unidirectional impact, and the stress state of the M-shaped test pieces and the two-side notch test pieces is richer than that of the rectangular test pieces;
TABLE 1 finite element numerical simulation parameter Table
Figure BDA0002775394280000081
Step three: constructing a virtual field constitutive parameter identification algorithm at any loading moment under dynamic conditions aiming at orthotropic elastic parameters, and assuming a plane stress state for a plane plate test piece adopted in the second step, thereby obtaining a balance equation
Figure BDA0002775394280000082
Wherein S is the surface area of the test piece;
select group 1 virtual field
Figure BDA0002775394280000091
The virtual field satisfies the virtual displacement on the left and right loading boundaries (x=0 and x=l)
Figure BDA0002775394280000092
And->
Figure BDA0002775394280000093
All are zero, so that the external virtual work under the action of external force is zero, therefore, the formula (7) is substituted into the formula (6)Obtaining the equilibrium equation corresponding to the virtual field 1, namely
Q xx ∫ S (2x-L)ε x dS+Q xy ∫ S (2x-L)ε y dS＝-ρ∫ S x(x-L)a x dS (8)
Because of the discretization of the finite element model elements, the integral sign in equation (8) should be approximated as a discrete sum, equation (8) being approximated as
Figure BDA0002775394280000094
Wherein n is the total number of finite element model units of the test piece (in the experiment, the number of points corresponding to the full-field deformation measurement data), and x (i) ，
Figure BDA0002775394280000095
Figure BDA0002775394280000096
S and S (i) Respectively representing the x-coordinate, strain epsilon of the ith cell x Acceleration a x And a cell area;
select group 2 virtual field
Figure BDA0002775394280000097
The corresponding second equilibrium equation is
Figure BDA0002775394280000098
Select group 3 virtual field
Figure BDA0002775394280000099
The corresponding third equilibrium equation is
Figure BDA0002775394280000101
Select group 4 virtual field
Figure BDA0002775394280000102
The corresponding fourth equilibrium equation is
Figure BDA0002775394280000103
So far, a quaternary once equation set about four rigidity coefficients to be solved can be constructed, and the four rigidity coefficients corresponding to any loading moment can be obtained by solving the equation set; by using
Figure BDA0002775394280000105
Programming a calculation program corresponding to the algorithm;
step four: substituting the finite element simulation data at different moments in the second step into the virtual field constitutive parameter identification algorithm program written in the third step at the single loading moment to represent the dynamic orthotropic elastic constants of the three test pieces at different high-speed impact loading moments, wherein the representation result of the first 10 microseconds is shown in the attached table 2; the attached table 2 shows that the characteristic results at different loading moments have larger fluctuation, and the parameter characteristic results of the M-type test piece and the double-notch test piece are obviously superior to those of rectangular test pieces with equal sections in precision and stability, wherein Q is as follows xx The characterization accuracy and stability are highest, the rectangular test piece cannot obtain an effective shear modulus characterization result, which is caused by insufficient shear stress states, and the stress state distribution diagram of each point in the first 10 microseconds under high-speed impact of the three test pieces in the figure 5 can verify the conclusion;
TABLE 2 characterization of the orthotropic elastic parameters of the three configurations at different impact loading times
Figure BDA0002775394280000104
Figure BDA0002775394280000111
Step five: virtual field constitutive parameter optimization recognition algorithm at multiple loading time under dynamic condition is constructed aiming at orthotropic elastic parameters, and inner virtual work and acceleration virtual work corresponding to the 1 st group virtual field are respectively defined as at the j loading time
Figure BDA0002775394280000112
And->
Figure BDA0002775394280000113
The internal virtual work and acceleration virtual work corresponding to the 2 nd group virtual field are +.>
Figure BDA0002775394280000114
And->
Figure BDA0002775394280000115
The internal virtual work and acceleration virtual work corresponding to the 3 rd group virtual field are respectively +.>
Figure BDA0002775394280000116
And->
Figure BDA0002775394280000117
The internal virtual work and acceleration virtual work corresponding to the 4 th group virtual field are respectively +.>
Figure BDA0002775394280000118
And->
Figure BDA0002775394280000119
On the basis of this, an objective function f is defined which is equal to the sum of the virtual work in the test piece and the acceleration virtual work at a plurality of loading moments, i.e.
Figure BDA00027753942800001110
Wherein the method comprises the steps ofk is the total number of the selected loading moments, in the embodiment, k is 10, and because the sum of the virtual work in the test piece and the virtual work of the acceleration is zero at any moment, the global optimal solution of four orthotropic elastic parameters at multiple moments can be obtained by minimizing the objective function f; by using
Figure BDA00027753942800001111
Programming a calculation program corresponding to the algorithm;
step six: substituting the finite element simulation data of the first 10 microsecond impact loading moment in the second step into the virtual field constitutive parameter optimization recognition algorithm program of the multiple loading moment written in the fifth step to obtain the dynamic orthotropic elastic constant global optimization characterization result of three test pieces in the first 10 microsecond of the high-speed impact loading stage; when solving, firstly inputting any initial value, starting iterative loop until operation is converged, and in this embodiment, the definition of upper and lower optimization is [10 ] 6 10 6 10 6 10 6 ]And [1 1 1 1 ]]The initial value is arbitrarily selected as [10000 10000 10000 10000 ]]The method comprises the steps of carrying out a first treatment on the surface of the The characterization results are shown in the attached table 3; the attached table 3 shows that compared with a single-moment characterization method, the global characterization precision of the orthotropic elastic constant can be remarkably improved by adopting a multi-moment global optimization characterization method, wherein the M-shaped test piece and the double-notch test piece can reach extremely high characterization precision, and the method is obviously superior to a rectangular test piece with an equal section.
TABLE 3 Global optimization characterization of dynamic orthotropic elastic constants for the three test pieces within the first 10 microseconds
Figure BDA0002775394280000121
Example 1 shows that the orthotropic elastic constant virtual field synchronous characterization method based on the special-shaped piece high-speed impact can realize multi-parameter single-time experimental synchronous characterization of the orthotropic elastic constant of the material under dynamic conditions, and has high accuracy and simple loading configuration.
Example 2: the orthotropic elastic constant virtual field synchronous characterization experimental method based on the special-shaped piece high-speed impact selects long fiber reinforced resin matrix composite materials as materials; the difference between this embodiment and embodiment 1 is that the deformation field and the corresponding strain field, strain rate field and acceleration field of the long fiber reinforced resin matrix composite test piece under high-speed impact condition are obtained by the ultra-high speed imaging system and digital image correlation operation, and other steps, such as test piece configuration, loading process, data substitution, virtual field selection, program operation, etc., are the same as those of embodiment 1.

Claims (2)

1. A high-speed impact abnormal part orthotropic elastic constant virtual field synchronous characterization method is characterized by comprising the following steps:
step 1, developing a high-speed impact experiment of the special-shaped test piece: spraying speckles on the surface of the special-shaped test piece; the air cannon is adopted to launch the bullet, and the bullet directly impacts one end of the special-shaped test piece at a high speed; shooting a digital image of an inertial acceleration stage of a test piece under high-speed impact; calculating a digital image by adopting digital image correlation to obtain a full-field deformation field of the test piece in an inertial acceleration stage under high-speed impact, and calculating the deformation field to obtain a strain field, a strain rate field, an acceleration field and acceleration a of each point;
step 2, constructing a virtual field constitutive parameter identification algorithm at any loading moment under a dynamic condition aiming at the orthotropic elastic parameter:
according to the equilibrium equation
Figure FDA0002775394270000011
Orthotropic elasticity, stress tensor sigma
Figure FDA0002775394270000012
Q xx ,Q yy ,Q xy And Q ss Anisotropic elastic parameters to be characterized; epsilon x ,ε y ,γ s Representing the strain field and the strain at each point;
wherein σ is the stress tensor, ρ is the material density, a is the acceleration vector, u * For a defined virtual displacement vector, a virtual strain tensor ε * From u * Deriving;
substituting the constitutive relation in equation 3 into equation 2, balance equation 2 is:
Figure FDA0002775394270000013
wherein S is the surface area of the test piece; selecting four independent virtual displacement fields u * Constructing a quaternary once equation set about four rigidity coefficients to be solved, and obtaining four rigidity coefficients corresponding to any loading moment by solving the equation set;
step 3, constructing a virtual field constitutive parameter optimization recognition algorithm with multiple loading moments under a dynamic condition aiming at the orthotropic elastic parameters:
defining the j-th loading moment, the 1 st group virtual field corresponds to the internal virtual work and the acceleration virtual work respectively as
Figure FDA0002775394270000021
And->
Figure FDA0002775394270000022
The internal virtual work and acceleration virtual work corresponding to the 2 nd group virtual field are +.>
Figure FDA0002775394270000023
And->
Figure FDA0002775394270000024
The internal virtual work and acceleration virtual work corresponding to the 3 rd group virtual field are respectively +.>
Figure FDA0002775394270000025
And->
Figure FDA0002775394270000026
The internal virtual work and acceleration virtual work corresponding to the 4 th group virtual field are respectively +.>
Figure FDA0002775394270000027
And->
Figure FDA0002775394270000028
On the basis of this, an objective function f is defined which is equal to the sum of the virtual work in the test piece and the acceleration virtual work at a plurality of loading moments, i.e.
Figure FDA0002775394270000029
Where k is the total number of selected loading moments;
and (3) as the sum of the virtual work in the test piece and the acceleration virtual work at any moment is zero, performing least square global optimization on the objective function f to obtain four dynamic orthotropic elastic parameters of the special-shaped plate under the high-speed impact condition.
2. The high-speed impact special-shaped piece orthotropic elastic constant virtual field synchronization characterization method according to claim 1, wherein the method comprises the following steps of: for non-special-shaped plates, notches, corners or holes are designed on the plates with the uniform cross section to form the special-shaped plates.
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