CN105157588A - Multi-dimensional synchronous optimized measurement method for strain localization band interval evolution rule - Google Patents
Multi-dimensional synchronous optimized measurement method for strain localization band interval evolution rule Download PDFInfo
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Abstract
The invention provides an observation method of an evolution rule of a strain localization band interval with a stress or strain. The method comprises: a digital image of a testing sample during a loading process is obtained by using a shooting device; a strain field with high smoothness is obtained by using a sub-pixel digital image correlation method and a bicubic spline interpolation method; strain data of each tested strain localization band are obtained; an initial value of iteration is set and one more dimension of any initial value is set than the number of strain localization bands, synchronous iteration is carried out continuously by using a swarm intelligence algorithm to reduce deviation between data and test solutions of all strain localization bands gradually, and then a unique strain localization band angle and respective different intercepts are obtained; and an interval between any two adjacent strain localization bands is calculated based on a distance formula between two parallel lines. The method has the following beneficial effects: accuracy and uniqueness of a measurement result can be guaranteed; a strain localization band interval evolution rule can be obtained; and automatic batch high-efficiency measurement can be realized.
Description
Technical Field
The invention relates to a strain localization zone spacing measurement technology, and belongs to the fields of geotechnical mechanics, geotechnical engineering, experimental mechanics, geomechanics, engineering material mechanical property tests and the like.
Background
Strain localization, which is a phenomenon in which strain observed before material failure is concentrated in a narrow band-shaped region, can be classified into shear strain localization, tensile strain localization, and compressive strain localization by load type. The strain localization phenomena can be observed at different levels, for example, reticular slip lines on the grain scale, crossed minor faults on the engineering scale, and reticular geological structures and seismic zones on the crust scale can all be attributed to the strain localization phenomena (Wang Chi, Panyi, Strain localization phenomena in geological disasters, geological disasters and environmental protection, 2001,12(4): 1-5; Wang Chi, Zhao Yangsheng, red-generation, etc.. the conjugate shear fracture zone numerical simulation of seismic mass models, disaster prevention and reduction engineering bulletins, 2004,24(2): 119-125). The strain localization phenomenon often exists in a network form, and thus, the measurement of the distance between the strain localization bands becomes an important problem which cannot be avoided in the research of the strain localization phenomenon.
Currently, two methods are mainly used for measuring the strain localization band spacing: the spacing between the macroscopic crack faces was measured using a ruler and digital imaging techniques as the spacing of the strain localizing tape. In fact, this measurement method has a large error, the measurement results vary from person to person, the workload is large, it is difficult to achieve automated, batch, high-efficiency measurement, the amount of data obtained is limited, and the pitch of the crack surface is measured, not the pitch of the strain localization zone. During the starting and development process of the strain localization belt, due to the difference of deformation stages and the adjustment of stress fields, the direction and the position of strain localization can be changed properly. Without any theory, it is believed that the strain-localized band spacing is equivalent to the crack face spacing. To accurately measure the strain-localized band spacing, attention must be paid to the strain field, which becomes non-uniform before cracks appear, the change is not easily observed by naked eyes, and a continuously developed digital image correlation method (Wang scholar, Duyao and Panyi, Experimental research of strain distribution and strain gradient of a uniaxial compression sand sample based on a DIC coarse-fine search method, geotechnical engineering report, 2012,34(11): 2050) 2057, Wang scholar, Duyao and Panyi, comparison of the digital image correlation method considering first-order and second-order displacement gradients in shear zone measurement, engineering mechanics, 2013,30(7): 282-reservoir 287, Wang scholar, Duyao and Panyi, digital image correlation method observation of local and overall volume strain of the uniaxial compression sand sample, geotechnical engineering report, 2014,36(9): 1648-reservoir 1656) provides a convenient condition for accurate measurement of a strain field. The digital image correlation method is a photometric mechanical method and has the advantages of simple measuring equipment, low requirement on measuring environment and high measuring precision.
The invention provides a method for measuring the distance between strain localization zones by adopting a digital image correlation method. The method is characterized in that a strain field with better smoothness, which is obtained by a sub-pixel digital image correlation method and a bicubic spline interpolation method, is used as a basis, the measurement problem of the unique strain localization band spacing is attributed to a multi-dimensional synchronous optimization problem, the deviation between each strain localization band data and a tentative solution (each line segment) is gradually reduced by utilizing a group intelligent algorithm through continuous synchronous iteration, and the measurement of the unique strain localization band angle and the strain localization band spacing of all data is finally realized.
Disclosure of Invention
In order to solve the problems of low precision, low efficiency, limited acquired data quantity and non-unique obtained result of the conventional strain localization band interval measurement method, the invention provides a multi-dimensional synchronous optimization measurement method of a strain localization band interval evolution rule based on a digital image correlation method, which improves the measurement efficiency and precision, can acquire abundant data quantity and has a unique obtained result.
The invention is characterized by comprising the following steps:
step 1: acquiring a digital image of the sample containing the speckle surface under the loading condition by using shooting equipment (a digital camera or a CCD camera);
step 2: acquiring a deformation field of the surface of the sample by using a sub-pixel digital image correlation method: strain of horizontal linexStrain of vertical lineyGamma, shear strainxyAnd maximum shear strain gammamax；
And step 3: setting a calculation region, and acquiring strain data of the center and the vicinity of each strain localization band, wherein the calculation region can be 1 quadrilateral region containing a plurality of strain localization bands, or a set of quadrilateral regions containing 1 strain localization band;
for the case where the calculation region is a 1 quadrilateral region containing multiple strain localization zones:
firstly, setting 1 quadrilateral calculation area containing a plurality of strain localization zones;
then, according to the strain field, determining the number m of strain localization zones with consistent trend;
then, various strain fields with better smoothness in a calculation area are obtained by utilizing an interpolation method;
finally, setting a plurality of elongated quadrilateral regions by using the roughly estimated angles and widths of the measured strain localization bands, wherein each elongated quadrilateral region only comprises 1 strain localization band, and acquiring strain data of the center of each strain localization band and the vicinity of the center;
for the case where the calculation region is a set of quadrilateral regions containing 1 strain localization zone:
firstly, determining the number m of strain localization zones with consistent trend according to a strain field;
then, setting a plurality of long and narrow quadrilateral regions as calculation regions by using the roughly estimated angles and widths of the measured strain localization bands, wherein each long and narrow quadrilateral region only comprises 1 strain localization band;
then, various strain fields with better smoothness in a calculation area are obtained by utilizing an interpolation method;
finally, strain data of the center of each strain localization zone and the vicinity of the strain localization zone are obtained;
and 4, step 4: setting n iteration initial values and related iteration parameters for each strain localization zone, wherein for any initial value (a series of parallel line segments), the dimension of the initial value is m +1 and comprises 1 slope and m intercepts, and acquiring the common slope and different intercepts of each line segment by continuously and synchronously iterating by using a group intelligent algorithm;
and 5: and calculating the distance between any two adjacent strain localization bands by using a distance formula between parallel lines.
Further wherein said acquiring a digital image of the specimen under load containing the speckle surface further comprises: if the natural texture on the surface of the sample can be used as a speckle field, the speckle field does not need to be manufactured manually, otherwise, the artificial speckle field is sprayed by using paint, pigment, ink and the like, the sample is loaded by using a testing machine or a loading device, and meanwhile, the image of the speckle field is recorded by using shooting equipment.
Further, the obtaining of the deformation field of the sample surface by using the sub-pixel digital image correlation method further comprises: selecting several recorded images, setting related calculation parameters and calculation modes, calculating displacement field and strain field of the images by using sub-pixel digital image correlation method, obtaining strain field by performing central difference on the displacement field, and obtaining maximum shear strain gammamaxByx、yAnd gammaxyTo obtain
Further, wherein the consistently oriented strain localization zone refers to a collection of strain localization zones in a network of strain localization zones that are substantially at the same angle.
Further, wherein the acquiring the strain data at and near the center of each strain localization zone further comprises: and setting a critical strain parameter, and taking data exceeding the critical strain parameter as data of the measured strain localization zone.
Further wherein the width direction dimension of the elongate quadrilateral areaThe average particle diameter of the material can be 20-60 times, namely 1-3 times of the width of the strain localization belt; the critical strain parameter is determined empirically and may generally be taken as γ in the calculated regionmax60% or more of the maximum value.
Further, the initial iteration value includes an initial value of a common slope of line segments corresponding to each strain localization zone and initial values of different intercepts, so that the dimension of the initial value is 1 more than the number m of the strain localization zones, and any initial iteration value is set to be Ωi＝{ki,b1i,b2i,...,bmiIn which k isiInitial value of common slope, { b1i,b2i,...,bmiThe values are the initial values of the different intercepts.
Further, the swarm intelligence algorithm can be selected from particle swarm optimization algorithm, genetic algorithm, differential evolution algorithm and other algorithms.
Further, the common slope and the different intercepts of the line segments mean that the m line segments determined by the parameters are closest to the strain data at and near the center of each strain localization zone, namely, the deviation reaches the minimum
Wherein, subscript l represents any one of n iteration initial values, and l is 1-n; c. CiThe number of data representing the ith strain localization zone, typically, the number of data for different strain localization zones is different, i being 1 to m; sijOrdinate of j-th data representing i-th strain localization zone, i being 1 to m, j being 1 to ci，sij＝sij(xij)，xijIs the abscissa of the data; f. ofijRepresenting the ordinate of the segment approximating the ith strain-localized band at the jth datum, due to fijIs a linear function, therefore, fij＝(kl,bil)＝klxij+bil，klIs the common slope of 1 initial value (line segments), bilIs a different intercept of 1 initial value,(s)ij-fij)2Representing the square of the deviation between 1 strain data point and 1 line segment, for all data c on one strain localization bandiSumming, representing the square of the deviation between the strain data of one strain-localized band and 1 line segment, and summing each strain-localized band to represent the square of the deviation between the strain data of each strain-localized band and each line segment, by continuously synchronized iterations, to arrive at the minimum vector Ω*＝{k*,b1*,b2*,...,bm*I.e. the only and best result.
Further, the synchronous iteration is a process of continuously updating an iteration initial value or a tentative solution, the updating principle of the tentative solution is different for different group intelligence algorithms, but the strategies of information sharing, mutual learning and influence, and elimination of the trial and the survival of the suitable person among different tentative solutions are basically considered, and the conditions of the end of the iteration include two conditions: 1) the iteration times reach the maximum algebra; 2) the iteration result has already tended to be stable (although the number of iterations has not reached the maximum number of generations).
Further, wherein the iteration parameters include: the maximum algebra, the number of initial iteration values, the threshold condition of iteration ending and the iteration parameters required by different group intelligent algorithms, for example, for the particle swarm optimization algorithm, the parameters such as the maximum speed of particle flight, the learning factor and the inertia constant are required.
Further, wherein the spacing d of any two adjacent strain localization zonesiIs given by the formula
di＝|b(i+1)*-bi*|sinθ*＝|b(i+1)*-bi*|sin[arctan(k*)],i＝1～(m-1)(3)
The multi-dimensional synchronous optimization measurement method for the evolution rule of the strain localization zone interval based on the digital image correlation method can realize automatic, rapid and accurate measurement of the strain localization zone interval, and has rich obtained information and can ensure the uniqueness of the measurement result.
Drawings
FIG. 1 is a flow chart of a multi-dimensional synchronous optimization measurement method for a strain localization band interval evolution law;
FIG. 2 is a schematic view of the digital image acquisition device in a loaded condition; in the figure, 1-sample, 2-surface containing speckle, 3-light source, 4-shooting device, 5-computer;
FIG. 3 is a program interface diagram of a digital image correlation method for autonomic development based on particle swarm optimization and Newton-Raphson iterative methods;
FIG. 4 is a schematic diagram of a multi-dimensional synchronous optimization process, wherein FIG. 4-a is setting a calculation region; FIG. 4-b is a graph illustrating the range of strain localization zones determined to be consistently oriented; FIG. 4-c is a graph of strain data taken at and near the center of each strain localization zone; 4-d are setting iteration initial values and iteration parameters; 4-e are the final results of the iteration (only the true solution that minimizes the objective function is given); in the figure, 6-calculation region, 7-strain localization zone, 7-1-strain localization zone with uniform trend (measured strain localization zone), 7-2-strain localization zone with uniform trend, 8-elongated quadrilateral region, 9-any data point, 10-an iteration initial value (such iteration initial value has n), 11-unique true solution;
FIG. 5 is a flow chart of a multi-dimensional synchronous optimization process based on a particle swarm optimization algorithm;
FIG. 6 is a schematic diagram of calculating the spacing of any two adjacent strain localization zones;
FIG. 7 shows different longitudinal strainsaMaximum shear strain gamma of unidirectional compressed sand samplemaxWherein FIG. 7-a is a graph ofaGraph of results at 0.08; FIG. 7-b isaGraph of results at 0.09; FIG. 7-c isaGraph of results at 0.11; FIG. 7-d isaGraph of results at 0.13; FIG. 7-e isaGraph of results at 0.14; FIG. 7-f isaGraph of results at 0.15; FIG. 7-g isaGraph of results at 0.16; in the figure, 12 — 3 quadrilateral areas bounding 3 strain localization zones;
FIG. 8 is a drawing showingaThe data, the iteration initial value and the multidimensional synchronous optimization process chart of 3 strain localization zones with consistent trend when the trend is 0.16, wherein a chart of fig. 8-a is a result chart when an iteration algebra N is 1; fig. 8-b is a result graph when the iteration algebra N is 10; fig. 8-c is a graph of the result when the iteration algebra N is 30; FIG. 8-d is the junction when the iterative algebra N is 100Fruit graph; in the figure, 13-15-iteration initial value; 16-data of strain localization zones; 17-true answer; 17-1 — true solution for band 1; 17-2 — true solution for lane 2; 17-3 — true solution for band 3;
FIG. 9 is a schematic view ofa0.16 and different iteration algebra;
FIG. 10 shows different longitudinal strainsaEvolution of the spacing of the measured strain localization zones.
Detailed Description
The following describes a specific embodiment of the method with reference to the drawings.
The invention relates to a multi-dimensional synchronous optimization measurement method for a strain localization band interval evolution law, a flow chart of which is shown in figure 1, and the method comprises the following steps:
step 1: as shown in fig. 2, a digital image of a surface 2 containing speckles of a sample 1 under loaded conditions is acquired by means of a camera device 4 (digital camera or CCD camera), a light source 3 is arranged in front of the camera device 4, and the captured image is stored in the hard disk of a computer 5;
this step is carried out as follows: firstly, an artificial speckle field is manufactured on one surface of a sample 1, and if the natural texture of the surface of the sample can meet the condition of being used as the speckle field, the artificial speckle field does not need to be manufactured; the sample 1 is then loaded by means of a testing machine or loading device, while at the same time an image of the speckle field is recorded by means of the camera device 4.
The artificial speckle field is a random speckle pattern sprayed on the surface of a sample by adopting paint, pigment, ink and the like.
Step 2: using a sub-pixel digital image correlation method (fig. 3), the deformation field of the sample surface is acquired: strain of horizontal linexStrain of vertical lineyGamma, shear strainxyAnd maximum shear strain gammamax；
This step is embodied as follows: firstly, selecting a plurality of typical strain field calculations from a large number of recorded images; then, setting related calculation parameters and a calculation mode, and calculating a displacement field of the image by using a sub-pixel digital image correlation method; then, carrying out central difference on the displacement field to obtain a strain field; finally, the maximum shear strain is calculated from the horizontal line strain, the vertical line strain and the in-plane shear strain.
The calculation parameters comprise: the size of the subarea, the distance between the measuring points, the number of the particles, the maximum flying speed of the particles and the like.
The calculation mode includes: an incremental mode and a full mode, wherein the incremental mode refers to that a previous image is taken as a pre-deformation image, and the obtained displacement field and strain field are increments; the full-scale mode is to use the first image as the image before deformation, and the obtained displacement field and strain field are full-scale.
The sub-pixel digital image correlation method can select a digital image correlation method (Duasian annals, Wangchi, a digital image correlation method based on Newton-Raphson iteration and PSO algorithm, computer engineering and application, 2012 and 48(34):184-189), and can avoid the defect that the traditional Newton-Raphson iteration method is easy to fall into local optimum and the defect that the initial value of iteration is not easy to determine. Although the method can simultaneously carry out related search on the displacement field and the strain field, the data of the strain field is abandoned and the central difference of the displacement field is generally adopted to obtain a new strain field in consideration of the fact that the precision of the strain field is generally not high.
The maximum shear strain field is obtained by 3 strain fields, the maximum shear strain field is always larger than zero, the deformation inside the strain localization zone is more obvious along with the continuation of the deformation, and the deformation outside the zone is increased slowly, so that the strain localization process can be well characterized.
And step 3: setting a calculation area, and acquiring strain data of the center and the vicinity of each strain localization zone;
this step is carried out as follows: first, by observing the strain field, a calculation region including a plurality of strain localization zones 7 is set (here, 1 quadrangular region including a plurality of strain localization zones is taken as the calculation region 6, as shown in fig. 4-a); then, according to the strain field, determining the number m of strain localization bands 7 with consistent trend (figure 4-b); then, carrying out bicubic spline interpolation on the strain field with limited data volume in the calculation area to improve the data volume and smoothness of the strain field without carrying out on the whole sample, thus reducing the workload of interpolation and improving the efficiency of interpolation; finally, as shown in fig. 4-b and 4-c, the roughly estimated angle and width of the measured strain localization zone 7-1 are used to eliminate the data outside the measured strain localization zone 7-1, and the strain data in the center of each measured strain localization zone 7-1 and its vicinity are obtained.
The strain localization zones with the same trend refer to a collection of a plurality of localization zones with basically same angles in a strain localization zone network, generally, the strain localization zones 7 in the strain localization zone network exist in a conjugate mode, namely two clusters, wherein any cluster is the strain localization zone 7-1 or 7-2 with the same trend, and the strain localization zone 7-1 with the same trend is taken as a measured strain localization zone.
The acquiring of the strain data at the center and the vicinity of each measured strain localization zone further comprises: firstly, setting proper critical strain parameters, and taking data exceeding the critical strain parameters as data of a measured strain localization zone 7-1; thereafter, the range of each of the measured strain localization zones 7-1 is empirically determined, and data outside these ranges is discarded.
The range of each measured strain localization band is limited by 1 narrow and long quadrilateral region 8, the narrow and long quadrilateral regions 8 are all located in the calculation region 6, two longer sides of the narrow and long quadrilateral regions 8 are parallel, the angle is set by experience, and for geotechnical materials, the direction of the shear strain localization band isAnd maximum principal stress (σ)3) The angle between the directions is generally 55 to 80 degrees; the distance between the two longer sides of the elongated quadrangular zone 8, i.e., the dimension in the width direction thereof, may be 1 to 3 times the width of the shear strain localized belt, i.e., 20 to 60 times the average particle diameter of the material.
The critical strain parameter may be taken as γ in the calculation region 6maxIs 60% or more of the maximum value of (a).
And 4, step 4: as shown in fig. 4-d, for each measured strain localization zone 7-1, n initial iteration values and related iteration parameters are set, for a certain initial iteration value 10, i.e., a series of parallel line segments, the dimension of the initial value is m +1, which includes 1 slope and m intercepts, and the common slope and the respective different intercepts of each line segment are obtained through continuous synchronous iteration by using a group intelligence algorithm.
The initial iteration value refers to a series of line segments in the calculation region 6, each line segment aims at 1 strain localization zone 7, the initial iteration value is completely determined by the slope and intercept of the line segments, and the origin of coordinates can be taken at the center of the calculation region 6; for a certain initial value of the iteration 10, the segments it contains are parallel to each other, so that the dimension of the initial value will be 1 more than the number m of strain-localized bands; for different initial values, all the line segments included in the initial values do not satisfy the requirement of being parallel to each other.
Setting any iteration initial value to be omegai＝{ki,b1i,b2i,...,bmiH, wherein i is 1-n, and n is the number of iteration initial values; it should be noted that the number of initial values of the iteration is not equal to the number of dimensions of the initial values, which are related to the number of strain localisation strips 7, which is related to the difficulty of the problem, but does not need to be too large for an easily solved optimization problem; k is a radical ofiCommon slope for initial values of either iteration, { b }1i,b2i,...,bmiThe different intercepts of any iteration initial value are obtained; in the iteration process, the iteration initial value is updated by the tentative solution, but the tentative solution still meets the characteristics of the iteration initial value: for any heuristic solution, the line segments it containsParallel to each other.
The group intelligent algorithm comprises a particle swarm optimization algorithm, a genetic algorithm, a differential evolution algorithm and the like. Different group intelligence algorithms have different performances and origins, which determine the update principles of heuristic solutions, but these group intelligence algorithms have the following commonalities: the method has strong global parallel search capability, and the strategies of information sharing, mutual learning and influence, and the strategies of eligibility and survival of suitable persons among different heuristic solutions are considered.
The synchronous iterative process is a process in which the trial solution is continuously approximated to the true solution, in which the deviations between the m line segments and the strain data at and near the center of the m strain localization zones are synchronously and gradually reduced, and the iterative or optimization process can be attributed to minimizing the objective function J, i.e., minimizing the objective function J
Wherein, subscript l represents any one of n iteration initial values, and l is 1-n; c. CiThe number of data representing the ith strain localization zone, typically, the number of data for different strain localization zones is different, i being 1 to m; sijOrdinate of j-th data representing i-th strain localization zone, i being 1 to m, j being 1 to ci，sij＝sij(xij)，xijIs the abscissa of the data; f. ofijRepresenting the ordinate of the segment approximating the ith strain-localized band at the jth datum, due to fijIs a linear function, therefore, fij＝(kl,bil)＝klxij+bil，klIs the common slope of 1 initial value (line segments), bilIs a different intercept of 1 initial value, sij-fijRepresenting the deviation between 1 data point 9 and 1 line segment in 1 trial, two summation calculations are required to obtain the square of the deviation of all data points 9 from all line segments in one trial: the sum of the squares of the deviations of all the data in 1 strain-localized band 7, on the 1 st, and the sum of the squares of the deviations of the individual strain-localized bands 7, on the 2 nd; the heuristic solution that minimizes the square of the above-mentioned deviation by continuous synchronous iteration is denoted as Ω*，Ω*＝{k*,b1*,b2*,...,bm*Which is unique, i.e. is the true solution 13 sought. If the data of each strain localization zone 7 are fitted respectively, the angle of each strain localization zone 7 cannot be guaranteed to be the same, so that for a plurality of line segments with slightly different angles, it is difficult to obtain the unique result of the strain localization zone spacing by adopting 1 determined formula. By setting the dimension of the iteration initial value to be 1 more than the number m of the strain localization zones, and,the inclusion of only one slope ensures the uniqueness and accuracy of the iteration result of the spacing of the strain localization zones 7, which is ensured because the iteration result of the angles of the strain localization zones 7 takes into account all data in the center of the strain localization zones 7 and in the vicinity thereof, which all have the same trend.
The iteration parameters include: maximum algebra, the number of initial values of iteration, threshold conditions for finishing iteration and specific parameters of intelligent algorithms of different groups. The following is a flow chart (fig. 5) and calculation steps for iteration using the particle swarm optimization algorithm:
(1) initializing particles in a calculation region 6, giving estimated values of central line angles and intercept according to the form of a measured strain localization zone 7, and generating initial values of N particles, wherein the dimension of each initial value is m +1, the current particle is a generation 1 particle, and N is 1;
(2) evaluating each particle, and calculating the quality of each particle by using the formula (1), namely evaluating the deviation degree of each particle from the strain localization band data;
(3) finding the optimal heuristic solution p for any particlebestFor any particle, in all iteration generations, find the optimal heuristic solution pidI.e. pbestSubscript i is the particle number, i is 1 to n, d is a certain one-dimensional number, and d is 1 to (m + 1);
(4) finding the optimal heuristic solution g among all particlesbestIn all iteration algebras, finding the optimal heuristic solution g in all particlesbest；
(5) Updating heuristic solution updates the flight velocity of the particle using the following equationAnd new position
Wherein,representing the speed of the ith particle in the d dimension in the (N +1) th generation; c. C1、c2For the acceleration constant, generally take c1＝c2＝2；r1And r2Respectively take on the value of [0, 1%]A random number in between; w is an inertia constant, the value decreases linearly with the increase of the iteration algebra N, and the maximum value w of the value decreases linearlymaxAnd a minimum value wmin1.4 and 0, respectively; n is a radical ofmaxIs a preset maximum iteration number;representing the coordinates of the ith particle in the d-dimension at generation N + 1. If the updated velocity of the particle exceeds the range-v in a certain dimensionmax，vmax]Then is bounded on the boundaries of that dimension. The updated coordinates of the particle are also bounded if they exceed the search field.
(6) And stopping the iteration if the condition of ending the iteration is met, namely the iteration result tends to be stable. Otherwise, the iteration algebra is increased by 1, and the calculation is continued until the condition of ending the iteration is met by returning to the step (2).
And 5: as shown in FIG. 6, the distance d between any two adjacent strain localization bands 7 is calculated by using the formula of the distance between two parallel linesiThe formula is easy to derive
di＝|b(i+1)*-bi*|sinθ*,i＝1～(m-1)(5)
Wherein, theta*Is the angle of the line segment, θ*And k is*In connection with, therefore
di＝|b(i+1)*-bi*|sin[arctan(k*)],i＝1～(m-1)(6)
When i is 1, d1Representing the spacing of the 1 st and 2 nd strain localization zones, and so on. The formula of point-to-line distance can also be adopted to calculate diBut require the points to be in a straight line.
FIG. 7 shows different longitudinal strainsaMaximum shear strain gamma of unidirectional compressed sand samplemaxThe result is obtained by adopting a digital image correlation method which is autonomously developed and based on particle swarm optimization and a Newton-Raphson iteration method. It can be found thataThe strain localization bands are clearer and clearer, the network pattern is more and more obvious, 3 strain localization bands with the same trend are selected as the measured object, wherein 3 quadrilateral areas 12 limiting the 3 strain localization bands are used for calculationAnd (4) a region. FIG. 8 is a drawing showingaData, iteration initial value and multi-dimensional synchronous optimization process chart of 3 strain localization bands with consistent trend at 0.16, wherein the particle number is 3, namely the iteration initial values 13-15 are 3 in total, are limited to space, and other parameters are not givenaA process diagram of time. It can be found that as the iteration algebra N increases, each tentative solution is continuously drawn to the data 16 of each strain localization zone, and finally, each tentative solution tends to the same target, which is the true solution 17. FIG. 9 is a schematic view ofaThe evolution diagram of the target function J at different iteration generations is 0.16, and it can be found that as the iteration generations N increase, the target function J continuously decreases, which means that the tentative solution continuously approaches to the true solution, and the iteration result tends to be stable when N is 60-100. FIG. 10 shows different longitudinal strainsaThe evolution diagram of the spacing of the strain-localized zones measured in time can be found to be differentaThe distance between the strain-localised zones varies with timeaIs the distance d between the real solution 17-1 for the 1 st strip and the real solution 17-2 for the 2 nd strip1With a decreasing trend, the distance d between the true solution 17-2 for the 2 nd strip and the true solution 17-3 for the 3 rd strip2There is an increasing trend.
Claims (8)
1. A multi-dimensional synchronous optimization measurement method for a strain localization band interval evolution law comprises the following specific steps:
step 1: acquiring a digital image of the sample containing the speckle surface under the loading condition by using a shooting device;
step 2: acquiring a deformation field of the surface of the sample by using a sub-pixel digital image correlation method: strain of horizontal linexStrain of vertical lineyGamma, shear strainxyAnd maximum shear strain gammamax；
And step 3: setting a calculation region, and acquiring strain data of the center and the vicinity of each strain localization band, wherein the calculation region can be 1 quadrilateral region containing a plurality of strain localization bands, or a set of quadrilateral regions containing 1 strain localization band;
for the case where the calculation region is a 1 quadrilateral region containing multiple strain localization zones:
firstly, setting 1 quadrilateral calculation area containing a plurality of strain localization zones;
then, according to the strain field, determining the number m of strain localization zones with consistent trend;
then, various strain fields with better smoothness in a calculation area are obtained by utilizing an interpolation method;
finally, setting a plurality of elongated quadrilateral regions by using the roughly estimated angles and widths of the measured strain localization bands, wherein each elongated quadrilateral region only comprises 1 strain localization band, and acquiring strain data of the center of each strain localization band and the vicinity of the center;
for the case where the calculation region is a set of quadrilateral regions containing 1 strain localization zone:
firstly, determining the number m of strain localization zones with consistent trend according to a strain field;
then, setting a plurality of long and narrow quadrilateral regions as calculation regions by using the roughly estimated angles and widths of the measured strain localization bands, wherein each long and narrow quadrilateral region only comprises 1 strain localization band;
then, various strain fields with better smoothness in a calculation area are obtained by utilizing an interpolation method;
finally, strain data of the center of each strain localization zone and the vicinity of the strain localization zone are obtained;
and 4, step 4: setting n iteration initial values and relevant iteration parameters for each strain localization zone, wherein for any initial value, namely a series of parallel line segments, the dimension of the initial value is m +1 and comprises 1 slope and m intercepts, and acquiring the common slope and the respective different intercepts of each line segment by continuously and synchronously iterating by using a group intelligent algorithm;
and 5: and calculating the distance between any two adjacent strain localization bands by using a distance formula between parallel lines.
2. The multi-dimensional synchronous optimization measurement method for the strain localization band interval evolution law according to claim 1, characterized in that the strain localization band interval measurement problem is attributed to a multi-dimensional synchronous optimization problem, and the deviation between the strain localization band data and the heuristic solution is gradually reduced through continuous synchronous iteration until the iteration end condition is satisfied.
The synchronous iteration refers to a process of approaching a tentative solution to a real solution, in which deviations between m line segments and strain data at and near the center of m strain localization zones are synchronously and gradually reduced, and the iteration or optimization process can be attributed to minimizing an objective function J, that is, minimizing an objective function J
Wherein, subscript l represents any one of n iteration initial values, and l is 1-n; c. CiThe number of data representing the ith strain localization zone, typically, the number of data for different strain localization zones is different, i being 1 to m; sijOrdinate of the jth data representing the ith strain localization zone, j being 1-ci，sij＝sij(xij)，xijIs the abscissa of the data; f. ofijRepresenting the ordinate of the segment approximating the ith strain-localized band at the jth datum, due to fijIs a linear function, therefore, fij＝(kl,bil)＝klxij+bil，klIs the common slope of 1 initial value (line segments), bilIs a different intercept of 1 initial value, sij-fijRepresents the deviation between 1 data point and 1 line segment in 1 heuristic solution; to obtain the square of the deviation of all data points from all line segments in a heuristic solution, two summation calculations are required: the sum of the squares of the deviations of all the data in 1 strain-localized band, on the 1 st, and on the 2 nd, on each strain-localized band; the heuristic solution that minimizes the square of the above-mentioned deviation is denoted Ω*，Ω*＝{k*,b1*,b2*,...,bm*It has uniqueness, i.e. is the true solution sought.
3. The method as claimed in claim 1, wherein for any one heuristic solution, the dimension is 1 more than the number m of the strain localization zones, and the common slope and the different intercepts of each line segment are included.
4. The multi-dimensional synchronous optimization measurement method for the interval evolution law of the strain localization zones according to claim 1, characterized in that the global parallel search capability of the group intelligent algorithm is utilized to synchronously search different intercepts and common slopes of each parallel line segment of the heuristic solution, the data of all the strain localization zones are considered, and the correctness and the uniqueness of the obtained result are ensured.
5. The multi-dimensional synchronous optimized measurement method for the distance evolution law of the strain localization zones according to claim 1, characterized in that an interpolation method is used to interpolate a strain field with limited data volume obtained by a sub-pixel digital image correlation method in the calculation region to obtain a smooth strain field, and the data of the strain localization zone to be measured is obtained according to the characteristics of the strain field;
the characteristics of the strain field include: (1) statistical information of a maximum shear strain field, a linear strain field or a shear strain field; (2) an estimate of the extent and angle of each strain localization zone, either by direct observation or empirically determined.
6. The multi-dimensional synchronous optimization measurement method for the space evolution law of the strain localization zones as claimed in claim 1, wherein the space d between any two adjacent strain localization zonesiIs calculated by the formula
di＝|b(i+1)*-bi*|sinθ*＝|b(i+1)*-bi*|sin[arctan(k*)],i＝1～(m-1)(2)
The subscript of the parameter represents the parameter that minimizes the objective function, and the distance between two adjacent strain localization zones can also be calculated by using a point-to-straight line distance formula, but the point is required to be on a straight line.
7. The method as claimed in claim 1, wherein the measured strain localization zones are oriented in the same direction, i.e. the angles are substantially the same.
8. The method for multidimensional synchronous optimization measurement of the distance evolution law of the strain localization zones as claimed in claim 1, wherein the law of the evolution of the distance of the strain localization zones with the stress or strain can be obtained by calculating the distance between adjacent strain localization zones in the sample under different stress or strain conditions.
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| CN107747916A (en) * | 2017-10-27 | 2018-03-02 | 辽宁工程技术大学 | A kind of measuring method of strain localization band dilative angle |
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