CN106777822B - Two-dimentional high-content particle enhancing composite material three-phase meso-mechanical model and method for building up - Google Patents
Two-dimentional high-content particle enhancing composite material three-phase meso-mechanical model and method for building up Download PDFInfo
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Abstract
The invention discloses two-dimentional high-content particle enhancing composite material three-phase meso-mechanical model and method for building up, belong to the technical field that particulate reinforced composite carefully sees emulation.The present invention is successfully established the parameter model of equal thickness interface topological structure around ellipse on the basis of oval enhancing particle is randomly generated, further consider that particle reaches the condition of stress balance under the promotion of boundary or external load, success is realized in the tightly packed given area constantly to contract of particle, and guarantee that particle does not overlap phenomenon between each other, the particulate reinforced composite constructed carefully sees the simulation model periodic boundary random with nature, there is no the choice problems of particle on cycle boundary, the available particulate reinforced composite microscopical structure model with very high-content of the modeling method proposed through the invention.
Description
Technical field
The invention discloses two-dimentional high-content particle enhancing composite material three-phase meso-mechanical model and method for building up, belong to particle
Enhancing composite material carefully sees the technical field of emulation.
Background technique
The particulate reinforced composites such as cement base, ceramic base, polymer matrix have been widely used in various engineering structures
In.However, due to the randomness and complexity of particulate reinforced composite microscopical structure, experimental technique often can only be surveyed qualitatively
The precision for measuring its microscopical structure and acquired results is often limited by existing test apparatus precision and human error.In addition, theoretical
Method simplify actual physics model on the basis of approximatively calculate corresponding Equivalent Mechanical performance, need to such as granule content compared with
Low many restrictive conditions are just effective.With the rapid development of computer hardware and software technology, pass through computer simulation particle
The complicated microscopical structure of enhancing composite material has become the research direction highly expected in the world and causes increasingly
The concern of more domestic and foreign scholars.Can numerical simulation technology overcome the above test and efficiently and accurately while theoretical method defect
The mechanical property that ground calculates high-content particle composite material faces a severe challenge.Therefore, the particle for establishing a kind of efficient complexity increases
It is very necessary that strong composite material, which sees simulation model carefully with the further analysis for realizing material mechanical performance,.
On the building method that Particles in Two Dimensions enhancing composite material carefully sees simulation model, major part scholar both domestic and external is logical
Cross the angle for simply determining elliptical centre coordinate and long axis and x-axis at random in a given region, i.e., it is random raw
Then ovalisation particle checks whether the oval particle currently generated at random intersects with the oval particle launched before,
If the oval particle currently generated at random is then cast out in intersection, if non-intersecting, continue to generate ellipse at random down
Grain.Although this method can relatively easily obtain the thin sight simulation model of the particulate reinforced composite of random distribution,
It is that only there is the thin sight simulation model that this method obtains lower packing density of particle can not thus simulate high-content particle enhancing
The microscopical structure of composite material.In addition, interface is universally present in various inhomogeneous composite materials, its microscopical structure feature
Macromechanics and transmission performance to material have significant impact.For the meso-level simulation of interfacial transition zone, domestic and foreign scholars
Using the boundary layer in nested one layer of oval particle exterior surface big oval next approximate characterization equal thickness.However, this method
There is preferable propinquity effect only in elliptical draw ratio (the ratio between long axis and short axle) lesser situation, when elliptical major diameter
When than becoming larger, the propinquity effect at oval particle long axis both ends is undesirable.
Summary of the invention
Goal of the invention of the invention is the deficiency for above-mentioned background technique, and it is high to provide the two dimension with periodic boundary
Content particles enhance composite material three-phase meso-mechanical model and method for building up, by high density ellipse particle, genuine interface layer and base
The three-phase particulate reinforced composite meso-mechanical model of body composition, solves that aspherical particle content in previous numerical simulation is low, boundary
The technical problems such as face is difficult to accurately to construct, periodic boundary is cumbersome.
The present invention adopts the following technical scheme that for achieving the above object
The method for building up of two-dimentional high-content particle enhancing composite material three-phase meso-mechanical model, two-dimentional high-content particle enhancing are multiple
Condensation material three-phase carefully see simulation model include matrix, boundary layer and enhance particle three-phase composite material, the enhancing particle with
Machine is closely packed in matrix, and the equal boundary layer of thickness is enclosed with around each enhancing particle, and method for building up includes such as
Lower step:
A, ellipse enhancing particle is generated at random in each zonule of big square area；
B, two boundaries of big square area arbitrary neighborhood are eliminated and replicate the ellipse enhancing adjacent with boundary is not eliminated
Particle forms the new boundary of big square area to the position for having eliminated boundary, does not eliminate boundary with the movement of identical rate,
Again and again, it constructs the new boundary of big square area and does not eliminate boundary until ellipse enhancing so that phase same rate is mobile
The area fraction of grain is met the requirements；
C, according to the ellipse enhancing particle for closing on eliminated boundary in the newest boundary forming process of big square area
Distribution mode does not eliminate the new ellipse enhancing of the external layout on boundary in the newest boundary forming process of big square area
Grain is to form the enhancing particle packing model with periodic boundary condition；
D, enhancing particle packing model in each ellipse enhancing particle appearance surface construction equal thickness boundary layer:
Ellipse enhancing particle under rectangular coordinate system is coordinately transformed to obtain unit circle, is obtained according to unit circle and its tangential relationship
The parametric equation of boundary layer under to rectangular coordinate system.
Further, in the method for building up of two-dimentional high-content particle enhancing composite material three-phase meso-mechanical model, the tool of step A
Body method are as follows: big square area is divided into several small square areas, is each small square area label, each small
At least one ellipse enhancing particle is generated in square area at random, is the ellipse enhancing in each small square area
Grain all writes coding identical with affiliated small square area label.
Further, in the method for building up of two-dimentional high-content particle enhancing composite material three-phase meso-mechanical model, step B's
Method particularly includes: the right margin and lower boundary for eliminating big square area increase the ellipse in the small square area of the first row
Strong particle replication answers the ellipse enhancing particle in the small square area of first row to the lower boundary position of big square area
The right margin position of big square area is made, the distance of duplication is the side length of current big square area, ellipse enhancing
The new boundary of big square area is defined after the completion of grain duplication, with the coboundary and a left side of the mobile big square area of identical rate
Boundary constructs the new boundary of big square area and does not eliminate boundary until ellipse so that phase same rate is mobile again and again
The area fraction of enhancing particle is met the requirements.
Further, in the method for building up of two-dimentional high-content particle enhancing composite material three-phase meso-mechanical model, step C's
Method particularly includes: it, will current last column and last in big square area after the newest boundary of big square area is formed
Ellipse enhancing particle in the small square area of a line copies to the outside of current big square area left margin and upper respectively
The outside on boundary, duplication distance are the side length of current big square area.
Method for building up as two-dimentional high-content particle enhancing composite material three-phase meso-mechanical model advanced optimizes scheme,
The parametric equation of boundary layer under the rectangular coordinate system that step D is obtained are as follows:
Wherein, (X1,Y1) indicate boundary layer outer boundary coordinate, θ indicate ellipse enhancing particle long axis and rectangular co-ordinate
It is the angle of lower x-axis, the major semiaxis that a, b respectively represent ellipse enhancing particle is long and semi-minor axis is long, (Xi,Yi) indicate ellipse
Enhance the centre coordinate of particle, t indicates that the thickness of boundary layer, φ indicate normal vector and unit circle institute at unit circle Arbitrary Boundaries point
Belong to the angle of rectangular co-ordinate x-axis, φ ∈ (0,2 π).
The present invention by adopting the above technical scheme, has the advantages that
1, the present invention is successfully established equal thickness interface topology around ellipse on the basis of oval enhancing particle is randomly generated
The parameter model of structure further considers that particle reaches the item of stress balance under the promotion on boundary (or under external load effect)
Part is successfully realized in the tightly packed given area constantly to contract of particle, and guarantees that weight does not occur between each other for particle
Folded phenomenon, the particulate reinforced composite constructed carefully see the simulation model periodic boundary random with nature, and there is no weeks
The choice problem of particle on phase boundary, the available particle enhancing with very high-content of the modeling method proposed through the invention
Composite material microscopical structure model, the single particle size ellipse grains enhancing composite material that the present invention constructs carefully see simulation model
Bulk density can reach 85%.
2, in order to accurately characterize the boundary layer of equal thickness around ellipse, the present invention utilizes the correlation theories such as geometric topology
The parameter model of equal thickness boundary layer around ellipse is proposed, constructs interface zone with Low rigidity, high porosity softening circle
The physical features in face can improve the problem that boundary layer propinquity effect is bad in the prior art.
Detailed description of the invention
Fig. 1 is the random Mathematical Model of heaped-up of single particle size ellipse grains with periodic boundary condition, and packing density of particle reaches
To 85%.
Fig. 2 is to consider that there are the cycle boundary models of equal thickness boundary layer around ellipse grains.
Fig. 3 is the block diagram of General Elliptic stochastic and dynamic accumulation program.
Fig. 4 is the schematic diagram of periodic boundary method for building up of the present invention.
Fig. 5 (a), Fig. 5 (b), Fig. 5 (c) are the schematic diagrames of ellipse grains equal thickness Interface Construction method.
Fig. 6 is the schematic diagram of the equal thickness interface result constructed using the equal thickness interface parameter equation derived above.
Specific embodiment
The technical solution of invention is described in detail with reference to the accompanying drawing.
A kind of method for building up of the two-dimentional high-content particle enhancing composite material three-phase meso-mechanical model with periodic boundary:
Firstly, establishing periodic boundary condition；Then, random accumulation ellipse enhancing particle；Finally, around construction oval surface etc.
Thickness boundary layer.It specifically includes the following steps:
Step 1: as shown in figure 4, generating several oval (being here one) at random in each small square area, and giving
Each oval coding is distinguished with showing, these codings are identical as the coding of small square area.Oval stochastic and dynamic accumulation
Program is as shown in Figure 3.
Step 2: the right margin of big square area and lower boundary being cancelled, as shown in phantom in Figure 4, and by the first row
Ellipse in small square area copies to downwards the following of big square area, by the ellipse in the small square area of first row
For shape particle replication to the right in big region, the distance of duplication is the side length of current big square area.
Step 3: according to Newton's second law and corresponding sports rule, with the mobile big square area of identical rate
Coboundary and left margin, as shown in figure 4, four boundaries of big square area are internally moved simultaneously, oval particle can be
It is internally moved under the action of boundary, and the oval particle for the overseas duplication in big square region that timely updates, then these are replicated
Ellipse particle inside big square area also can be internally squeezed with identical rate, as what two sides particle formed encloses
Wall.When particle than it is sparse when internal particle is formed from this two sides particle in order to prevent " enclosure wall " gap in drill out, can be with
In step 2 outside the several layers of ellipses to big square area of more duplications.By repeatedly construct the new boundary of big square area and with
The mobile big square area of phase same rate does not eliminate boundary, successfully realizes that particle is tightly packed constantly to the given of contract
In region, and guarantee that particle does not overlap phenomenon between each other, the particulate reinforced composite constructed carefully sees simulation model
With naturally random periodic boundary, there is no the choice problems of particle on cycle boundary.
Step 4: when the particle area score for the big square interior constantly shunk reaches specified requirement, stopping boundary
Movement, and by big square area last column and last line small square area in ellipse copy to respectively
The outside of big square area left margin and the outside (side length that duplication distance is big square area at this time) of coboundary.Most
Eventually, the model inside big square area just has periodic boundary condition, as shown in Fig. 4 right figure.
Step 5: on the basis of step 4, the boundary layer of an equal thickness is constructed in each oval particle exterior surface,
It ultimately forms the two-dimentional high-content particle enhancing composite material three-phase with periodic boundary and carefully sees simulation model.For some
The particulate reinforced composite such as composite materials such as concrete, ceramic base and polymer matrix, accurately construct ellipse on the basis of step 4
Circle possesses the equal thickness outer shell of respective physical characteristic to modeling interface region around outer surface.
The interface of the extra-granular equal thickness provided in step 5, detailed process is as follows for the derivation of parametric equation:
Firstly, in rectangular coordinate system X1Y1The oval of lower any position can become one the by coordinate transform twice
Three rectangular coordinate system X3Y3Under unit circle, as shown in Fig. 5 (a), Fig. 5 (b), Fig. 5 (c).Assuming that in rectangular coordinate system X3Y3
In, there are straight line L and unit circle tangent, point of contact coordinate is A (cos (φ), sin (φ)), then we can be very simply
Write out the general equation of this straight line are as follows:
Sin (φ) y+cos (φ) x-1=0
Because transformation of coordinates does not change the relative positional relationship of object under coordinate system, in rectangular coordinate system X2Y2
Lower straight line must be tangent with ellipse, at this time X under rectangular coordinate system2Y2Straight line L ' indicate, the slope of L ' are as follows: k=asin
(φ)/(bcos (φ)), and straight line L ' and elliptical point of contact coordinate are as follows: A ' (acos (φ), bsin (φ)).So
Normal direction unit vector at our available oval upper A '
According to the addition of vector, we are available rectangular coordinate system X2Y2Take up an official post any the coordinate of anticipating at lower interface:
Wherein, (X2,Y2) it is that certain is put in rectangular coordinate system X on boundary layer outer boundary2Y2Under coordinate, t is the thickness of boundary layer
Degree, (x2,y2) it is corresponding oval above certain coordinate put.The coordinate of A ' point, which is substituted into above formula, can obtain expression are as follows:
So far, coordinate system X has been obtained2Y2Under ellipse grains ambient interfaces parametric equation, as long as then being transformed to original
The coordinate system of beginning, the expression formula of coordinate transform are as follows:
X1=cos (θ) X2-sin(θ)Y2+Xi
Y1=sin (θ) X2+cos(θ)Y2+Yi
By X2, Y2Expression substitute into above formula, can obtain:
Wherein: θ is the angle of x-axis under ellipse grains long axis and rectangular coordinate system, and a, b respectively represent the length half of ellipse grains
Axial length and semi-minor axis are long, XiAnd YiIndicate that the centre coordinate of ellipse grains, t are the thickness of interfacial transition zone, X1And Y1Indicate interface
The coordinate of transition region outer boundary, φ are the parameter of this parametric equation, and variation range is (0,2 π).As a result as shown in Figure 6.
Using method for building up of the invention, two-dimentional high-content particle enhancing composite material three-phase can be generated and carefully see emulation mould
Type, the model emulation include matrix, boundary layer and the three-phase composite material for enhancing particle, are deposited in enhancing particle random close
In matrix, the equal boundary layer of thickness is enclosed with around each enhancing particle.
Consider that there are the cycle boundary model of equal thickness boundary layer is as shown in Figure 2 around ellipse grains, it is seen then that construct
Particulate reinforced composite carefully sees simulation model with the random periodic boundary of nature, and there is no particles on cycle boundary to take
House problem.The random Mathematical Model of heaped-up of single particle size ellipse grains with periodic boundary condition is as shown in Figure 1, packing density of particle
Reach 85%, that is, the available particulate reinforced composite with very high-content of the modeling method proposed through the invention is thin
See structural model.
Claims (5)
1. the method for building up of two-dimentional high-content particle enhancing composite material three-phase meso-mechanical model, which is characterized in that the two dimension is high
Content particles enhancing composite material three-phase carefully sees the three-phase composite material that simulation model includes matrix, boundary layer and enhancing particle,
It is deposited in matrix to the enhancing particle random close, is enclosed with the equal boundary layer of thickness around each enhancing particle,
Method for building up includes the following steps:
A, ellipse enhancing particle is generated at random in each zonule of big square area；
B, two boundaries of big square area arbitrary neighborhood are eliminated and replicate the ellipse enhancing particle adjacent with boundary is not eliminated
Form the new boundary of big square area to the position for having eliminated boundary, do not eliminate boundary so that identical rate is mobile, week and
Ground is renewed, the new boundary of big square area is constructed and does not eliminate boundary until ellipse enhances particle so that phase same rate is mobile
Area fraction is met the requirements；
C, according to the distribution for the ellipse enhancing particle for closing on eliminated boundary in the newest boundary forming process of big square area
Mode, do not eliminated in the newest boundary forming process of big square area the new ellipse enhancing particle of external layout on boundary with
Form the enhancing particle packing model with periodic boundary condition；
D, enhancing particle packing model in each ellipse enhancing particle appearance surface construction equal thickness boundary layer: to straight
Ellipse enhancing particle under angular coordinate system is coordinately transformed to obtain unit circle, is obtained directly according to unit circle and its tangential relationship
The parametric equation of boundary layer under angular coordinate system.
2. the method for building up of two-dimentional high-content particle enhancing composite material three-phase meso-mechanical model according to claim 1, special
Sign is, step A's method particularly includes: big square area is divided into several small square areas, is each small square
Region labeling generates at least one ellipse enhancing particle at random in each small square area, is each small square region
Ellipse enhancing particle in domain all writes coding identical with affiliated small square area label.
3. the method for building up of two-dimentional high-content particle enhancing composite material three-phase meso-mechanical model according to claim 2, special
Sign is, step B's method particularly includes: the right margin and lower boundary for eliminating big square area, by the small square region of the first row
Ellipse enhancing particle replication in domain, will be ellipse in the small square area of first row to the lower boundary position of big square area
For circle enhancing particle replication to the right margin position of big square area, the distance of duplication is the side of current big square area
It is long, the new boundary of big square area is defined after the completion of ellipse enhancing particle replication, with the mobile big square of identical rate
The coboundary in region and left margin are constructed the new boundary of big square area and are not disappeared with the movement of phase same rate again and again
Except boundary until the area fraction of ellipse enhancing particle is met the requirements.
4. the method for building up of two-dimentional high-content particle enhancing composite material three-phase meso-mechanical model according to claim 3, special
Sign is, step C's method particularly includes: after the newest boundary of big square area is formed, will currently in big square area most
It is left that ellipse enhancing particle in latter column and the small square area of last line copies to current big square area respectively
The outside on boundary and the outside of coboundary, duplication distance are the side length of current big square area.
5. the foundation of the according to claim 1 or 2 or 3 or 4 two-dimentional high-content particle enhancing composite material three-phase meso-mechanical models
Method, which is characterized in that the parametric equation of boundary layer under the rectangular coordinate system that step D is obtained are as follows:
Wherein, (X1,Y1) indicate boundary layer outer boundary coordinate, θ indicate ellipse enhancing particle long axis and rectangular coordinate system under
The angle of x-axis, the major semiaxis that a, b respectively represent ellipse enhancing particle are long and semi-minor axis is long, (Xi,Yi) indicate ellipse enhancing
The centre coordinate of particle, t indicate that the thickness of boundary layer, φ indicate straight belonging to normal vector and unit circle at unit circle Arbitrary Boundaries point
The angle of angular coordinate x-axis, φ ∈ (0,2 π).
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| CN111414677B (en) * | 2020-03-03 | 2022-10-14 | 河海大学 | Method for calculating transmission performance of multiphase high-content particle material |
| CN112461718B (en) * | 2020-11-18 | 2022-08-26 | 中国石油大学(华东) | Method for representing relationship between porosity and particle size distribution |
| CN112395681A (en) * | 2020-11-30 | 2021-02-23 | 三峡大学 | Numerical model construction method for concrete coarse aggregate, interface transition zone and porosity |
| CN113221416B (en) * | 2021-05-14 | 2022-06-24 | 上海工程技术大学 | Method for constructing two-dimensional microstructure of particle-reinforced composite material |
| CN116486967B (en) * | 2023-05-12 | 2023-10-03 | 哈尔滨工业大学 | Method for generating random distribution of shell particles with controllable particle spacing and area ratio |
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