CN111027210B - Rigidity and toughness adjusting method for bionic staggered laminated thin plate structure - Google Patents
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Abstract
The invention discloses a rigidity and toughness adjusting method for a bionic staggered laminated thin plate structure, and belongs to the technical field of structural design of bionic composite materials. The adjusting method is based on building a structural cellular constitutive model and obtaining a structural effective elastic modulus and a structural toughness expression, adjusts the rigidity and the toughness of the bionic staggered laminated thin plate structure by reasonably selecting the value of a dimensionless geometric parameter and a dimensionless material parameter, and can realize a larger rigidity adjusting range and higher structural toughness. The invention has the advantages of relatively simple adjustment mode and larger adjustment range, and can provide technical support and method reference for the design of a bionic staggered laminated thin plate structure.
Description
Technical Field
The invention belongs to the technical field of bionic composite material structure design, and particularly relates to a rigidity and toughness adjusting method for a bionic staggered laminated thin plate structure.
Background
The living things and the natural environment form excellent functions and perfect structures under the long-term interaction, and the unification of the structures, the functions, the local parts and the whole is realized. The structural bionic is based on engineering mechanics, and a novel engineering structure and a functional material are created by simulating a composite structure and excellent functions of a natural biological material. For example, in the process of climbing and jumping among rocks, the limbs of goats can bear severe dynamic load, which shows that the skeletons of the legs of goats play good roles of buffering, isolating vibration and resisting external impact in the process of running. Therefore, people try to explore and develop a bionic composite material structure which has the same outstanding mechanical properties as leg bones, such as high strength, high toughness, strong bearing capacity and the like, by researching the internal microstructure of the leg bones of the goats, so as to effectively solve the problem of vibration impact frequently encountered in engineering practice.
The research shows that the skeleton is a natural biological tissue mainly composed of hard minerals and soft collagen, and the key factor of the excellent performance of the skeleton is that the hard minerals and the soft collagen exist in the skeleton and are distributed in a multistage staggered and laminated arrangement. In recent years, inspired by the microstructure of the inner part of the skeleton, researchers in this field proposed a bionic staggered laminated thin plate structure consisting of hard bodies for simulating hard minerals and soft matrices for simulating soft collagen, the hard bodies of finite length being uniformly staggered in the soft matrices, see English non-patent document "extended and organized model for the elastic properties of laminated composites and its application 3D printed Structures, Youngso Kim, et al, Composite Structures189(2018) 27-36." (subject: extended analysis model of elastic properties of laminated composites and its application in three-dimensional printed Structures, author: Youngso Kim et al, published: Composite Structures, year 2018, volume: 189, page 27-36).
When the existing bionic staggered laminated thin plate structure is subjected to external force, the hard body bears most of load, and the internal stress is mainly transmitted through the shearing deformation of the soft matrix. However, the existing structure only considers two components of hard minerals and soft collagen existing in bones, neglects sacrificial bonds widely existing in organic components of the bones, has the problems of relatively fixed structural rigidity, insufficient structural toughness and incapability of effective adjustment, and is difficult to meet the application requirement under the action of larger impact load. That is, up to now, no good design method has been developed to achieve such adjustment of structural rigidity and toughness.
Disclosure of Invention
The invention mainly aims to provide a method for adjusting the rigidity and toughness of a bionic staggered laminated thin plate structure, and aims to solve the technical problem that the rigidity and toughness of the existing bionic staggered laminated composite structure cannot be effectively adjusted, so that the application requirement is difficult to meet.
In order to achieve the above object, the present invention provides a rigidity and toughness adjustment method for a bionic staggered laminated thin plate structure, where the bionic staggered laminated thin plate structure includes a plurality of hard bodies arranged in parallel, a plurality of soft bases arranged in parallel, and a plurality of breakable bodies, where the hard bodies and the soft bases are both in a strip shape and are sequentially staggered in a vertical direction, the breakable bodies are disposed between two adjacent hard bodies and can be broken under an external axial tensile load, the bionic staggered laminated thin plate structure can be obtained by first performing two mirror images in vertical and horizontal directions on one cell and then performing a linear array, and the cell is structurally symmetric with respect to a central point of the soft base located inside, and the rigidity and toughness adjustment method includes the following steps: firstly, defining a phase 0 and a phase 1 of a cellular, and respectively establishing a constitutive model of the cellular under two phase states of the phase 0 and the phase 1; secondly, respectively obtaining the effective elastic modulus of the cells under the phase 0 and the phase 1 and the decrease rate of the effective elastic modulus from the phase 0 to the phase 1, and selecting a dimensionless geometric parameter eta and a dimensionless material parameter alpha to adjust the rigidity of the structure; and thirdly, obtaining an expression of the structural toughness, and adjusting the structural toughness by adopting the dimensionless geometric parameter eta and the dimensionless material parameter alpha.
The rigidity and toughness adjusting method comprises the following detailed steps:
firstly, defining a phase 0 and a phase 1 of a cell, and respectively establishing a constitutive model of the cell under two phase states of the phase 0 and the phase 1 by adopting a shear hysteresis model;
wherein phi is 2b/(2b + h) which is the approximate volume fraction of the hard body,
is the volume average stress of the cellular structure; sinh represents a hyperbolic sine function, cosh represents a hyperbolic cosine function, tanh represents a hyperbolic tangent function, and tanh represents a hyperbolic tangent function; σ and τ denoteNormal and shear stresses, subscripts 1a, 1b, 1c, 1d, 2, 3a, and 3b representing the corresponding cellular regions; ρ ═ l a B is the length-width ratio of the overlapped hard body region, λ ═ l a H is the aspect ratio of the soft matrix,. eta. -. l a /l b The length ratio of the overlapped region to the non-overlapped region of the hard body, alpha ═ E e /E m The tensile modulus ratio of the breakable body to the rigid body, β ═ G/E m The ratio of the shear modulus of the soft matrix to the tensile modulus of the hard matrix; b and h are the widths of the hard and soft matrices, l a And l b Length of the soft substrate and breakable body, respectively, /) a And l b Can also be considered as uniform overlapping length and non-overlapping length of the duromer, respectively; e m Elastic modulus of a hard body, E e Is the elastic modulus of the fracturable body, and G is the shear modulus of the soft matrix;
is a dimensionless parameter that reflects the overall geometric and material effects;
phase 1 is the phase state after the fracturable body is fractured, and the constitutive model of the elementary cell under phase 1 is as follows:
wherein, coth represents a hyperbolic cosecant function, csch represents a hyperbolic cosecant function;
secondly, respectively obtaining the effective elastic modulus of the unit cells under the phase 0 and the phase 1 and the reduction rate of the effective elastic modulus from the phase 0 to the phase 1 according to a calculation formula of volume average stress and strain, and selecting a dimensionless geometric parameter eta and a dimensionless material parameter alpha to adjust the rigidity of the structure;
effective elastic modulus of 0-phase unit cell
Comprises the following steps:
wherein a ═ ktan (k) is a custom dimensionless parameter;
effective modulus of elasticity of 1-phase unit cell
Comprises the following steps:
rate of decrease in effective modulus of elasticity from phase 0 to phase 1
Comprises the following steps:
adjusting the rigidity of the bionic staggered laminated thin plate structure by reasonably selecting a dimensionless geometric parameter eta and a dimensionless material parameter;
thirdly, defining the structural toughness as the specific energy dissipation when the breakable body breaks, obtaining an expression of the structural toughness, and adjusting the structural toughness by adopting a dimensionless geometric parameter eta and a dimensionless material parameter alpha;
toughness T of cellular structure cell The expression of (a) is:
wherein,
ultimate tensile stress for a breakable body;
and adjusting the toughness of the bionic staggered laminated thin plate structure by reasonably selecting the values of the dimensionless geometric parameter eta and the dimensionless material parameter alpha.
The dimensionless geometric parameter η has a first critical value η c1 ：
Effective modulus of elasticity of phase 1
Increases as η increases; when eta is eta ═ eta c1 Effective modulus of elasticity of 1 phase
99.7% of the maximum limit value.
Said dimensionless geometric parameter η having a second critical value η c2 ：
Effective modulus of elasticity of phase 0
Increases as η increases; when eta is equal to eta c2 Effective modulus of elasticity of phase 0
99.7% of the maximum limit value.
Said dimensionless geometric parameter η has a third critical value η c3 ：
Effective elastic modulus decrease rate of 0 phase to 1 phase
Decreases as η increases; when eta is eta ═ eta c3 Effective modulus of elasticity decrease rate of 0 phase to 1 phase
100.3% of the minimum limit value.
Said dimensionless geometric parameter η also having a fourth critical value η c4 ：
Structural toughness T cell Decreases as η increases; when eta is eta ═ eta c4 Structural toughness T cell 100.3% of the minimum limit value.
A third critical value eta when the material composition of the bionic staggered laminated thin-plate structure is determined c3 The lower limit of the range is selected for the dimensionless geometrical parameter η.
A fourth critical value eta when the material composition of the bionic staggered laminated thin-plate structure is determined c4 The upper limit of the range is selected for the dimensionless geometrical parameter η.
Preferably, the dimensionless material parameter α ranges from 0.01 to 0.1.
Preferably, the dimensionless geometric parameter η has a value in the range of 5 to 500.
The beneficial effects obtained by the invention are mainly reflected as follows:
the rigidity and toughness of the bionic staggered laminated thin-plate structure are adjusted by reasonably selecting the value of a dimensionless geometric parameter eta and a dimensionless material parameter alpha, so that the large rigidity adjusting range and the high structure toughness can be realized, and the bionic staggered laminated thin-plate structure has the advantages of relatively simple adjusting mode and large adjusting range. In addition, the invention can provide important technical support and method reference for the design of a bionic staggered laminated thin-plate structure with a preset breakable body.
Drawings
In order to more clearly illustrate the embodiments or technical solutions of the present invention, the drawings used in the embodiments or technical solutions of the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the structures shown in the drawings without creative efforts.
FIG. 1 is a schematic diagram of a bionic staggered laminated thin plate structure with a preset breakable body;
FIG. 2 is a schematic of the structure and a zone-dividing diagram of a single cell;
FIG. 3 is a schematic illustration of material property parameters and structural geometry parameters of an individual cell;
FIG. 4 is a stress definition and distribution plot of the cell structure in the "0" phase;
FIG. 5 is a stress definition and distribution plot of the cell structure under the "1" phase;
FIG. 6a is a graph of the effect of geometric and material parameters on effective elastic modulus;
FIG. 6b is a graph of the effect of geometric and material parameters on the rate of decrease of effective elastic modulus;
FIG. 7 is a graph of an analysis of the effect of geometric and material parameters on structural toughness;
FIG. 8 is a flow chart of a rigidity and toughness adjusting method of the bionic staggered laminated thin-plate structure.
Reference numerals or symbolic illustrations of the present invention:
| reference numerals or symbols | Name or meaning | Reference numerals or symbols | Name or meaning |
| 1 | Hard body | 1a | Hard body a |
| 2 | |
1b | |
| 3 | |
1c | |
| 4 | |
1d | |
| 5 | Cellular cell | F | External |
| 3a | Fracturable body a | 3b | Fracturable body b |
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The skeleton is a natural biological material mainly composed of hard minerals and soft collagen, and can be divided into two different types of compact bone and cancellous bone from outside to inside, wherein the compact bone mainly affects the mechanical properties such as the strength, the rigidity, the structural toughness and the like of the whole skeleton. The inventor of the application researches and discovers that a 'sacrificial bond' structure is also widely existed in the microstructure of micron to nanometer scale in the compact bone, and is an important factor of the compact bone with excellent energy dissipation capability. A "sacrificial bond" structure is a connection between molecules or microstructures and typically comprises two groups of bonds that are at least 1 strong and 1 weak, which are defined as relatively weak bonds that break in advance before the strong bonds fail to break under a load. When external load is applied to the biological material with the sacrificial bond structure, the sacrificial bond structure dissipates external input energy through the pre-breaking of the weak connecting bonds, so that the strong connecting bonds can be reserved and continue to play a connecting role, and the integral integrity of the structure is ensured.
Inspired by the mechanism that the bone is fractured under the microscopic scale to enhance the toughness of the structure through the sacrificial bond, on the basis of the existing bionic staggered laminated thin-plate structure, the inventor of the application provides the bionic staggered laminated thin-plate structure with a rupturable body in advance, and the structure of the bionic staggered laminated thin-plate structure is shown in fig. 1. As can be seen from fig. 1, the biomimetic staggered laminated thin plate structure with prearranged breakable bodies comprises a plurality of hard bodies 1 arranged in parallel, a plurality of soft bases 2 arranged in parallel and a plurality of breakable bodies 3; the hard bodies 1 and the soft matrix 2 are both in a strip shape and are sequentially staggered in the vertical direction; the shape of the breakable body 3 is also in a strip shape, is arranged between the two hard bodies 1, and can be broken under the action of an external axial tensile load F; a cavity 4 is also present between the two soft substrates 2.
From the structural characteristics, the bionic staggered laminated thin-film structure with the preset breakable bodies has periodicity and repeatability, and can be obtained by firstly carrying out two mirror images in the vertical and horizontal directions and then carrying out a linear array on a cell 5 shown in fig. 2. Specifically, first, a cell 5 is mirrored in the vertical direction, that is, mirrored about an axis in the horizontal direction, to obtain a structure composed of two cells; then, mirroring the obtained structure formed by the two unit cells in the horizontal direction, namely mirroring the structure about an axis in the vertical direction to obtain a minimum structure formed by the four unit cells; finally, the obtained minimum structure composed of the four cells is linearly arrayed in the horizontal and vertical two-dimensional directions, and the overall structure shown in fig. 1 can be obtained. Therefore, it can be said that the single unit cell 5 is a minimum analysis unit of the bionic staggered laminated thin-plate structure preset with the breakable body. As can be seen from fig. 2, the single cell 5 can be further divided into hard bodies 1a, 1b, 1c, 1d, 2, 3a, 3b and cavities 4, wherein the hard bodies 1a and 1d are actually one hard body connected to each other, and they only have different internal stress distribution states, and are labeled with different reference numerals for convenience of analysis. Similarly, the hard bodies 1b and 1c are also integrated.
Furthermore, as can be seen from fig. 2, the single cell 5 is structurally symmetrical with respect to the center point of the soft matrix 2 located inside, that is, the cell 5 is rotated 180 ° around the center point of the soft matrix 2, and can coincide with the original structural pattern; alternatively, the individual cells 5 are structurally antisymmetric about a horizontal axis (the direction is the same as the structural length direction) at the center point of the over-soft matrix.
Aiming at the bionic staggered laminated thin-plate structure preset with the breakable body, the invention provides an effective rigidity and toughness adjusting method, which comprises the following specific implementation processes:
firstly, defining a phase 0 and a phase 1 of a cell, and respectively establishing constitutive models of the cell in two phase states;
since the breakable body 3 in the cellular cell 5 will break under the action of external force, so that the structural characteristics of the cellular cell 5 before and after the break change, two "phase states" are defined for the cellular cell 5, respectively: "0 phase" -the phase before the fragmentation of the cleavable body 3, and "1 phase" -the phase after the fragmentation of the cleavable body 3. When the breakable body 3 breaks under the action of load, the cellular unit 5 will gradually change from "phase 0" to "phase 1", which reflects the change of mechanical parameters such as rigidity and toughness of the whole structure.
1) Constitutive model of cellular structure under' 0 phase
Referring to the cell structure shown in fig. 2, for convenience of description, a planar rectangular coordinate system o-xy is established, in which the x-axis direction is the same as the length direction of the hard bodies 1 and the soft bases 2, and the y-axis direction is perpendicular to the x-axis direction and the same as the width direction of the hard bodies 1 and the soft bases 2. FIG. 3 further shows the material property parameters of each region within the unit cell 5 and the geometrical parameters of the structure, assuming that the material in all regions is linear elastic material, wherein E m Is the elastic modulus of the hard body 1, E e The modulus of elasticity of the breakable body 3, G the shear modulus of the soft matrix; b and h are the widths of the hard body 1 and the soft body 2, respectively, l a And l b Respectively, the length of the soft base 2 and the breakable body 3, wherein l a Can also be regarded as a uniform overlapping length of the hard bodies 1, and b can also be considered as non-overlapping lengths of the duromer 1; the width and thickness of the breakable body 3 are the same as those of the rigid body 1 (since the object of the present invention is a thin plate structure, the dimension in the thickness direction is not shown in fig. 1, 2 and 3), so that a single rigid body 1 (i.e., the whole of the rigid body 1b and the rigid body 1 c) having a length l is obtained a +l b I.e. the length of an individual hard body 1 is equal to the sum of the length of a soft matrix 2 and the length of a breakable body 3.
Based on the division of the cellular structure region shown in fig. 2, fig. 4 shows the definition and distribution of internal stress when the cell 5 in phase 0 is deformed by an external axial tensile load F. As can be seen from fig. 4, the hard body 1 and the breakable body 3 can only withstand normal stress, and the soft matrix 2 can only withstand shear stress. The breakable body 3 is a region where breaking failure can occur, and the criterion of maximum tensile stress is taken as the criterion of breaking.
To facilitate the description of the mechanical model, several dimensionless geometric parameters and materials are definedMaterial parameters, wherein the geometric parameters comprise: length-width ratio rho ═ l of overlapped duromer region a B, length-width ratio of soft matrix lambda ═ l a H, length ratio eta of hard body overlapping area to non-overlapping area is l a /l b The approximate volume fraction phi of the hard body is 2b/(2b + h); the material parameters include: the tensile modulus ratio alpha of the breakable body to the rigid body is E e /E m The ratio beta of the shear modulus of the soft matrix to the tensile modulus of the hard matrix is G/E m 。
Under the coordinate system o-xy defined in FIG. 2, the mechanical constitutive model of the unit cell under "phase 0" is established. For zones 1a, 1b and 2, a shear hysteresis model was used, with:
where σ and τ denote the positive stress in the hard body and the shear stress in the soft matrix, respectively, and subscripts 1a and 1b denote the corresponding hard body regions.
Assuming that the stress distribution in the breakable bodies 3a, 3b and the hard bodies 1c, 1d is uniform, under this assumption, the boundary conditions can be written as:
σ 1a (0)＝σ 1b (l a )＝σ 1c ＝σ 1d (2)
from the force balance relationship between the area 3b and the area 1b or between the area 3a and the area 1a, another boundary condition can be derived as follows:
furthermore, from the force balance relationship of the entire cell, the following equation holds:
where phi is the aforementioned approximate volume fraction of the duromer,
is the volume average stress of the cellular structure.
By solving equation (1) by using the boundary condition equations (2) and (3) and simplifying the equation (4), the stress distributions of the hard material regions 1a and 1b and the soft matrix region 2 in the "0 phase" state can be obtained as follows
Wherein α ═ E e /E m ,β＝G/E m ,ρ＝l a /b,λ＝l a /h,η＝l a /l b Are dimensionless geometric parameters or dimensionless material parameters which have been defined previously; sinh represents a hyperbolic sine function, and cosh represents a hyperbolic cosine function; k is a dimensionless parameter reflecting the combined geometric and material effects of the regions 1a, 1b and 2, and is expressed as follows
The stresses in the breakable body regions 3a and 3b and the hard body regions 1c and 1d can be further determined as follows by the simultaneous relational expressions (2), (3) and (4)
In the formula, tanh represents a hyperbolic tangent function.
The relation between the stress and the displacement in each region of the unit cell is completely described by the formula (5) and the formula (7), and the combination of the formula (5) and the formula (7) is a constitutive relation model of the unit cell structure under the '0 phase'.
2) Constitutive model of cellular structure under' 1 phase
The "phase 1" is the phase state of the cell after the breakable body 3 is broken, in this case, the breakable body 3 has been broken under the tensile load, only the hard bodies 1a, 1b, 1c, 1d and the soft matrix 2 bear the force, and the stress definition and distribution diagram of the cell structure in phase 1 are shown in fig. 5.
At phase 1, the shear hysteresis models of regions 1a, 1b, and 2 remain the same as for equation (1); however, the boundary conditions will change as follows:
furthermore, consider that the entire cellular structure is in force balance, σ 1c And σ 1d Satisfies the following conditions:
wherein phi is the approximate volume fraction of the duromer,
is the volume average stress of the cellular structure.
The boundary condition formula (8) is used to solve the formula (1) and simplify the formula, so that a constitutive model of the '1-phase' cellular structure can be obtained
In the formula, coth represents a hyperbolic cosecant function, and csch represents a hyperbolic cosecant function.
Secondly, respectively obtaining the effective elastic modulus of the structure under the phase 0 and the phase 1 and the decrease rate of the effective elastic modulus from the phase 0 to the phase 1, and selecting a dimensionless geometric parameter eta and a dimensionless material parameter alpha to adjust the rigidity of the structure;
in this example, the effective modulus of elasticity is used to describe the stiffness of the overall structure. Mean stress according to volume
And average strain
The calculation formula of (2):
the effective elastic modulus of the cells in the '0 phase' can be obtained
Is composed of
Where a ═ ktanh (k) is a dimensionless parameter defined for the sake of writing simplification.
And effective modulus of elasticity in the "1 phase
Is composed of
Combined stand
And
can obtain the product
The above formula (14) indicates that the effective elastic modulus of the structure inevitably decreases when the unit cell changes from "0 phase" to "1 phase". The rate of decrease in effective elastic modulus is defined as:
selecting a dimensionless geometric parameter eta and a dimensionless material parameter alpha as independent variables, and reasonably selecting the values of the two parameters to realize the adjustment of the structural rigidity.
The dimensionless geometric parameter η and the dimensionless material parameter α are specifically analyzed for effective elastic modulus
And rate of decrease of effective modulus
The influence of (c). In the simulation, the value range of the geometric parameter eta is 5-500, the value range of the material parameter alpha is 0.01-0.1, and the values of other parameters are shown in the following table 1.
TABLE 1 evaluation of simulation parameters
| Parameter(s) | β | ρ | λ | φ | A |
| Value taking | 0.4 | 2 | 10 | 0.9091 | 1.928 |
Obtaining a dimensionless geometric parameter eta and a dimensionless material parameter alpha to the effective elastic modulus
And rate of decrease of effective modulus
The influence analysis graphs of (a) are shown in fig. 6a and 6b, respectively. As can be seen from fig. 6a and 6b, as η increases,
and
will gradually increase, but the rate of increase will continuously decay and eventually gradually approach its limit, i.e.
As can be seen from both equation (14) and figure 6a,
independent of the parameter α, i.e. η is
The only influencing factor. For this purpose, a first threshold value η of the dimensionless geometrical parameter η can be defined c1 When η ═ η c1 When the temperature of the water is higher than the set temperature,
99.7% of its maximum limit value will be reached, at which point the following holds
From this, can find
However, it is possible to use a single-layer,
is simultaneously influenced by eta and alpha, an
Will grow as a increases. Thus, a second threshold value eta of the dimensionless geometrical parameter eta can be defined c2 When eta is equal to eta c2 When the temperature of the water is higher than the set temperature,
will reach 99.7% of its maximum limit at which point
From this, can find
As can be seen from FIG. 6b, the effective elastic modulus decays
Will decrease with increasing η and eventually approach a minimum limit, i.e.
Thus, the first dimensionless geometric parameter η can be defined as wellThree critical values eta c3 When η ═ η c3 When the temperature of the water is higher than the set temperature,
will reach 100.3% of its limit value, at which point
From this, can find
In general, it is desirable that the range of stiffness adjustment of the biomimetic cross laminated sheet structure designed is as large as possible, i.e., the effective elastic modulus decrease rate of the unit cell is desired
As small as possible, that is, η should be as large as possible. In this regard, both η and α should be set to be maximum under structural stiffness and design constraints. Thus, when the material composition is determined, i.e. alpha is timed, eta c3 The lower limit of the range is selected for η, i.e., the lower limit of η design is determined by the stiffness adjustment range requirements.
And thirdly, obtaining an expression of the structural toughness, and adjusting the structural toughness by adopting the dimensionless geometric parameter eta and the dimensionless material parameter alpha.
Material toughness is generally defined as the maximum stored energy per unit mass before the material breaks. In the present embodiment, the structural toughness refers to a toughness variation amount related to the structural configuration and structural parameters, and this special toughness is defined as the specific energy dissipation when the breakable body 3 breaks, which also reflects the additional toughness increase caused by the bionic staggered laminated thin-film structure with the preset breakable body in the process of "phase change" compared with the traditional bionic staggered laminated structure.
In this example, the stress-strain response of the structure is assumed to be unidirectional and hysteresis characteristics are not consideredProperties, the normalized "structural toughness" of the cells is denoted T cell And is defined as
Wherein,
and
critical average stresses in phase 0 and phase 1, respectively, expressed as
In the formula,
is the ultimate tensile stress of the breakable body 3.
While
Is the critical average strain expressed as
It is noted that the fracture of the fracturable entity occurs repeatedly within each periodic cell, and the "structural toughness" T of the entire biomimetic structure can be calculated by simple superposition, i.e., by
T＝∑T cell (29)
Without loss of generality, one cell is selected for analysis, and the structural toughness of the cell can be deduced to be
The effect of the pair was analyzed and the results are shown in fig. 7. As can be seen from FIG. 7, as α increases from 0.01 to 0.1, the structural toughness T cell Will gradually fall. It can also be seen that as η increases, the structural toughness T cell Will decrease with a decreasing decay slope and eventually approach a minimum limit, i.e. the value of
Thus, a fourth threshold η of η may be defined c4 When η ═ η c4 Structural toughness of T cell Will reach 100.3% of its limit value, at which point
From this can be calculated
In order to obtain a higher structural toughness T cell The α and η of the unit cell should be set as small as possible. Thus, when the structural material is determined, the upper limit of the η selection range is η c4 This is the T of the cellular structure cell As determined by the requirements.
By combining the above analysis and specific implementation processes, the flow of the stiffness and toughness adjusting method of the bionic staggered lamination thin-plate structure of the invention can be summarized in fig. 8. The invention can effectively adjust the structural rigidity and toughness only by reasonably taking values of two dimensionless parameters, namely the geometric parameter eta and the material parameter alpha, thereby having the advantage of relatively simple adjustment mode. In addition, the bionic staggered laminated thin plate structure can achieve a large rigidity range and high structural toughness, and therefore the bionic staggered laminated thin plate structure has the advantage of a large adjusting range.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention, and all equivalent structural changes made by using the contents of the present specification and the drawings, or any other related technical fields, which are directly or indirectly applied to the present invention, are included in the scope of the present invention.
Claims (10)
1. A rigidity and toughness adjusting method of a bionic staggered laminated thin plate structure is characterized in that, the bionic staggered laminated thin plate structure comprises a plurality of hard bodies (1) which are arranged in parallel, a plurality of soft matrixes (2) which are arranged in parallel and a plurality of breakable bodies (3), the hard bodies (1) and the soft base bodies (2) are both in a strip shape and are sequentially staggered in the vertical direction, the breakable body (3) is arranged between two adjacent hard bodies (1) and can be broken under the action of external axial tensile load, the bionic staggered laminated thin-plate structure can be obtained by firstly carrying out two mirror images in the vertical and horizontal directions and then carrying out linear array on one cell (5), the cellular elements (5) are structurally and centrally symmetrical about a central point of the soft matrix (2) located inside, and the rigidity and toughness adjusting method comprises the following steps: firstly, defining a 0 phase and a 1 phase of a cellular cell (5), and respectively establishing a constitutive model of the cellular cell (5) under two phase states of the 0 phase and the 1 phase; secondly, respectively obtaining the effective elastic modulus of the cells (5) under the phase 0 and the phase 1 and the decrease rate of the effective elastic modulus from the phase 0 to the phase 1, and selecting a dimensionless geometric parameter eta and a dimensionless material parameter alpha to adjust the rigidity of the structure; and thirdly, obtaining an expression of the structural toughness, and adjusting the structural toughness by adopting the dimensionless geometric parameter eta and the dimensionless material parameter alpha.
2. The method for adjusting the rigidity and toughness of a bionic staggered laminated thin plate structure as claimed in claim 1, wherein the method for adjusting the rigidity and toughness comprises the following detailed steps:
firstly, defining a phase 0 and a phase 1 of a cell (5), and respectively establishing a constitutive model of the cell in two phase states of the phase 0 and the phase 1 by adopting a shear hysteresis model;
phase 0 is the phase state before the fracturable body (3) is fractured, and the constitutive model of the elementary cell (5) under phase 0 is as follows:
wherein phi is 2b/(2b + h) which is the approximate volume fraction of the hard body,
is the volume average stress of the cellular structure; sinh represents a hyperbolic sine function, cosh represents a hyperbolic cosine function, tanh represents a hyperbolic tangent function, and tanh represents a hyperbolic tangent function; σ and τ represent the normal and shear stresses, respectively, and subscripts 1a, 1b, 1c, 1d, 2, 3a, and 3b represent the corresponding cellular regions; ρ ═ l a B is the length-width ratio of the overlapped hard body region, λ ═ l a H is the aspect ratio of the soft matrix,. eta. -. l a /l b The length ratio of the overlapped region to the non-overlapped region of the hard body, alpha ═ E e /E m The tensile modulus ratio of the breakable body to the rigid body, β ═ G/E m The ratio of the shear modulus of the soft matrix to the tensile modulus of the hard matrix; b and h are the widths of the hard body (1) and the soft matrix (2), respectively, l a And l b Respectively the length of the soft matrix (2) and the breakable body (3) | a And l b Can also be considered as a uniform overlapping length and a non-overlapping length of the duromer (1), respectively; e m Is the elastic modulus of the hard body (1), E e Is the modulus of elasticity of the breakable body (3), G is the shear modulus of the soft matrix (2);
is a dimensionless parameter that reflects the overall geometric and material effects;
phase 1 is the phase state after the fracturable body (3) is fractured, and the constitutive model of the elementary cell (5) under phase 1 is as follows:
wherein, coth represents a hyperbolic cosecant function, csch represents a hyperbolic cosecant function;
secondly, respectively obtaining the effective elastic modulus of the unit cells under the phase 0 and the phase 1 and the reduction rate of the effective elastic modulus from the phase 0 to the phase 1 according to a calculation formula of volume average stress and strain, and selecting a dimensionless geometric parameter eta and a dimensionless material parameter alpha to adjust the rigidity of the structure;
effective elastic modulus of 0-phase unit cell
Comprises the following steps:
wherein a ═ K tanh (K) is a self-defined dimensionless parameter;
effective elastic modulus of 1-phase lower unit cell
Comprises the following steps:
rate of decrease in effective modulus of elasticity from phase 0 to phase 1
Comprises the following steps:
adjusting the rigidity of the bionic staggered laminated thin plate structure by reasonably selecting a dimensionless geometric parameter eta and a dimensionless material parameter;
thirdly, defining the structural toughness as the specific energy dissipation when the breakable body breaks, obtaining an expression of the structural toughness, and adjusting the structural toughness by adopting a dimensionless geometric parameter eta and a dimensionless material parameter alpha;
toughness T of cellular structure cell The expression of (a) is:
wherein,
is the ultimate tensile stress of the breakable body (3);
and adjusting the toughness of the bionic staggered laminated thin plate structure by reasonably selecting the values of the dimensionless geometric parameter eta and the dimensionless material parameter alpha.
3. The method of adjusting stiffness and toughness of a biomimetic cross-laminated sheet structure of claim 1, wherein the dimensionless geometric parameter η has a first critical value η c1 ：
Effective modulus of elasticity of phase 1
Increases as η increases; when eta is eta ═ eta c1 Effective modulus of elasticity of 1 phase
99.7% of the maximum limit value.
4. The method of claim 2, wherein the dimensionless geometric parameter η has a second threshold η c2 ：
Effective modulus of elasticity of phase 0
Increases as η increases; when eta is eta ═ eta c2 Effective modulus of elasticity of the 0 phase
99.7% of the maximum limit value.
5. The method of claim 3, wherein the dimensionless geometric parameter η has a third threshold η c3 ：
Effective elastic modulus decrease rate of 0 phase to 1 phase
Decreases as η increases; when eta is eta ═ eta c3 Rate of decrease in effective elastic modulus of 0 phase to 1 phase
100.3% of the minimum limit value.
6. The method of claim 4, wherein the dimensionless geometric parameter η further comprises a fourth threshold η c4 ：
Structural toughness T cell Decreases as η increases; when eta is eta ═ eta c4 Structural toughness T cell 100.3% of the minimum limit value.
7. The method of claim 1 or 5, wherein the third threshold η is determined when the material composition of the biomimetic cross laminated sheet structure is determined c3 The lower limit of the range is selected for the dimensionless geometrical parameter η.
8. The method of claim 1 or 6, wherein the fourth threshold η is determined when the material composition of the biomimetic cross laminated sheet structure is determined c4 The upper limit of the range is selected for the dimensionless geometrical parameter η.
9. The method for adjusting the rigidity and toughness of the bionic staggered lamination thin plate structure as claimed in claim 1, wherein the dimensionless material parameter α has a value ranging from 0.01 to 0.1.
10. The method for adjusting the rigidity and toughness of the bionic staggered laminated sheet structure as claimed in claim 1, wherein the dimensionless geometric parameter η has a value in the range of 5-500.
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