CN113936753A - Impact-resistant bionic staggered structure containing viscoelastic matrix - Google Patents

Impact-resistant bionic staggered structure containing viscoelastic matrix Download PDF

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CN113936753A
CN113936753A CN202111069212.1A CN202111069212A CN113936753A CN 113936753 A CN113936753 A CN 113936753A CN 202111069212 A CN202111069212 A CN 202111069212A CN 113936753 A CN113936753 A CN 113936753A
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CN113936753B (en
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聂云清
罗青
刘畅
季浩然
段富强
张涵
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Abstract

The invention discloses an impact-resistant bionic staggered structure containing a viscoelastic matrix, and belongs to the technical field of structural design of bionic composite materials. In order to improve the energy consumption characteristic of the existing bionic staggered laminated composite structure under the impact load, the invention provides the bionic staggered composite structure which takes a hard body thin plate as a reinforcing body and a viscoelastic material as a matrix, and under the action of the impact load, the matrix can dissipate impact energy through viscosity, so that the impact resistance of the whole structure is improved. The invention better simulates the staggered structure composed of hard mineral substance reinforcement and soft protein matrix in the biological materials such as bones, shell pearl layers and the like, and has better shock resistance.

Description

Impact-resistant bionic staggered structure containing viscoelastic matrix
Technical Field
The invention belongs to the technical field of structural design of bionic composite materials, and particularly relates to an impact-resistant bionic staggered structure containing a viscoelastic matrix.
Background
Over millions of years of evolution, many organisms have developed biocomposites with higher strength and better toughness, and mammalian bones are an important tissue structure in higher organisms and are one of the most representative natural biological hard materials. The bones have excellent comprehensive mechanical properties including light weight, high stiffness, high strength, high damping, strong fracture toughness and the like, so that the bones can support the weight of animals, resist external force and impact and protect internal soft organs.
Bones are mainly composed of three components: collagen matrix, mineral reinforcement (hydroxyapatite) and water. These three components change with the age of the animal, and the proportion of the three components in different types of bones also differs significantly, which is one of the main reasons for influencing the mechanical properties of bones. The skeleton structure has the characteristics of multiple levels and multiple scales, and the nano-scale structure is formed by staggered arrangement of hard hydroxyapatite crystals as a reinforcement and soft collagen molecules as a matrix. The Young modulus of the hydroxyapatite is about 130GPa, and the strength is about 100 MPa; the shear modulus of collagen is about 1.25GPa, the Young modulus is about 50 to 100MPa, and the strength is about 20 MPa; the young's modulus of bones ranges from 8 to 24GPa, the strength is about 100MPa, and bones take full advantage of the advantages (stiffness and deformability) of both components while avoiding their disadvantages (brittleness and poor load-bearing capacity).
The existing bionic staggered composite structure mainly utilizes the staggered arrangement of hard reinforcements and soft matrixes to ensure that the structure achieves the characteristics of light weight, high rigidity and high toughness, and the static property of the structure is improved. However, the load borne by the actual structure is mostly complex dynamic load, the biological structure also bears the dynamic load in the actual environment, the main energy consumption mode of the structure in the skeleton is the viscosity of the collagen matrix, and the collagen matrix is introduced into the structural design, so that the impact-resistant bionic staggered structure containing the viscoelastic matrix is invented, and the impact resistance property of the structure can be improved.
Disclosure of Invention
The invention aims to provide an impact-resistant bionic staggered structure containing a viscoelastic matrix, and aims to improve the energy consumption characteristic of the existing bionic staggered structure under the impact load and improve the impact resistance of the structure.
The purpose of the invention is realized by the following technical scheme:
the utility model provides a bionical staggered structure that shocks resistance that contains viscoelastic base member which characterized in that includes a plurality of parallel arrangement's stereoplasm reinforcement (1) and has soft base member (2) of viscoelastic characteristic, stereoplasm reinforcement (1) are rectangular shape and staggered arrangement in proper order on vertical direction, inlay in soft base member (2).
Furthermore, the bionic staggered structure has periodicity and repeatability, multiple cyclic mirroring can be performed on one unit cell structure (3) in the vertical direction, then multiple cyclic mirroring is performed on the unit cell structure in the horizontal direction again, the whole structure of the bionic staggered structure is obtained, and the unit cell structure (3) is a minimum analysis unit of the bionic staggered structure.
Furthermore, the unit cell structure (3) is composed of an upper hard reinforcement (1a), a lower hard reinforcement (1b) and a soft matrix (2), the soft matrix (2) fills the cavity part except the upper hard reinforcement and the lower hard reinforcement, the upper hard reinforcement (1a) and the lower hard reinforcement (1b) have the same size, and the height and the length of the upper hard reinforcement (1a) and the lower hard reinforcement (1b) are b and L respectivelyhThe thickness of the soft matrix (2) is h, and the unit cell structure length is L.
Furthermore, the hard reinforcement body (1) is made of a linear elastic material, generates linear elastic deformation and can store impact energy, the constitutive relation of the hard reinforcement body accords with Hooke's law,
σ＝λTr(ε)I+2με
where σ is the stress tensor, ε is the strain tensor, Tr () is the trace of the matrix, μ is the shear modulus, I is the identity matrix, λ is the Lame constant,
Figure BDA0003259495690000021
e is the elastic modulus of the material, and v is the Poisson's ratio;
the soft matrix (2) is a viscoelastic material, generates viscoelastic deformation, can store and dissipate energy, has constitutive relation in accordance with a Kelvin-Voigt constitutive model, and can be expressed as
Figure BDA0003259495690000022
Where σ is the stress tensor, ε is the strain tensor,
Figure BDA0003259495690000023
is the derivative of the strain tensor with respect to time, λ is the Lame constant, Tr () is the trace of the matrix, μ is the shear modulus, I is the identity matrix, θμAnd thetaλIs characterized by a lag time of
Figure BDA0003259495690000024
η is the viscosity coefficient.
The invention also provides a method for analyzing the dynamic characteristics of the single cell structure of the impact-resistant bionic staggered structure containing the viscoelastic matrix, which utilizes ABAQUS finite element software and specifically comprises the following steps:
s1, establishing a unit cell structure geometric model which is a two-dimensional plane model;
s2, endowing material attributes to the hard reinforcement body and the soft matrix, wherein the hard reinforcement body material constitutive model adopts a linear elasticity constitutive model in ABAQUS, and the soft matrix material viscoelasticity constitutive model is realized by compiling a VUMAT constitutive subprogram;
s3, creating an analysis step, wherein the analysis step is a Dynamic Explicit display dynamics analysis step in ABAQUS/Explicit, and the time step is an automatic time step;
s4, defining boundary conditions and impact load
Constraining the longitudinal displacement of the upper and lower boundaries of the unit cell structure; respectively applying coupling constraint to the left side and the right side of the unit cell structure to enable the transverse displacement of the left side and the transverse displacement of the right side to be equal, and applying stress impact loads to the left side and the right side of the model;
the impact load type is back peak sawtooth wave impact;
s5, dividing grids, wherein the grid unit type is a four-node plane stress unit;
s6, submit Job, and solve.
Further, the viscoelastic constitutive subroutine VUMAT described in sub-step S2 requires defining a stress increment Δ σ and a viscous energy consumption increment Δ Ediss，
The stress increment delta sigma can be obtained by deriving time according to the Kelvin-Voigt constitutive model
Figure BDA0003259495690000031
In the formula, sigma is stress tensor, epsilon is strain tensor, delta t is time increment, delta epsilon is strain tensor increment, lambda is Lame constant, Tr () is trace of matrix, mu is shear modulus, I is unit matrix, thetaμAnd thetaλIs characterized by a lag time of
Figure BDA0003259495690000032
Eta is a viscosity coefficient;
said viscous energy consumption increase Δ EdissIs defined by the formula
Figure BDA0003259495690000033
Wherein λ is Lame constant, θμAnd thetaλFor a characteristic lag time,. DELTA.t is the time increment,. DELTA.epsilonijIs the increment of the (i, j) th strain tensor, ni、njFor the dimension of the strain tensor ε, Σ represents the summation operator, δijIs the symbol Kronecker, when i ═ j, δij1, δ when i ≠ jij＝0。
The beneficial technical effects of the invention are as follows: the invention designs an impact-resistant bionic staggered structure containing a viscoelastic matrix, and under the action of impact load, the structure can dissipate energy through the viscosity of the matrix, so that the impact resistance of the bionic staggered structure is greatly improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or 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 view of an impact-resistant biomimetic staggered structure comprising a viscoelastic matrix;
FIG. 2 is a schematic diagram of a unit cell structure;
FIG. 3 is a schematic view of a unit cell structure in a vertically cyclic mirror image;
FIG. 4 is a flow chart of finite element simulation steps;
FIG. 5 is a schematic illustration of a post peak sawtooth impact load being loaded;
FIG. 6 is a schematic diagram of a finite element model and applied loads and boundary conditions;
FIG. 7 is taA Von Mises stress cloud plot at time;
FIG. 8 shows 10taA Von Mises stress cloud plot at time;
FIG. 9 is a graph of the variation of the external force work and the viscous energy consumption of the substrate with dimensionless time.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the 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.
Animal bones are composed of mineral reinforcements and protein matrixes which are arranged in a staggered mode under the nanoscale, wherein researches show that the protein matrixes have viscoelastic properties and can dissipate energy under the action of impact load. Based on the above, the present invention provides an impact-resistant bionic interlaced structure with a viscoelastic matrix, the structure of which is shown in fig. 1. As can be seen from FIG. 1, the bionic staggered structure containing the viscoelastic matrix comprises a plurality of hard reinforcements (1) which are arranged in parallel and a soft matrix (2) with viscoelastic property; the hard reinforcement bodies (1) are in a matrix and are sequentially staggered in the vertical direction and are embedded in the soft matrix (2). The hard reinforcement is elastically deformed by a line to store impact energy, and the soft matrix is deformed by viscoelasticity to store and dissipate energy.
The whole structure has periodicity and repeatability, a unit cell structure (3) shown in figure 2 can be subjected to multiple cyclic mirroring in the vertical direction to form a structure shown in figure 3, then the unit cell structure shown in figure 2 is subjected to multiple cyclic mirroring in the horizontal direction again to obtain a bionic staggered whole structure shown in figure 1, and the unit cell structure (3) is a minimum analysis unit of the bionic staggered structure. The unit cell structure (3) is a minimum analysis unit of the whole structure, and can be analyzed to reflect the mechanical characteristics of the whole structure. As shown in FIG. 2, the detail structure of the unit cell structure (3) is mainly composed of a hard reinforcing member 1a, a hard reinforcing member 1b, and a soft substrate 2.
For the sake of convenience of description, the dimensional parameters, b and L, in the unit cell structure (3) are illustratedhThe height and the length of the hard reinforcement 1a and the hard reinforcement 1b are respectively, h is the thickness of the middle soft matrix, and L is the length of the unit cell structure. The material parameters defined are as follows, Eh、vhAnd ρhElastic modulus, Poisson's ratio and density, respectively, of the hard reinforcementm、ηm、vmAnd ρmRespectively, the elastic modulus, viscosity coefficient, poisson's ratio and density of the soft matrix.
The hard reinforcement (1) is made of a linear elastic material, generates linear elastic deformation and can store impact energy, the constitutive relation of the hard reinforcement conforms to Hooke's law,
σ＝λTr(ε)I+2με
where σ is the stress tensor and ε is the strainThe variation number, Tr () is the trace of the matrix, mu is the shear modulus, I is the identity matrix, lambda is the Lame constant,
Figure BDA0003259495690000051
e is the elastic modulus of the material, and v is the Poisson's ratio;
the soft matrix (2) is a viscoelastic material, generates viscoelastic deformation, can store and dissipate impact energy, and has a constitutive relation conforming to a Kelvin-Voigt constitutive model and expressed as
Figure BDA0003259495690000052
Where σ is the stress tensor, ε is the strain tensor,
Figure BDA0003259495690000053
is the derivative of the strain tensor with respect to time, λ is the Lame constant, Tr () is the trace of the matrix, μ is the shear modulus, I is the identity matrix, θμAnd thetaλIs characterized by a lag time of
Figure BDA0003259495690000054
η is the viscosity coefficient.
The ABAQUS finite element software is adopted to perform simulation verification on the energy consumption characteristic of the bionic staggered structure containing the viscoelastic matrix under the impact load, the finite element simulation steps are shown in figure 4, and the specific steps are as follows:
step S1, establishing a geometric model of the unit cell structure, wherein the geometric model is a two-dimensional plane model as shown in FIG. 2;
step S2, endowing the hard reinforcement body and the soft substrate with material properties, wherein the hard reinforcement body material constitutive model adopts a linear elasticity constitutive model in ABAQUS, and the material parameters are directly input;
the soft matrix material viscoelasticity constitutive model is realized by writing a VUMAT constitutive subprogram, wherein a stress increment and a viscous energy consumption increment need to be defined in the subprogram, and the soft matrix material viscoelasticity constitutive model is realized by the following steps:
a substep S21, deriving the stress increment delta sigma according to the Kelvin-Voigt constitutive model and time
Figure BDA0003259495690000055
In the formula, sigma is stress tensor, epsilon is strain tensor, delta t is time increment, delta epsilon is strain tensor increment, lambda is Lame constant, Tr () is trace of matrix, mu is shear modulus, I is unit matrix, thetaμAnd thetaλIs characterized by a lag time of
Figure BDA0003259495690000056
Eta is a viscosity coefficient;
substep S22, said viscous energy consumption increment Δ EdissIs defined by the formula
Figure BDA0003259495690000057
Wherein λ is Lame constant, θμAnd thetaλFor a characteristic lag time,. DELTA.t is the time increment,. DELTA.epsilonijIs the increment of the (i, j) th strain tensor, ni、njFor the dimension of the strain tensor ε, Σ represents the summation operator.
Step S3, creating an analysis step, wherein the analysis step is a Dynamic Explicit display dynamics analysis step in ABAQUS/Explicit, and the time step is an automatic time step;
step S4, defining boundary conditions and impact load
Constraining the longitudinal displacement of the upper and lower boundaries of the unit cell structure; applying coupling constraint to the left side and the right side of the unit cell structure respectively to ensure that the transverse displacement of the left side and the transverse displacement of the right side are equal;
impact loads σ (t) are applied to the left and right sides of the model, and σ (t) is a rear-peak sawtooth wave impact, as shown in FIG. 5maxIs the load amplitude, taThe load duration.
Step S5, dividing grids, wherein the grid unit type is a four-node plane stress unit, the unit number is 6179, the node number is 6384, and a finite element unit model and a schematic diagram of applied loads and boundary conditions are shown in FIG. 6;
in step S6, Job is submitted for solution.
The materials and geometrical parameters used in the finite element model are shown in the following table:
TABLE 1 finite element model parameters
Parameter(s) Numerical value
L 5mm
Lh 4.5mm
b 0.5mm
h 0.1mm
Eh 105GPa
vh 0.27
ρh 2000kg
Em 3.56GPa
vm 0.27
ηm 5Pa·s
ρm 1000kg
σmax 10MPa
ta 1×10-7s
And under the action of the post-peak sawtooth wave impact load, the dynamic response characteristic of the unit cell structure is obtained through ABAQUS finite element software. FIG. 7 is taThe maximum Von Mises stress of the Von Mises stress cloud chart at the moment reaches 44.99MPa, and the maximum Von Mises stress cloud chart is 10t in the graph 8aIn a Von Mises stress cloud chart at the moment, the maximum Von Mises stress is 9.34MPa, and the maximum stress of a unit cell structure is obviously reduced due to the energy consumption effect of a viscoelastic matrix. FIG. 9 is a graph of the external force working and the matrix viscous energy consumption along with the dimensionless time t/taThe graph shows that the viscous energy consumption of the matrix is gradually increased along with the gradual increase of the analysis time, and the energy consumption is 10taAt the moment, the viscous energy consumption reaches 50% of the input work, the viscoelastic matrix can dissipate the input energy of the impact load, and the impact resistance of the structure is effectively improved.
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and it will be apparent to those skilled in the art that various modifications and variations can be made in the embodiment of the present application. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims (6)

1. The utility model provides a bionical staggered structure that shocks resistance that contains viscoelastic base member which characterized in that includes a plurality of parallel arrangement's stereoplasm reinforcement (1) and has soft base member (2) of viscoelastic characteristic, stereoplasm reinforcement (1) are rectangular shape and staggered arrangement in proper order on vertical direction, inlay in soft base member (2).
2. The impact-resistant bionic staggered structure containing the viscoelastic matrix as claimed in claim 1, characterized in that the bionic staggered structure has periodicity and repeatability, and can be subjected to multiple cyclic mirroring in the vertical direction by a unit cell structure (3), and then to multiple cyclic mirroring in the horizontal direction again to obtain an overall structure of the bionic staggered structure, wherein the unit cell structure (3) is a minimum analysis unit of the bionic staggered structure.
3. The impact-resistant bionic staggered structure containing the viscoelastic matrix as claimed in claim 2, characterized in that the unit cell structure (3) is composed of an upper hard reinforcement (1a), a lower hard reinforcement (1b) and a soft matrix (2), the soft matrix (2) fills the cavity part except the upper and lower hard reinforcements, the upper hard reinforcement (1a) and the lower hard reinforcement (1b) have the same size, and the height and the length thereof are b and L respectivelyhThe thickness of the soft matrix (2) is h, and the unit cell structure length is L.
4. The impact-resistant bionic staggered structure containing the viscoelastic matrix as claimed in any one of claims 1 to 3, wherein the hard reinforcing body (1) is a linear elastic material, is subjected to linear elastic deformation and can store impact energy, and the constitutive relation of the structure conforms to Hooke's law:
σ＝λTr(ε)I+2με
where σ is the stress tensor, ε is the strain tensor, Tr () is the trace of the matrix, μ is the shear modulus, I is the identity matrix, λ is the Lame constant,
Figure FDA0003259495680000011
e is the elastic modulus of the material, and v is the Poisson's ratio;
the soft matrix (2) is a viscoelastic material, generates viscoelastic deformation, can store and dissipate energy, and has an constitutive relation conforming to a Kelvin-Voigt constitutive model, and the constitutive relation is expressed as follows:
Figure FDA0003259495680000012
where σ is the stress tensor, ε is the strain tensor,
Figure FDA0003259495680000013
is the derivative of the strain tensor with respect to time, λ is the Lame constant, Tr () is the trace of the matrix, μ is the shear modulus, I is the identity matrix, θμAnd thetaλIs characterized by a lag time of
Figure FDA0003259495680000014
η is the viscosity coefficient.
5. A method for performing kinetic analysis of a single cell structure comprising an impact-resistant biomimetic interlaced structure with a viscoelastic matrix according to any of claims 1-4, using ABAQUS finite element software, comprising the steps of:
s1, establishing a unit cell structure geometric model which is a two-dimensional plane model;
s2, endowing material attributes to the hard reinforcement body and the soft matrix, wherein the hard reinforcement body material constitutive model adopts a linear elasticity constitutive model in ABAQUS, and the soft matrix material viscoelasticity constitutive model is realized by compiling a VUMAT constitutive subprogram;
s3, creating an analysis step, wherein the analysis step is a Dynamic Explicit display dynamics analysis step in ABAQUS/Explicit, and the time step is an automatic time step;
s4, defining boundary conditions and impact load
Constraining the longitudinal displacement of the upper and lower boundaries of the unit cell structure; respectively applying coupling constraint to the left side and the right side of the unit cell structure to enable the transverse displacement of the left side and the transverse displacement of the right side to be equal, and applying stress impact loads to the left side and the right side of the model;
the impact load type is back peak sawtooth wave impact;
s5, dividing grids, wherein the grid unit type is a four-node plane stress unit;
s6, submit Job, and solve.
6. Method for performing kinetic analyses according to claim 5, characterized in that said viscoelastic constitutive subroutine VUMAT, in sub-step S2, requires definition of the stress increment Δ σ and of the viscous dissipation increment Δ Ediss，
The stress increment delta sigma can be obtained by deriving time according to the Kelvin-Voigt constitutive model
Figure FDA0003259495680000021
In the formula, sigma is stress tensor, epsilon is strain tensor, delta t is time increment, delta epsilon is strain tensor increment, lambda is Lame constant, Tr () is trace of matrix, mu is shear modulus, I is unit matrix, thetaμAnd thetaλIs characterized by a lag time of
Figure FDA0003259495680000022
Eta is a viscosity coefficient;
said viscous energy consumption increase Δ EdissIs defined by the formula
Figure FDA0003259495680000023
Wherein λ is Lame constant, θμAnd thetaλFor a characteristic lag time,. DELTA.t is the time increment,. DELTA.epsilonijIs the increment of the (i, j) th strain tensor, ni、njFor the dimension of the strain tensor ε, Σ represents the summation operator, δijIs the symbol Kronecker, when i ═ j, δij1, δ when i ≠ jij＝0。
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