CN111814382B - Wavefront recognition method for propagation of non-planar wave in multicellular material - Google Patents
Wavefront recognition method for propagation of non-planar wave in multicellular material Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 41
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- 238000006073 displacement reaction Methods 0.000 claims abstract description 8
- 238000004088 simulation Methods 0.000 claims description 17
- 210000004027 cell Anatomy 0.000 claims description 16
- 230000035939 shock Effects 0.000 claims description 13
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- 238000010899 nucleation Methods 0.000 claims description 12
- 230000001788 irregular Effects 0.000 claims description 7
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- 238000012512 characterization method Methods 0.000 claims description 4
- 238000013507 mapping Methods 0.000 claims description 4
- 230000001902 propagating effect Effects 0.000 claims description 4
- 238000010297 mechanical methods and process Methods 0.000 claims description 3
- 210000002421 cell wall Anatomy 0.000 claims description 2
- 230000001419 dependent effect Effects 0.000 claims description 2
- 230000000694 effects Effects 0.000 claims 1
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- 238000004519 manufacturing process Methods 0.000 abstract description 5
- 238000004806 packaging method and process Methods 0.000 abstract description 5
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- XAGFODPZIPBFFR-UHFFFAOYSA-N aluminium Chemical compound [Al] XAGFODPZIPBFFR-UHFFFAOYSA-N 0.000 description 7
- 229910052782 aluminium Inorganic materials 0.000 description 7
- 239000006261 foam material Substances 0.000 description 6
- 238000012360 testing method Methods 0.000 description 4
- 238000003892 spreading Methods 0.000 description 3
- 239000013598 vector Substances 0.000 description 3
- 238000005516 engineering process Methods 0.000 description 2
- NRNCYVBFPDDJNE-UHFFFAOYSA-N pemoline Chemical compound O1C(N)=NC(=O)C1C1=CC=CC=C1 NRNCYVBFPDDJNE-UHFFFAOYSA-N 0.000 description 2
- 230000007704 transition Effects 0.000 description 2
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- 229910000838 Al alloy Inorganic materials 0.000 description 1
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- 230000006835 compression Effects 0.000 description 1
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Abstract
The invention discloses a wavefront recognition method for non-planar wave propagation in a multicellular material, which is based on a grid node displacement field generated by numerical simulation software, adopts a local strain field calculation method based on a least square discrete local deformation gradient, adopts a continuous medium mechanical calculation method to convert Green strain tensor into engineering strain tensor, and determines a non-planar wavefront position by an octahedral equivalent strain calculation method, thereby solving the problem of recognition of the non-planar wave in the multicellular material, providing a more accurate calculation method for recognizing the non-planar wave wavefront under the general application environment that a foam macrostructure presents a complex structure or a load is in a non-single direction, and simultaneously providing a powerful tool for recognizing propagation rules of the non-planar wavefront in the cellular material and laying a research foundation. The invention can be applied to basic scientific research and engineering design of anti-explosion and impact-resistant protection designs such as aerospace, military protection, automobile manufacturing, product packaging and the like.
Description
Technical Field
The invention relates to the technical field of multi-cell material shock wave front recognition, in particular to a wave front recognition method for non-plane waves propagating in multi-cell materials under explosion or impact conditions.
Background
The multicellular material is used as an impact protection buffer material, is widely applied to aerospace, military protection, automobile manufacture, product packaging and the like, and the propagation rule of the impact wave in the multicellular material has basic scientific research significance for antiknock impact protection design and important guiding significance for military and civil protection, and the identification technology of the impact wave front in discontinuous media such as the multicellular material is an important subject for research in the field.
At present, in the technical field of multi-cell material shock wave front recognition, the method is divided into two routes. The first route is an experimental means, as shown in fig. 1, a high-speed image of a multicellular material test piece under dynamic compression is shot through high-speed photography, then analysis is carried out through DIC digital correlation technique, a strain distribution field on the surface of the test piece is obtained, and the position of a wave front is determined according to the strain jump position; the second route is numerical simulation and theoretical calculation, a strain distribution field in a test piece cannot be obtained based on an experimental means, displacement field data at a unit node under an impact condition is obtained by adopting a multi-cell material microscopic numerical simulation method, a Green strain tensor at the node is obtained by adopting a local strain field calculation method based on a least square discrete local deformation gradient, and the strain is converted into strain in an impact direction through continuous medium mechanics, so that a strain jump position is identified, and a wavefront position is determined.
Of the two routes in the technical field of multi-cell material shock wave wavefront recognition, the first experimental route is limited by the fact that high-speed photography can only shoot the dynamic deformation of the outer surface of a test piece, and the internal deformation and the form of a shock wave wavefront cannot be obtained; the second numerical simulation+theoretical calculation route can only identify plane shock wave fronts in the multicellular material, and non-plane waves cannot be identified or interface identification is inaccurate because only positive strain components are considered and shear strain components are not involved. Based on the above, the present invention is proposed to solve the problem of recognizing the non-planar wave inside the multicellular material.
Disclosure of Invention
The present invention aims to solve the above problems by providing a wavefront recognition method for propagation of non-planar waves in multicellular material.
To achieve the above object, the present disclosure provides a wavefront recognition method of propagation of a non-planar wave in a multicellular material, including:
establishing a numerical simulation model of the multicellular material by a microscopic numerical simulation method, and carrying out dynamic numerical simulation under explosion or impact conditions;
obtaining a local strain field of the multicellular material by a local strain field calculation method;
converting the Green strain tensor into an engineering strain tensor by adopting a continuous medium mechanical calculation method;
the octahedral equivalent strain field formed by each node of the material is obtained by an octahedral equivalent strain calculation method, and the non-planar wavefront position is determined by software.
Alternatively, the multicellular material is modeled as a finite element model, pi at a designated macroscopic region of the material 0 The N nucleation points are distributed according to a uniform probability distribution, and the distance delta between the nucleation points is controlled to be not smaller than a given distance delta min ；
Generating cell edge and cell surface geometric information through MATLAB software, and performing grid division on cell surfaces to obtain a numerical simulation model of the multicellular material in finite element software ABAQUS.
Alternatively, for a multicellular material of regular mesostructure, a finite element model is constructed periodically using a finite element method.
Alternatively, for multicellular materials of random mesostructure, a finite element model is constructed using 3D-Voronoi random mesostructure.
Alternatively, in the multicellular material, discrete local deformation gradients based on least squares are used to describe discrete displacement fields resulting from multicellular material, resulting in local strain fields for the multicellular material.
Alternatively, the positive strain component and the shear strain component at the material node form an engineering strain tensor, and the Green strain tensor is solved by a continuous medium mechanical method.
Alternatively, the engineering strain tensor is mapped from 2 th order to 0 th order, and the octahedral equivalent strain calculation method is adopted to perform 0 th order characterization on the octahedral equivalent strain, so that an octahedral equivalent strain field is formed.
Optionally, according to the octahedral equivalent strain field formed by each node of the material, interpolation is performed on the three-dimensional discrete octahedral equivalent strain field through MATLAB software to obtain a three-dimensional continuous strain field, so that the purpose of identifying the non-plane wave front is achieved.
The invention has the beneficial effects that:
the invention relates to a wavefront recognition method for spreading non-planar waves in a multicellular material, which is based on a microscopic numerical simulation method and a local strain field calculation method, converts Green strain tensor into engineering strain tensor by adopting a continuous medium mechanical calculation method, and determines the recognition method of the equivalent strain field jump position and the non-planar wavefront position by an octahedral equivalent strain calculation method, thereby solving the recognition problem of the non-planar waves in the multicellular material, providing a more accurate calculation method for recognizing the non-planar wave wavefront under the general application environment that a foam macrostructure presents a complex structure or a load is non-unidirectional, and providing a powerful tool for recognizing the spreading rule of the non-planar wave wavefront in the cellular material, and laying a research foundation. The invention can be applied to basic scientific research and engineering design of anti-explosion and impact-resistant protection designs such as aerospace, military protection, automobile manufacturing, product packaging and the like.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
The accompanying drawings are included to provide a further understanding of the disclosure, and are incorporated in and constitute a part of this specification, illustrate the disclosure and together with the description serve to explain, but do not limit the disclosure. In the drawings:
FIG. 1 is a schematic diagram of the microstructure geometry of an aluminum foam according to the example;
FIG. 2 is a numerical model of the microstructure of aluminum foam of the example;
FIG. 3 is a cross-sectional view of a numerical simulated equivalent stress of an aluminum foam microstructure according to the example;
FIG. 4 is a mid-plane cross-sectional view of the ε 11 positive strain field under the aluminum foam microstructure local strain method described in the examples;
FIG. 5 is a graph of ε under the local strain of the microstructure of aluminum foam described in the examples eff A mid-plane cross-sectional view of an octahedral equivalent strain field.
Detailed Description
Specific embodiments of the present disclosure are described in detail below with reference to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating and illustrating the disclosure, are not intended to limit the disclosure.
The invention relates to a wavefront recognition method for spreading non-planar waves in a multicellular material, which is based on a grid node displacement field generated by numerical simulation software, adopts a local strain field calculation method based on a least square discrete local deformation gradient to obtain a Green strain tensor at a node, converts the Green strain tensor into an engineering strain tensor through continuous medium mechanics, adopts an octahedral equivalent strain calculation method to determine an equivalent strain field jump position and a non-planar wavefront position, thereby solving the problem of recognizing the non-planar waves in the multicellular material, providing a more accurate calculation method for recognizing the non-planar wave wavefront under the general application environment that a foam macrostructure presents a complex structure or a load is non-unidirectional, and simultaneously providing a powerful tool for recognizing the propagation rule of the non-planar wavefront in the cellular material and laying a research foundation. The invention can be applied to basic scientific research and engineering design of anti-explosion and impact-resistant protection designs such as aerospace, military protection, automobile manufacturing, product packaging and the like.
The specific implementation process is as follows:
1. mesoscopic numerical simulation method
The multicellular material is divided into a regular type and a random type microstructure, and for the multicellular material with the regular type microstructure, a finite element method can be utilized to directly and periodically build a model. For multicellular materials with irregular microscopic structures, such as foam materials, a finite element model is built by adopting a 3D-Voronoi random microscopic structure, and pi is firstly formed in a designated macroscopic area of the material 0 The N nucleation points are distributed according to a uniform probability distribution, and the distance delta between the nucleation points is controlled to be not smaller than a given distance delta min ：
δ min ＝(1-k)·δ 0 (1)
(1) Wherein k is the irregularity in the foam material characterizing the microstructure; delta 0 Is the minimum distance of any nucleation point piece of a decahedron Kelvin cell edge topology structure:
(2) Wherein V is cell Is the volume of a unit cell.
After the nucleation points are generated under the conditions, generating cell edges and cell surface geometric information through a Voronoi function in MATLAB. The cell surface is subjected to grid division by adopting a Hypermesh shell unit, and the foam cell wall thickness is set to be t in finite element software ABAQUS. And obtaining a numerical simulation model of the foam microstructure, and carrying out dynamic numerical simulation under explosion or impact conditions.
2. Local strain field calculation method
In the process of obtaining the non-planar shock wave of the microstructure of the foam material, not only the positive strain component at the node point is considered, but also the shear strain component at the node point is considered. The two components form an engineering strain tensor and are solved by the Green strain tensor through a continuous medium mechanical method.
Characterization of local deformation according to Green strain tensor E in continuous medium mechanics:
(3) Where F is the deformation gradient, I is the unit tensor, and superscript T denotes the tensor. In the multicellular material, discrete local deformation gradient based on the least square method is adopted to describe discrete displacement fields brought by multicellular property, so that local strain fields of the multicellular material are obtained.
Defining the node configuration of the foam material before deformation as omega 0 The deformed node is configured to be the current configuration omega 1 . Node i and its neighboring node j are in configuration Ω 0 And configuration omega 1 The relative displacement vectors in (a) are U respectively ij and uij ：
U ij ＝X i -X j (4)
u ij ＝x i -x j (5)
wherein ,Xi and Xj Is the configuration omega of node i and adjacent node j 0 Position vector, x i and xj Is the configuration omega of node i and adjacent node j 1 Is included in the position vector. Based on the assumption of local uniform deformation in continuous medium mechanics, the existence of a unique deformation gradient F between a node i and an adjacent node j will form a configuration omega 0 Mapping to configuration Ω 1 The method comprises the following steps:
u ij ＝F·U ij
(6)
because of the discrete type and the complexity of the microstructure of the multicellular material, the optimal deformation gradient F of the node i is obtained by the least square method of mapping the deformation gradients of all the configurations of the node i and other nodes in a certain range of the field of the node i i ：
If the equation and hence the determinant of the second term is 0, then it is assumed that node i is in a zero strain state at this time. Wherein the domain radius R of node i is set to 0.5R, R being the average radius of the cell.
3. Method for converting Green strain tensor E into engineering strain tensor E1
The Green strain tensor E obtained by the formula (7) and the formula (3) is:
wherein ,est Is a component of the Green strain tensor E, and subscripts s and t take 1,2,3, respectively.
For engineering strain tensor E 1 ：
wherein ,εst Is a component of the Green strain tensor E, and subscripts s and t take 1,2,3, respectively. For engineering strain tensor E 1 The mid-diagonal upper component ε ss The component of the Green strain tensor E can be expressed as:
engineering strain tensor E 1 The mid-off-diagonal upper component ε st The component of the Green strain tensor E can be expressed as:
4. octahedral equivalent strain calculation method
E obtained above 1 Representing the strain state at the node, but its attribute is the engineering strain tensor, which is highly dependent on the type and direction of the load when mapped to the foam microstructure. For example in the simplest case: the foam microstructure is a regular hexahedron with normal lines of each surface pointing to the x, y or z axis, and the load is in a single direction and along the x axisIf the foam microstructure is considered to be macroscopically uniform and continuous, the shock wave is a plane wave in the foam microstructure, in which case ε is obtained from formula (10) 11 The positive strain field, through strain jump position identification, can confirm the shock wave wavefront position. However, if the foam microstructure exhibits a non-regular hexahedral structure or the load is not unidirectional, the shock wave in the foam microstructure is a non-planar wave and the positive strain field determined by equation (10) cannot accurately identify the shock wave wavefront position from the strain relief position due to the presence of shear strain. The invention provides a method for adopting octahedral equivalent strain, which considers the influence of positive strain and shear strain and tenses engineering strain E 1 Complete consideration is made. Octahedral equivalent strain ε eff The method comprises the following steps:
5. non-plane wave front recognition method
According to the octahedral equivalent strain field formed by each node obtained through calculation, the ScatteredInterpolant function in MATLAB software is used for interpolating the three-dimensional discrete octahedral equivalent strain field to obtain a three-dimensional continuous strain field, so that the purpose of identifying the non-planar wave front is achieved.
Examples:
the macroscopic foam has a region size of 80mm×20mm, 600 nucleation points distributed according to uniform probability are randomly scattered in the region, the irregularity k of the microstructure is set to 0.2, and the minimum given distance delta between the nucleation points can be obtained according to the formula (1) and the formula (2) min About 3.3mm, the microstructure geometry of the aluminum foam is shown in figure 1. Grid division is carried out by adopting an S4R shell unit, the cell wall thickness of a foam material is set to be 0.045mm, an aluminum alloy is adopted as a foam material base material, an elastic ideal shaping material model is adopted, and the density is 2.77g/cm 3 Young's modulus of 69GPa, poisson's ratio of 0.3 and yield strength of 170MPa. In order to generate non-planar shock wave, a spherical shell is adopted at the impact end, a flat plate is adopted at the supporting end, and an explosion shock wave with characteristic time of 50 mu s and amplitude of 20MPa acts on the inner part of the spherical shellThe numerical model of the concave surface and the microstructure of the aluminum foam is shown in figure 2. The middle section of the equivalent stress distribution obtained after the numerical calculation is shown in fig. 3, and according to the principle that the front and back stress, strain and speed of the wavefront can generate abrupt transition, the abrupt transition interface cannot be identified, namely the position of the wavefront cannot be directly identified. After the displacement field information is output, the epsilon under the condition of positive strain is only considered by adopting a local strain method, namely the formulas (3) - (10) 11 A positive strain field, wherein the plane cross section is shown in figure 4; epsilon under the conditions of positive strain and shear strain can be considered simultaneously by adopting a local strain method and an octahedral equivalent strain calculation method, namely the formulas (3) - (12) eff The positive strain field, wherein the plane section is shown in figure 5, can more accurately identify the jump interface, thereby more accurately acquiring the position and morphological characteristics of the wave front.
The invention is based on the existing microscopic numerical simulation technology and local strain field calculation method, adopts a continuous medium mechanical calculation method to convert Green strain tensor into engineering strain tensor, and provides an identification method for determining the equivalent strain field jump position and the non-planar wavefront position through an octahedral equivalent strain calculation method, thereby solving the identification problem of non-planar waves in a multicellular material, providing a more accurate calculation method for identifying non-planar wave fronts in general application environments such as complex structures of foam macrostructures or non-single load directions, and providing a powerful tool for recognizing propagation rules of non-planar wave fronts in cellular materials. The invention can be applied to basic scientific research and engineering design of anti-explosion and impact-resistant protection designs such as aerospace, military protection, automobile manufacturing, product packaging and the like.
In addition, the specific features described in the foregoing embodiments may be combined in any suitable manner, and in order to avoid unnecessary repetition, the present disclosure does not further describe various possible combinations.
Moreover, any combination between the various embodiments of the present disclosure is possible as long as it does not depart from the spirit of the present disclosure, which should also be construed as the disclosure of the present disclosure.
Claims (3)
1. A method for wavefront recognition of a non-planar wave propagating in a multicellular material, comprising:
establishing a numerical simulation model of a multicellular material by a microscopic numerical simulation method, and carrying out dynamic numerical simulation under explosion or impact conditions, wherein the multicellular material is divided into a regular microscopic structure and a random microscopic structure; for the multicellular material with an irregular microscopic structure, a finite element model is constructed by adopting a 3D-Voronoi random microscopic structure, and the method specifically comprises the following steps:
in the designated macro-area of the materialΠ 0 Distributing N nucleation points according to uniform probability distribution and controlling the distance between the nucleation pointsδNot less than a given distanceδ min ：
(1)
（1） in the formula ,kcharacterizing irregularities of the microstructure in the multicellular material that is of an irregular microstructure;δ 0 is the minimum distance of any nucleation point piece of a decahedron Kelvin cell edge topology structure:
(2)
（2） in the formula ,V cell is the volume of a unit cell;
generating nucleation points under the above conditions, generating cell edge and cell surface geometric information through a Voronoi function in MATLAB, meshing cell surfaces by adopting Hypermesh shell units, setting the cell wall thickness of a multicellular material with an irregular microscopic structure as t in finite element software ABAQUS, obtaining a numerical simulation model of the multicellular material microscopic structure with the irregular microscopic structure, and carrying out dynamic numerical simulation under explosion or impact conditions;
obtaining a local strain field of the multicellular material by a local strain field calculation method; the method comprises the following steps:
acquiring a positive strain component at a node and a shear strain component at the node in a non-planar shock wave process of a multi-cellular material microstructure of an irregular microstructure, wherein the two components form an engineering strain tensor and are solved by a Green strain tensor through a continuous medium mechanical method;
characterization of local deformation according to Green strain tensor E in continuous medium mechanics:
(3)
（3） in the formula ,Fis a deformation gradient which is a gradient of the deformation,Iis the tensor of the unit, superscriptTMeans for representing tensors, in the multicellular material, using a discrete local deformation gradient based on a least square method to describe a discrete displacement field resulting from multicellular properties, resulting in a local strain field for the multicellular material;
converting the Green strain tensor into an engineering strain tensor by adopting a continuous medium mechanical calculation method;
obtaining an octahedral equivalent strain field formed by each node of the material by an octahedral equivalent strain calculation method, and determining the position of a non-planar wavefront by software; the method comprises the following steps:
the engineering strain tensor obtained above represents the strain state at the node, but the attribute is the engineering strain tensor, and the mapping to the multi-cell material microstructure of the irregular microstructure is highly dependent on the type and direction of the load; taking positive strain and shear strain effects into consideration, carrying out complete consideration on engineering strain tensors, mapping the engineering strain tensors from 2-order to 0-order, carrying out 0-order characterization on the octahedral equivalent strain by adopting an octahedral equivalent strain calculation method, thereby forming an octahedral equivalent strain field and an octahedral equivalent strainε eff The method comprises the following steps:
(12)
wherein ,ε st is a component of the Green strain tensorSubscript ofsAndttaking 1,2 and 3 respectively.
2. The method of wavefront recognition of a non-planar wave propagating in a multicellular material of claim 1 wherein: for the multicellular material with a regular microscopic structure, a finite element model is periodically constructed by using a finite element method.
3. The method of wavefront recognition of a non-planar wave propagating in a multicellular material of claim 1 wherein: according to the octahedral equivalent strain fields formed by the nodes of the material, interpolation is carried out on the three-dimensional discrete octahedral equivalent strain fields through MATLAB software to obtain three-dimensional continuous strain fields, so that the purpose of identifying non-plane wave fronts is achieved.
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| 颗粒金属材料冲击压缩细观数值模拟;乔良 等;高压物理学报;第27卷(第06期);863-871 * |
| 高速冲击下多胞材料细观结构中波传播规律;李伟 等;装备环境工程;第18卷(第5期);87-93 * |
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