CN112762124A - Negative poisson ratio honeycomb structure with random curved edge - Google Patents
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F7/00—Vibration-dampers; Shock-absorbers
- F16F7/12—Vibration-dampers; Shock-absorbers using plastic deformation of members
- F16F7/121—Vibration-dampers; Shock-absorbers using plastic deformation of members the members having a cellular, e.g. honeycomb, structure
Abstract
The invention provides a negative Poisson ratio honeycomb structure with any curved edge, which comprises a plurality of unit cell structures and is characterized in that: each unit cell structure is a special-shaped plane quadrangle formed by two curved edges and two vertical edges, the curved edges are vertically and symmetrically clamped between the vertical arms at the two sides, the vertical arms at the two sides are bilaterally symmetrical, and the included angle between the curved edges and the vertical arms is smaller than 90 degrees; each unit cell structure is duplicated along the horizontal direction and is arranged in a staggered duplication mode along the vertical direction. The invention has good negative Poisson ratio effect, can obviously reduce peak impact force relative to an inwards concave hexagonal honeycomb structure when loaded, namely has higher compression force efficiency, and has more excellent energy absorption capacity.
Description
Technical Field
The invention relates to the field of mechanics metamaterials, in particular to a negative Poisson ratio honeycomb structure with any curved edge.
Background
The concept of poisson's ratio was first discovered and proposed by french scientists, and means that when a material is unidirectionally pulled or pressed, the material is deformed to elongate (or contract) in the direction of a load, and at the same time, the material is deformed to shorten (or elongate) in the direction perpendicular to the load. The negative of the ratio of the strain in the vertical direction to the strain in the load direction is called the poisson's ratio of the material.
For most materials, it is generally believed that if it is stretched (compressed) in one direction, it contracts (expands) in transverse cross-section. Negative poisson's ratio material structures attract a lot of attention because negative poisson's ratio shows the opposite characteristic when bearing axial load. The macroscopic effect generated by the characteristic is that the local density of the material is increased when the material is loaded, so that more materials can be gathered to resist the load, and therefore higher elastic modulus, shear modulus and storage modulus, better resilience toughness and fracture resistance are generated, and the material is improved along with the enhancement of the negative Poisson ratio effect under the load. Therefore, the negative Poisson's ratio material structure has wide application prospect in the field of impact-resistant and deformation damage-resistant part design.
Under the action of impact load, different cell structure forms can have a remarkable influence on the local dynamic mechanical behavior of the material. At present, the negative poisson ratio structure is mainly an internal concave hexagonal structure, and therefore, a new cell structure is needed to realize the negative poisson ratio multi-cell material deformation mechanism.
Disclosure of Invention
In view of the above technical problems, the present invention provides a novel negative poisson ratio honeycomb structure with any curved edge, which realizes better compression force efficiency and energy absorption capability.
In order to solve the technical problems, the invention adopts the following technical scheme:
a negative poisson's ratio honeycomb structure with arbitrary curved sides, comprising a plurality of unit cell structures, characterized in that: each unit cell structure is a special-shaped plane quadrangle formed by two smooth curved edges and two vertical edges, the curved edges are vertically and symmetrically clamped between the vertical arms at the two sides, the vertical arms at the two sides are bilaterally symmetrical, and the included angle between the curved edges and the vertical arms is less than 90 degrees; each unit cell structure is duplicated along the horizontal direction and is arranged in a staggered duplication mode along the vertical direction.
Each unit cell structure is a closed quadrangle formed by two symmetrical curved sides up and down and symmetrical vertical arms at two ends of the curved sides, and a plurality of unit cell structures are connected in the horizontal direction in a mode of sharing the vertical arms end to end, so that a continuous unit layer is formed in the horizontal direction in an extending mode; the plurality of unit layers are connected to each other in a vertical direction by sharing a curved side.
Further, the shape of the curved edge is one or more extraction lines of a sine function and a power function.
Furthermore, the shape of the curved edge is an extraction line of a power function, the extraction line takes a smooth power function curve, and the curve is copied and turned over by 180 degrees and then is axisymmetric to obtain the curved edge, so that the included angle between the two ends of the curved edge and the straight edge of the connected vertical arm is smaller than 90 degrees.
Furthermore, the shape of the curved edge is an extraction line of the power function, the extraction line is obtained by turning a section of smooth power function curve, translating the curve and connecting the curve with the curve before turning in a tangent manner to form a section of curve connection, and the included angle between the two ends of the curve connection and the straight edge of the connected vertical arm is smaller than 90 degrees.
Furthermore, the shape of the curved edge is a sine function extraction line, the curved edge is formed after the sine curve with the set period is axisymmetric, and the included angle between the two ends of the curved edge and the connected vertical arm is less than 90 degrees.
Further, the curved edge is a sine curve of one period length.
Further, the curved edge and the vertical arm are thin shells.
Further, the curved edge and the vertical arm are made by at least one of stamping, extrusion or 3D printing forming.
Furthermore, the curved edge and the vertical arm are made of metal aluminum.
Therefore, the invention provides a negative Poisson ratio honeycomb structure with any curved edge, which comprises a plurality of single cell structures, wherein each single cell structure consists of two curved edges and two vertical edges, the curved edges are vertically symmetrical, the vertical arms at two sides are bilaterally symmetrical, the included angle between the curved edges and the vertical arms is smaller than 90 degrees, the curved edges are extracted from a function curve, for an aperiodic curve of a power function, a section of smooth curve can be taken and copied and turned over at 180 degrees, then axial symmetry is carried out, and the included angle between the two curved edges and the straight edges is smaller than 90 degrees, so that the negative Poisson ratio structure similar to inner six deformation can be obtained, or the power function curve is turned and translated to be tangent, and a section of smooth curve with the included angle smaller than 90 degrees can be extracted as the curved edges; for a smooth periodic curve like a sine function, a period can be taken as a curved edge, axial symmetry is guaranteed, an included angle between the curved edge and a straight arm is guaranteed to be smaller than 90 degrees, and a negative Poisson's ratio structure similar to an inner hexagon can be obtained; the cells are horizontally replicated and vertically replicated in a staggered manner to obtain a multi-cell structure.
Compared with the prior art, the invention has the following beneficial effects: the invention has good negative Poisson ratio effect, can obviously reduce peak impact force relative to an inwards concave hexagonal honeycomb structure when loaded, namely has higher compression force efficiency, and has more excellent energy absorption capacity. Compared with the traditional concave hexagonal structure, the negative Poisson ratio structure with any curved edge has stronger energy absorption capacity, can obviously reduce peak impact force and has better compression efficiency.
Drawings
FIG. 1 is a schematic diagram of a unit cell structure of a negative Poisson ratio honeycomb structure with an arbitrary curved side, and a curved side is obtained by power function inversion as an example.
FIG. 2 is a schematic diagram of the unit cell structure of the negative Poisson ratio honeycomb structure with any curved side, and the curved side is obtained by taking the tangency of power functions as an example.
FIG. 3 is a schematic diagram of the unit cell structure of the negative Poisson ratio honeycomb structure with arbitrary curved sides, taking the curved sides of sine functions as an example.
FIG. 4 is a schematic diagram of a negative Poisson ratio multi-cell honeycomb structure with sinusoidal edges introduced in the embodiment of the invention.
Fig. 5 shows a schematic representation of the sinusoidal equation for the curved ribs 2 in the embodiment of the invention.
FIG. 6 is a schematic diagram of a negative Poisson ratio unit cell structure with a sine curve side introduced in the embodiment of the invention.
Fig. 7 is a schematic impact diagram of all honeycomb models in the embodiment of the present invention (taking a multi-cell structure with sinusoidal edges as an example).
FIG. 8 is a schematic diagram of specific energy absorption of three honeycomb structures with 30m/s impact in an embodiment of the invention.
FIG. 9 is a schematic diagram of specific energy absorption of three honeycomb structures at 90m/s impact in an embodiment of the present invention.
Detailed Description
The novel negative poisson's ratio honeycomb structure with any curved edge of the invention is described in detail below with reference to the accompanying drawings and examples.
Fig. 1-2 show an embodiment of a negative poisson's ratio structure introducing a power function curved edge, and fig. 3 shows an embodiment of a negative poisson's ratio structure introducing a sine function curved edge. Both embodiments are planar structures. The curved edge structure with various shapes can be arranged according to the actual requirement by the person skilled in the art, and the curved edge structure belongs to the protection scope of the invention.
As can be seen from fig. 1-2, for the aperiodic curve of the power function, a smooth curve can be taken and copied and inverted at 180 degrees, and then axisymmetric, and an included angle between two curved sides and a straight side is ensured to be less than 90 degrees, so that a negative poisson's ratio single cell structure a1 shaped like a sextuple can be obtained, or the power function curve is inverted and translated to be tangent, so that a smooth curve with an included angle of less than 90 degrees can be extracted as a negative poisson's ratio single cell structure a2 with a curved side; for a smooth periodic curve like a sine function, a period can be taken as a curved edge, axial symmetry is guaranteed, an included angle between the curved edge and a straight arm is guaranteed to be smaller than 90 degrees, and the negative Poisson ratio unit cell structure A3 similar to an inner hexagon can be obtained. The negative Poisson ratio single-cell structures of each embodiment are respectively copied along the horizontal direction and are alternatively copied along the vertical direction, so that the multi-cell structures under the embodiment are obtained, namely a plurality of A1 multi-cell power function negative Poisson ratio structures, a plurality of A2 multi-cell power function negative Poisson ratio structures and a plurality of A3 multi-cell sine curved side negative Poisson ratio structures. The novel negative Poisson ratio honeycomb structure with any curved edge comprises a plurality of single cell structures, each single cell structure is a plane quadrangle formed by two curved edges and two vertical edges, the curved edges are vertically symmetrically clamped between the vertical arms at two sides, the vertical arms at two sides are bilaterally symmetrical, and the included angle between the curved edge and the vertical arm is smaller than 90 degrees; each unit cell structure is copied along the horizontal direction and is copied in a staggered manner along the vertical direction, and then the multi-cell structure is obtained.
The type of function may not be limited as long as a smooth curved edge structure is formed.
Taking a negative poisson ratio structure with sine curved edges as an example for specific explanation, as shown in fig. 3-6, the negative poisson ratio honeycomb structure with sine curved edges comprises a plurality of unit cell structures 1 (as shown in fig. 3), each unit cell structure 1 is composed of two sine curved edges, two equal-length vertical edges at the outer side are supporting cell arms 3, two concave sine curved edges at the inner side are bending ribs 2, and an included angle between each supporting cell arm 3 and each bending rib 2 is smaller than 90 degrees, so that a complete plane unit cell structure 1 is formed; the plurality of unit cell structures 1 are connected to each other in a horizontal direction by sharing one supporting cell arm 3, thereby extending in the horizontal direction to form one continuous unit layer. The multiple unit layers are mutually connected in the vertical direction in a mode of sharing the bent ribs 2, and the like, so that a multi-layer cross-arranged concave honeycomb negative Poisson's ratio structure is formed.
Preferably, the bent ribs 2 and the vertical arms of the supporting cell arms 3 are thin shells.
The material for preparing the bent ribs 2 and the vertical arms of the supporting cell arms 3 is preferably metallic aluminum.
Preferably, the bent ribs 2 and the vertical arms of the support cell arms 3 are made by one or more of stamping, extrusion or 3D printing.
The basic function equation for the sinusoid shown in fig. 5 is:
the curve period is known to be 10 mm. Taking a period length of the sine curve, and replacing the concave side edge of the concave hexagonal cell element with the sine curve of the period length, thereby obtaining the novel bending rib 2 of the concave cell element with the negative Poisson ratio; as shown in FIG. 6, |1The period length l of two sine curve bending ribs which are distributed in an up-and-down symmetrical way2The arm length on both sides of the cell, t the wall thickness, and b the out-of-plane thickness of the cell.
For the honeycomb material, the energy absorption characteristic evaluation index can reflect the energy absorption capacity of the honeycomb material, and mainly comprises specific energy absorption, compression force efficiency and the like. Wherein, the specific energy absorption, i.e. the energy absorbed by the material per unit mass, can be expressed as
In the formula: energy absorbed by unit volume of honeycomb
Wherein ε is the strain εcrFor initial strain,. epsilondFor locked-in strain, Δ ρ is the relative density of the honeycomb material, ρsIs the density of the matrix material. As can be seen from the formula, the energy absorption capacity of the structure increases with increasing specific energy absorption value. The compressive force efficiency is the ratio of the platform stress to the initial stress peak, and can reflect the flatness of the stress-strain curve. The greater the compressive force efficiency, which indicates that the material is more efficient at absorbing energy after the same instantaneous high load, can be represented by the following formula:
in the formula: fp、FmRespectively a platform load and an initial peak load; sigmap、σmPlatform stress, initial peak stress, respectively.
In order to compare the energy absorption characteristics of the sinusoidal honeycomb structure, a regular hexagonal honeycomb structure and an inner hexagonal honeycomb structure are selected as a comparison group, and the three honeycomb structures are subjected to nonlinear dynamic explicit analysis by adopting HYPERMESH/LSDYNA joint simulation. As shown in fig. 7, a honeycomb specimen was placed between left and right rigid plates. The honeycomb material is metal aluminum, an ideal elastic-plastic model is adopted, the out-of-plane thickness along the z-axis direction is 1mm, and left and right rigid plates (left and right thick vertical lines) are defined as rigid bodies. In the calculation process, a SHELL163 thin-SHELL unit is selected for the honeycomb structure to be dispersed, and 5 integration points are defined along the thickness direction in order to guarantee the calculation accuracy and the convergence. And finally determining the grid size to be 0.7mm through multiple trial calculation and sensitivity analysis. The left end of the honeycomb structure is bound with the rigid body at the fixed end, the upper side and the lower side of the honeycomb structure are free in the plane, the right end of the honeycomb structure and the rigid body at the impact end adopt a plane-surface automatic contact algorithm, and the friction factor is 0.17; in order to prevent the structures from penetrating each other after impact, a single-side automatic contact algorithm is arranged among all the cells in the honeycomb. In addition, in order to ensure that the honeycomb always meets the plane strain state in the impact process, the out-of-plane displacement of all nodes in the test piece is limited. The model was impacted with velocities of 30m/s and 90m/s, respectively, and the results were obtained.
The results are shown in FIGS. 8 and 9: in the middle and high speed impact, the energy absorption curves of the 0.5mm sine curve honeycomb and the concave hexagon honeycomb are similar and are positioned above the conventional regular hexagon honeycomb for a long time, which shows that the energy absorption characteristics of the two are superior to those of the conventional regular hexagon honeycomb, and in addition, as can be seen from fig. 5, when v is 30m/s and epsilon is about 0.4, the specific energy absorption advantages of the 0.5mm sine curve honeycomb and the concave hexagon honeycomb are the maximum and are improved by at least 40% compared with the conventional regular hexagon honeycomb. Further combining with the initial impact force data, when v is 30m/s, the peak impact force of the sinusoidal honeycomb structure with a being 0.5mm is 75.6N, and the concave hexagonal honeycomb is 94.9N, so that although the specific energy absorption level of the sinusoidal honeycomb structure and the concave hexagonal honeycomb is close to each other at medium-high speed, the sinusoidal honeycomb structure has the peak impact force which is about 20% lower than that of the latter, namely, the compression force efficiency is higher, which further proves that the energy absorption capacity of the sinusoidal honeycomb structure is superior to that of other conventional structural honeycombs.
Claims (9)
1. A negative poisson's ratio honeycomb structure with arbitrary curved sides, comprising a plurality of unit cell structures, characterized in that: each unit cell structure is a special-shaped plane quadrangle formed by two curved edges and two vertical edges, the curved edges are vertically and symmetrically clamped between the vertical arms at the two sides, the vertical arms at the two sides are bilaterally symmetrical, and the included angle between the curved edges and the vertical arms is smaller than 90 degrees; each unit cell structure is duplicated along the horizontal direction and is arranged in a staggered duplication mode along the vertical direction.
2. The negative poisson's ratio honeycomb structure with arbitrary curved sides as claimed in claim 1, wherein: the curved edge shape is one or more extraction lines of a sine function and a power function.
3. The negative poisson's ratio honeycomb structure with arbitrary curved sides as claimed in claim 1, wherein: the shape of the curved edge is an extraction line of a power function, the extraction line takes a section of smooth power function curve, and the curve is copied and turned over by 180 degrees and then is axisymmetric to obtain the curved edge, so that the included angle between the two ends of the curved edge and the straight edge of the connected vertical arm is smaller than 90 degrees.
4. The negative poisson's ratio honeycomb structure with arbitrary curved sides as claimed in claim 1, wherein: the shape of the curved edge is an extraction line of a power function, the extraction line is obtained by turning a section of smooth power function curve, translating the curve and tangentially connecting the curve with the curve before turning to form a section of curved connecting line, and the included angle between the two ends of the curved connecting line and the straight edge of the connected vertical arm is smaller than 90 degrees.
5. The negative poisson's ratio honeycomb structure with arbitrary curved sides as claimed in claim 1, wherein: the shape of the curved edge is a sine function extraction line, the curved edge is formed after the sine curve with the set period is axisymmetric, and the included angle between the two ends of the curved edge and the connected vertical arm is less than 90 degrees.
6. The negative poisson's ratio honeycomb structure with arbitrary curved sides as claimed in claim 1, wherein: the curved edge is a sinusoid of one period length.
7. The negative poisson's ratio honeycomb structure with arbitrary curved sides as claimed in claim 1, wherein: the curved edge and the vertical arm are thin shells.
8. The negative poisson's ratio honeycomb structure with arbitrary curved sides as claimed in claim 1, wherein: the curved edge and the vertical arm are made in at least one of stamping, extruding or 3D printing forming modes.
9. The negative poisson's ratio honeycomb structure with arbitrary curved sides as claimed in claim 1, wherein: the curved edge and the vertical arm are made of metal aluminum.
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| CN115199693A (en) * | 2022-09-16 | 2022-10-18 | 南京航空航天大学 | Optimize reentrant corner constitutional unit and panel |
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