CN113420346B - Non-reciprocal bending mechanics metamaterial and design method thereof - Google Patents
Non-reciprocal bending mechanics metamaterial and design method thereof Download PDFInfo
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- CN113420346B CN113420346B CN202110761002.2A CN202110761002A CN113420346B CN 113420346 B CN113420346 B CN 113420346B CN 202110761002 A CN202110761002 A CN 202110761002A CN 113420346 B CN113420346 B CN 113420346B
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Abstract
The application discloses a non-reciprocal bending mechanics metamaterial and a design method thereof, wherein the non-reciprocal bending mechanics metamaterial comprises a plurality of unit cell structures which are periodically arranged and connected with each other in a three-dimensional space; along the first direction, the unit cell structure comprises a first subsection, a second subsection and a third subsection, and along the second direction, the unit cell structure further comprises a fourth subsection and a fifth subsection which are oppositely arranged; along the third direction, the unit cell structure further comprises a sixth subsection and a seventh subsection which are oppositely arranged; according to the non-reciprocal bending mechanical metamaterial provided by the invention, the space inversion symmetry of a three-dimensional structure is broken and the nonlinearity is introduced, so that the asymmetric positive and negative bending rigidity characteristics which are not possessed by natural materials are realized, and a new paradigm is provided for mechanical functional metamaterials.
Description
Technical Field
The invention relates to the field of mechanical metamaterial structure design, in particular to a non-reciprocal bending mechanical metamaterial and a design method thereof.
Background
According to the maxwell-Betty reciprocity theorem in continuous medium mechanics, the positive and negative bending deformation of most natural materials should keep symmetrical reciprocity. Under the action of forward and reverse bending moment loads with the same size, the forward and reverse bending deflection and corner response of the material are kept symmetrical and consistent, and the material has symmetrically-same forward and reverse bending stiffness.
If the limitation of the maxwell-betty reciprocity theorem can be broken through, a non-reciprocal flexible material with asymmetric forward and backward bending rigidity characteristics is prepared, and extraordinary mechanical properties which natural materials do not have are obtained, more degrees of freedom are provided for the design of a mechanical system. However, the current non-reciprocal bending material is still very scarce, and the development and design of the material still face a great challenge.
Disclosure of Invention
The invention aims to solve the problem of shortage of the nonreciprocal bending material. Therefore, the invention discloses a non-reciprocal bending mechanics metamaterial and a design method thereof.
On one hand, the invention provides a non-reciprocal mechanical metamaterial capable of bending, which comprises a plurality of unit cell structures which are periodically arranged and connected with each other in a three-dimensional space;
along a first direction, the unit cell structure comprises a first section, a second section and a third section;
the first subsection comprises four first connecting rods which are respectively a first connecting rod A, a first connecting rod B, a first connecting rod C and a first connecting rod T, first ends of the four first connecting rods are connected to a first end point, second ends of the four first connecting rods are all located in a first plane, the first end point is located between the first plane and the second subsection along the first direction, and the first end point and the first plane are spaced by a first distance;
The second sub-part comprises four second connecting rods which are respectively a second connecting rod, a second connecting rod, a second third connecting rod and a second third connecting rod, first ends of the four second connecting rods are connected to a second end point, second ends of the four second connecting rods are all located in a second plane, the second end point is located between the second plane and the first sub-part along the first direction, and the second end point and the second plane are spaced at a second distance;
the third subsection comprises four third connecting rods which are respectively a third connecting rod, a third polypropylene connecting rod and a third T connecting rod, first ends of the four third connecting rods are connected to a third end point, second ends of the four third connecting rods are all located in a third plane, the third end point is located between the third plane and the second subsection along the first direction, and a third distance is reserved between the third end point and the third plane;
the orthographic projection of the first connecting rod on the second plane is overlapped with the orthographic projection of the third connecting rod on the second plane, the orthographic projection of the second connecting rod on the third plane is staggered with the orthographic projection of the first connecting rod on the third plane, the orthographic projection of the first end point on the first plane, the orthographic projection of the second end point on the first plane and the orthographic projection of the third end point on the first plane are overlapped, and the first plane, the second plane and the third plane are parallel to each other along the first direction;
In the second direction, the unit cell structure further comprises a fourth part and a fifth part which are oppositely arranged;
the fourth part comprises four fourth connecting rods, namely a fourth connecting rod, a fourth third connecting rod and a fourth third connecting rod, wherein the first ends of the four fourth connecting rods are connected to a fourth end point, and the fourth node and the second ends of the four fourth connecting rods are positioned in a fourth plane;
wherein the second ends of the fourth connecting rod and the first A connecting rod are connected to a first node, the second ends of the fourth connecting rod and the first B connecting rod are connected to a second node, the second ends of the fourth C connecting rod and the third E connecting rod are connected to a third node, the second ends of the fourth T connecting rod and the third E connecting rod are connected to a fourth node, and the second end of the second M connecting rod is connected to the fourth end point;
the fifth part comprises four fifth connecting rods, namely a fifth connecting rod A, a fifth connecting rod B, a fifth connecting rod C and a fifth connecting rod T, wherein the first ends of the four fifth connecting rods are connected to a fifth endpoint, and the fifth endpoint and the second ends of the four fifth connecting rods are positioned in a fifth plane;
Wherein the second ends of the fifth A connecting rod and the first T connecting rod are connected to a fifth node, the second ends of the fifth B connecting rod and the first C connecting rod are connected to a sixth node, the second ends of the fifth C connecting rod and the third C connecting rod are connected to a seventh node, the second ends of the fifth T connecting rod and the third T connecting rod are connected to an eighth node, and the second end of the second C connecting rod is connected to the fifth end point;
an orthographic projection of the fourth connecting rod on the fourth plane is overlapped with an orthographic projection of the fifth connecting rod on the fourth plane, an orthographic projection of the fourth end point on the fourth plane is overlapped with an orthographic projection of the fifth end point on the fourth plane, and the fourth plane and the fifth plane are parallel along the second direction;
along a third direction, the unit cell structure further comprises a sixth subsection and a seventh subsection which are oppositely arranged;
the sixth branch comprises four sixth connecting rods which are respectively a sixth connecting rod A, a sixth connecting rod B, a sixth connecting rod C and a sixth connecting rod D, first ends of the four sixth connecting rods are connected to a sixth end point, and the sixth end point and second ends of the four sixth connecting rods are located in a sixth plane;
A second end of the sixth A connecting rod is connected to the first node, a second end of the sixth B connecting rod is connected to the fifth node, a second end of the sixth C connecting rod is connected to the eighth node, a second end of the sixth D connecting rod is connected to the fourth node, and a second end of the second D connecting rod is connected to the sixth endpoint;
the seventh subsection comprises four seventh connecting rods which are respectively a seventh first connecting rod, a seventh second connecting rod, a seventh third connecting rod and a seventh third connecting rod, the first ends of the four seventh connecting rods are connected to a seventh end point, and the seventh end point and the second ends of the four seventh connecting rods are all positioned in a seventh plane;
a second end of the seventh first connecting rod is connected to the second node, a second end of the seventh second connecting rod is connected to the sixth node, a second end of the seventh third connecting rod is connected to the seventh node, a second end of the seventh fixed connecting rod is connected to the third node, and a second end of the second connecting rod is connected to the seventh endpoint;
an orthographic projection of the sixth connecting rod on the sixth plane is overlapped with an orthographic projection of the seventh connecting rod on the sixth plane, an orthographic projection of the sixth endpoint on the sixth plane is overlapped with an orthographic projection of the seventh endpoint on the sixth plane, and the sixth plane and the seventh plane are parallel in the third direction;
Wherein the first plane and the fourth plane are perpendicular, the sixth plane is perpendicular to the first plane, and the sixth plane is perpendicular to the fourth plane; and the first direction, the second direction and the third direction intersect pairwise.
Preferably, the non-reciprocal bending mechanical metamaterial is a material with asymmetric positive and negative bending rigidity characteristics.
Preferably, the first node, the second node, the third node, the fourth node, the fifth node, the sixth node, the seventh node, and the eighth node are eight vertexes of a cuboid respectively, and the second endpoint is the center of the cuboid.
Preferably, the first pitch, the second pitch and the third pitch are all equal to δ.
Preferably, the height of the cuboid is the distance l between the first node and the fourth node, and 0 & ltdelta & lt 0.5 l.
Preferably, the unit cell structure is rotated by 180 degrees by taking a connecting line of the first end point, the second end point and the third end point as an axis and then is coincided with the unit cell structure.
Preferably, along the first direction, adjacent unit cell structures share the first or third section;
Along the second direction, adjacent unit cell structures share the fourth or fifth section;
and/or adjacent unit cell structures share the sixth or seventh division in the third direction.
Preferably, the cross-sectional shapes of the first connecting rod, the second connecting rod, the third connecting rod, the fourth connecting rod, the fifth connecting rod, the sixth connecting rod and the seventh connecting rod are circular, rectangular or annular.
Preferably, the non-reciprocal bending mechanical metamaterial is prepared by a three-dimensional additive manufacturing method;
the preparation material of the non-reciprocal bending mechanical metamaterial is polymer or metal.
In yet another aspect, the present invention provides a method of designing any one of the above non-reciprocal flexural mechanical metamaterials by breaking the spatial inversion symmetry of the three-dimensional structure and introducing non-linearity to achieve asymmetric forward and reverse bending stiffness.
Compared with the prior art, the non-reciprocal bending mechanical metamaterial and the design method thereof provided by the invention have the following beneficial effects:
the non-reciprocal bending mechanical metamaterial provided by the invention can break the limitation of the Maxwell-Betty reciprocity theorem, has the characteristics of asymmetric positive and negative bending rigidity which natural materials do not have, and provides a new paradigm for mechanical functional metamaterials.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the application and together with the description serve to explain the application and not to limit the application. In the drawings:
FIG. 1 is a front view of a non-reciprocal flexural mechanical metamaterial provided in accordance with the present invention;
FIG. 2 is a top view of a non-reciprocal flexural mechanical metamaterial provided in accordance with the present invention;
FIG. 3 is a side view of a non-reciprocal flexural mechanical metamaterial provided in accordance with the present invention;
FIG. 4 is a schematic diagram of the structure of the cell of FIG. 1;
FIG. 5 is a schematic diagram of a rectangular parallelepiped space formed by eight nodes in the unit cell structure of FIG. 4;
FIG. 6 is a front view of the cell structure of FIG. 4;
FIG. 7 is a left side view of the cell structure of FIG. 4;
FIG. 8 is a top view of the cell structure of FIG. 4;
FIG. 9 is a three-point bending load-deflection curve of the non-reciprocal bending mechanical metamaterial in FIG. 1.
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. It should be noted that the described embodiments are merely some embodiments, rather than all embodiments, of the invention and are merely illustrative in nature and in no way intended to limit the invention, its application, or uses. The protection scope of the present application shall be subject to the definitions of the appended claims.
Referring to fig. 1 to 9, fig. 1 is a front view of a non-reciprocal flexural mechanical metamaterial according to the present invention, fig. 2 is a top view of the non-reciprocal flexural mechanical metamaterial according to the present invention, fig. 3 is a side view of the non-reciprocal flexural mechanical metamaterial according to the present invention, and fig. 4 is a schematic structural view of a unit cell structure in fig. 1; fig. 5 is a schematic diagram of a rectangular parallelepiped space formed by eight nodes in the unit cell structure of fig. 4, fig. 6 is a front view of the unit cell structure of fig. 4, fig. 7 is a left view of the unit cell structure of fig. 4, fig. 8 is a top view of the unit cell structure of fig. 4, and fig. 9 is a three-point bending load-deflection curve of the non-reciprocal bending mechanical metamaterial of fig. 1. The non-reciprocal mechanical metamaterial 100 provided by the embodiment: in a three-dimensional space, the three-dimensional space comprises a plurality of unit cell structures 200 which are periodically arranged and are mutually connected, and the unit cell structures 200 have the characteristic of space inversion symmetry loss; along the first direction X, the unit cell structure 200 comprises a first subsection 10, a second subsection 20 and a third subsection 30; the first section 10 includes four first connecting rods 11, namely a first connecting rod a 11a, a first connecting rod b 11b, a first connecting rod c 11c and a first connecting rod D11D, first ends of the four first connecting rods 11 are connected to a first end point Q1, second ends of the four first connecting rods 11 are all located in a first plane S1, along the first direction X, the first end point Q1 is located between the first plane S1 and the second section 20, and a first distance D1 is formed between the first end point Q1 and the first plane S1; the second section 20 comprises four second connecting rods 21, namely a second connecting rod 21a, a second connecting rod 21b, a second connecting rod 21c and a second third connecting rod 21D, wherein the first ends of the four second connecting rods 21 are connected to a second end point Q2, the second ends of the four second connecting rods 21 are all located in a second plane S2, the second end point Q2 is located between the second plane S2 and the first section 10 along the first direction X, and the second end point Q2 has a second spacing D2 from the second plane S2; the third section 30 comprises four third connecting rods 31, namely a third connecting rod 31a, a third connecting rod 31b, a third connecting rod 31c and a third connecting rod 31D, wherein the first ends of the four third connecting rods 31 are connected to a third end point Q3, the second ends of the four third connecting rods 31 are all located in a third plane S3, the third end point Q3 is located between the third plane S3 and far away from the second section 20 along the first direction X, and the third end point Q3 and the third plane S3 have a third distance D3; the orthographic projection of the first connecting rod 11 on the second plane S2 is overlapped with the orthographic projection of the third connecting rod 31 on the second plane S2, the orthographic projection of the second connecting rod 21 on the third plane S3 is staggered with the orthographic projection of the first connecting rod 11 on the third plane S3, the orthographic projection of the first endpoint Q1 on the first plane S1, the orthographic projection of the second endpoint Q2 on the first plane S1 and the orthographic projection of the third endpoint Q3 on the first plane S1 are overlapped, and the first plane S1, the second plane S2 and the third plane S3 are parallel to each other along the first direction X; in the second direction Y, the unit cell structure 200 further includes a fourth division 40 and a fifth division 50, which are oppositely disposed; the fourth section 40 includes four fourth connecting bars 41, namely a fourth connecting bar 41a, a fourth connecting bar 41b, a fourth connecting bar 41c and a fourth connecting bar 41d, wherein the first ends of the four fourth connecting bars 41 are connected to a fourth end point Q4, and the fourth end point Q4 and the second ends of the four fourth connecting bars 41 are located in a fourth plane S4; wherein, the second ends of the fourth connecting rod 41a and the first connecting rod 11a are connected to the first node P1, the second ends of the fourth connecting rod 41b and the first second connecting rod are connected to the second node P2, the second ends of the fourth third connecting rod 41c and the third connecting rod 31b are connected to the third node P3, the second ends of the fourth third connecting rod 41d and the third connecting rod 31a are connected to the fourth node P4, and the second end of the second fourth connecting rod 21a is connected to the fourth node Q4; the fifth subsection 50 includes four fifth connecting rods 51, a fifth a connecting rod 51a, a fifth b connecting rod 51b, a fifth c connecting rod 51c and a fifth d connecting rod 51d, the first ends of the four fifth connecting rods 51 are connected to a fifth end point Q5, and the fifth end point Q5 and the second ends of the four fifth connecting rods 51 are located in a fifth plane S5; wherein the second ends of the fifth a connecting rod 51a and the first t connecting rod 11d are connected to a fifth node P5, the second ends of the fifth b connecting rod 51b and the first c connecting rod 11c are connected to a sixth node P6, the second ends of the fifth c connecting rod 51c and the third P connecting rod 31c are connected to a seventh node P7, the second ends of the fifth t connecting rod 51d and the third t connecting rod 31d are connected to an eighth node P8, and the second end of the second P connecting rod 21c is connected to a fifth end point Q5; the orthographic projection of the fourth connecting rod 41 on the fourth plane S4 is overlapped with the orthographic projection of the fifth connecting rod 51 on the fourth plane S4, the orthographic projection of the fourth end point Q4 on the fourth plane S4 is overlapped with the orthographic projection of the fifth end point Q5 on the fourth plane S4, and the fourth plane S4 is parallel to the fifth plane S5 in the second direction Y; along the third direction Z, the unit cell structure 200 further includes a sixth section 60 and a seventh section 70 disposed opposite to each other; the sixth section 60 includes four sixth connecting rods 61, namely a sixth first connecting rod 61a, a sixth second connecting rod 61b, a sixth third connecting rod 61c and a sixth third connecting rod 61d, wherein the first ends of the four sixth connecting rods 61 are connected to a sixth end point Q6, and the sixth end point Q6 and the second ends of the four sixth connecting rods 61 are located in a sixth plane S6; the second end of the sixth a connecting rod 61a is connected to the first node P1, the second end of the sixth b connecting rod 61b is connected to the fifth node P5, the second end of the sixth c connecting rod 61c is connected to the eighth node P8, the second end of the sixth d connecting rod 61d is connected to the fourth node P4, and the second end of the second d connecting rod 21d is connected to the sixth end point Q6; the seventh section 70 comprises four seventh connecting rods 71, namely a seventh a connecting rod 71a, a seventh b connecting rod 71b, a seventh c connecting rod 71c and a seventh d connecting rod 71d, wherein the first ends of the four seventh connecting rods 71 are connected to a seventh end point Q7, and the seventh end point Q7 and the second ends of the four seventh connecting rods 71 are located in a seventh plane S7; the second end of the seventh first connecting rod 71a is connected to the second node P2, the second end of the seventh second connecting rod 71b is connected to the sixth node P6, the second end of the seventh third connecting rod 71c is connected to the seventh node P7, the second end of the seventh third connecting rod 71d is connected to the third node P3, and the second end of the second connecting rod 21b is connected to the seventh end point Q7; the orthographic projection of the sixth connecting rod 61 on the sixth plane S6 is overlapped with the orthographic projection of the seventh connecting rod 71 on the sixth plane S6, the orthographic projection of the sixth endpoint Q6 on the sixth plane S6 is overlapped with the orthographic projection of the seventh endpoint Q7 on the sixth plane S6, and the sixth plane S6 and the seventh plane S7 are parallel in the third direction Z; wherein the first plane S1 is perpendicular to the fourth plane S4, the sixth plane S6 is perpendicular to the first plane S1, and the sixth plane S6 is perpendicular to the fourth plane S4; and the first direction X, the second direction Y and the third direction Z are intersected pairwise.
Optionally, the non-reciprocal bending mechanical metamaterial 100 is a material having asymmetric positive and negative bending stiffness characteristics.
It can be understood that, because most natural materials are subjected to bending deformation, under the action of bending loads with the same magnitude and opposite directions, the positive and negative bending deformation responses of the materials are always kept symmetrical and consistent. In other words, most natural materials have symmetrically identical positive and negative bending stiffnesses. This rule is related to the reciprocity referred to by the maxwell-bekis reciprocity theorem in continuous media mechanics. If the constraint of maxwell-bekis reciprocity theorem can be broken through, the non-mutually-flexible material with asymmetric forward and reverse bending rigidity characteristics is prepared, and the extraordinary mechanical properties which are not possessed by natural materials are obtained, so that more degrees of freedom are provided for the design of a mechanical system. Based on the structure, the metamaterial with the non-reciprocal bending mechanics provided by the invention is formed by periodically arranging and connecting unit cell structures in a three-dimensional space. When the metamaterial is bent in an XZ plane or an XY plane, the metamaterial has extraordinary asymmetric positive and negative bending rigidity characteristics. This non-reciprocal bending property results from two physical conditions: the metamaterial XZ has the defects of plane symmetry and structural nonlinear deformation. Meanwhile, as can be seen from the three-point bending load-deflection curve shown in fig. 9, under the same magnitude of load, the forward bending deflection of the metamaterial is smaller than the reverse bending deflection. Therefore, the positive and negative bending stiffness of the metamaterial is asymmetric, and when the load reaches 8N, the positive bending stiffness is 1.8 times of the negative bending stiffness.
In some optional embodiments, as shown in fig. 1 to fig. 9, in the non-reciprocal bending mechanical metamaterial 100 provided by the present embodiment, the first node P1, the second node P2, the third node P3, the fourth node P4, the fifth node P5, the sixth node P6, the seventh node P7, and the eighth node P8 are eight vertexes of a cuboid W, respectively; the second end point Q2 is the center of the rectangular parallelepiped W.
It can be understood that the first node P1, the second node P2, the third node P3, the fourth node P4, the fifth node P5, the sixth node P6, the seventh node P7 and the eighth node P8 in the unit cell structure 200 of the non-reciprocal bending mechanical metamaterial 100 are respectively connected with the connected nodes to form a rectangular parallelepiped, and the second end Q2 is further set as the center of the rectangular parallelepiped W to determine the structure of the non-reciprocal bending mechanical metamaterial 100.
Optionally, the first distance D1, the second distance D2, and the third distance D3 are all equal to δ, that is, D1 ═ D2 ═ D3 ═ δ.
It can be understood that the first end point Q1, the second end point Q2 and the third end point Q3 in the non-reciprocal bending mechanical metamaterial 100 correspond to the centers of the first plane S1, the second plane S2 and the third plane S3 and move up and down by the displacement amount δ, and move out of the first plane S1, the second plane S2 and the third plane S3; optionally, the fourth end point Q4, the fifth end point Q5, the sixth end point Q6 and the seventh end point Q7 are equivalent to the centers of the fourth plane S4, the fifth plane S5, the sixth plane S6 and the seventh plane S7 and move up and down by the displacement amount δ, but since the extending directions and the moving directions of the fourth plane S4, the fifth plane S5, the sixth plane S6 and the seventh plane S7 are parallel, the fourth end point Q4, the fifth end point Q5, the sixth end point Q6 and the seventh end point Q7 move in a plane.
Optionally, the height of the cuboid W is the distance l between the first node P1 and the fourth node P4, and 0 < δ < 0.5 l. That is, the displacement δ of the first endpoint Q1, the second endpoint Q2, the third endpoint Q3, the fourth endpoint Q4, the fifth endpoint Q5, the sixth endpoint Q6 and the seventh endpoint Q7 is related to the distance l between the first node P1 and the fourth node P4 of the height of the cuboid W, which may further limit the structure of the non-reciprocal bending mechanical metamaterial 100, and limit 0 < δ < 0.5 l.
Optionally, the unit cell structure 200 is rotated 180 degrees by using a connecting line of the first end point Q1, the second end point Q2, and the third end point Q3 as an axis and then coincides with itself, so as to ensure that the metamaterial structure for the non-reciprocal bending mechanics metamaterial has dual rotational symmetry in a YZ plane, but not limited to this, the distance between the first node P1 and the fifth node P5, such as the distance between the first node P1 and the second node P2, may also be set, and at this time, the unit cell structure 200 is rotated 90 degrees by using the connecting line of the first end point Q1, the second end point Q2, and the third end point Q3 as an axis and then coincides with itself, so as to ensure that the metamaterial structure for the non-reciprocal bending mechanics metamaterial has quadruple rotational symmetry in the YZ plane, and may also achieve a certain technical effect.
In some optional embodiments, continuing with fig. 1 to 9, in the non-reciprocal flexural mechanical metamaterial 100 provided in this embodiment, a length of the fourth connecting rod 41a, a length of the fourth connecting rod 41b, a length of the fifth a connecting rod 51a, a length of the fifth b connecting rod 51b, a length of the sixth a connecting rod 61a, a length of the sixth b connecting rod 61b, a length of the seventh a connecting rod 71a, and a length of the seventh b connecting rod 71b are all equal to e 1; the length of the fourth third connecting rod 41c, the length of the fourth third connecting rod 41d, the length of the fifth third connecting rod 51c, the length of the fifth third connecting rod 51d, the length of the sixth third connecting rod 61c, the length of the sixth third connecting rod 61d, the length of the seventh third connecting rod 71c and the length of the seventh third connecting rod 71d are equal to e 2; e1 > e 2.
In some alternative embodiments, continuing with fig. 1 to 9, the present embodiment provides a non-reciprocal flexural mechanical metamaterial 100, in which adjacent unit cell structures 200 share the first or third sections 10 or 30 along the first direction X; along the second direction Y, the adjacent unit cell structures 200 share the fourth division 40 or the fifth division 50; and/or adjacent unit cell structures 200 share the sixth or seventh section 60, 70 in the third direction Z. And then a plurality of adjacent unit cell structures 200 are periodically arranged to obtain the non-reciprocal bending mechanical metamaterial 100. In fig. 1 to 3, it is only illustrated that adjacent unit cell structures 200 share the first partition 10 or the third partition 30 along the first direction X, but the present invention is not limited thereto, and the non-reciprocal bending mechanical metamaterial 100 may be provided with a plurality of unit cell structures 200 respectively in at least one of the first direction X, the second direction Y, and the third direction Z, and the plurality of unit cell structures 200 in specific directions may be provided according to actual situations, and will not be described in detail below.
Optionally, the cross-sectional shapes of the first connecting rod 11, the second connecting rod 21, the third connecting rod 31, the fourth connecting rod 41, the fifth connecting rod 51, the sixth connecting rod 61 and the seventh connecting rod 71 are circular, rectangular or annular. The cross-sectional shapes of the first connecting rod 11, the second connecting rod 21, the third connecting rod 31, the fourth connecting rod 41, the fifth connecting rod 51, the sixth connecting rod 61 and the seventh connecting rod 71 are not limited, and the non-reciprocal bending mechanical metamaterial 100 can be ensured.
Optionally, the non-reciprocal bending mechanical metamaterial 100 is prepared by a three-dimensional additive manufacturing method, but not limited thereto, the non-reciprocal bending mechanical metamaterial 100 may be prepared by other methods as long as the non-reciprocal bending mechanical metamaterial 100 has asymmetric forward and reverse bending stiffness characteristics, and other preparation methods capable of realizing the non-reciprocal bending mechanical metamaterial also belong to the protection scope. The material for preparing the non-reciprocal bending mechanical metamaterial 100 may be resin, nylon, aluminum, copper, steel, aluminum alloy, or titanium alloy, but is not limited thereto, and other materials capable of realizing the non-reciprocal bending mechanical metamaterial 100 also belong to the protection scope of the present invention.
In some optional embodiments, the invention further provides a method for the non-reciprocal flexural mechanical metamaterial, and the non-reciprocal flexural mechanical metamaterial realizes asymmetric forward and reverse flexural rigidity by breaking the space inversion symmetry of a three-dimensional structure and introducing nonlinearity. Namely, the non-reciprocal bending mechanical metamaterial with asymmetric positive and negative bending rigidity characteristics can be obtained based on the method.
According to the embodiments, the application has the following beneficial effects:
the non-reciprocal bending mechanical metamaterial provided by the invention can break the limitation of the Maxwell-Betty reciprocity theorem, has the characteristics of asymmetric positive and negative bending rigidity which natural materials do not have, and provides a new paradigm for mechanical functional metamaterials.
While the invention has been described in detail and with reference to specific embodiments thereof by way of example, it will be understood by those skilled in the art that the foregoing examples are illustrative only and are not intended to limit the scope of the invention. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention. The scope of the invention is defined by the appended claims.
Claims (8)
1. A non-reciprocal mechanical metamaterial with bending property is characterized by comprising a plurality of unit cell structures which are periodically arranged and connected with each other in a three-dimensional space;
along a first direction, the unit cell structure comprises a first subsection, a second subsection and a third subsection;
the first subsection comprises four first connecting rods which are respectively a first connecting rod A, a first connecting rod B, a first connecting rod C and a first connecting rod T, first ends of the four first connecting rods are connected to a first end point, second ends of the four first connecting rods are all located in a first plane, the first end point is located between the first plane and the second subsection along the first direction, and the first end point and the first plane are spaced by a first distance;
the second sub-part comprises four second connecting rods which are respectively a second connecting rod, a second connecting rod, a second third connecting rod and a second third connecting rod, first ends of the four second connecting rods are connected to a second end point, second ends of the four second connecting rods are all located in a second plane, the second end point is located between the second plane and the first sub-part along the first direction, and the second end point and the second plane are spaced at a second distance;
The third subsection comprises four third connecting rods which are respectively a third connecting rod, a third polypropylene connecting rod and a third T connecting rod, first ends of the four third connecting rods are connected to a third end point, second ends of the four third connecting rods are all located in a third plane, the third end point is located between the third plane and the second subsection along the first direction, and a third distance is reserved between the third end point and the third plane;
the orthographic projection of the first connecting rod on the second plane is overlapped with the orthographic projection of the third connecting rod on the second plane, the orthographic projection of the second connecting rod on the third plane is staggered with the orthographic projection of the first connecting rod on the third plane, the orthographic projection of the first end point on the first plane, the orthographic projection of the second end point on the first plane and the orthographic projection of the third end point on the first plane are overlapped, and the first plane, the second plane and the third plane are parallel to each other along the first direction;
in the second direction, the unit cell structure further comprises a fourth part and a fifth part which are oppositely arranged;
The fourth part comprises four fourth connecting rods which are respectively a fourth connecting rod, a fourth third connecting rod and a fourth connecting rod, the first ends of the four fourth connecting rods are connected to a fourth end point, and the fourth end point and the second ends of the four fourth connecting rods are all positioned in a fourth plane;
wherein the second end of the fourth connecting rod and the second end of the first A connecting rod are connected to a first node, the second end of the fourth connecting rod and the second end of the first B connecting rod are connected to a second node, the second end of the fourth C connecting rod and the second end of the third B connecting rod are connected to a third node, the second end of the fourth C connecting rod and the second end of the third B connecting rod are connected to a fourth node, and the second end of the second C connecting rod is connected to the fourth end point;
the fifth part comprises four fifth connecting rods, namely a fifth A connecting rod, a fifth B connecting rod, a fifth C connecting rod and a fifth T connecting rod, wherein the first ends of the four fifth connecting rods are connected to a fifth endpoint, and the fifth endpoint and the second ends of the four fifth connecting rods are positioned in a fifth plane;
Wherein the second ends of the fifth A connecting rod and the first T connecting rod are connected to a fifth node, the second ends of the fifth B connecting rod and the first C connecting rod are connected to a sixth node, the second ends of the fifth C connecting rod and the third C connecting rod are connected to a seventh node, the second ends of the fifth T connecting rod and the third T connecting rod are connected to an eighth node, and the second end of the second C connecting rod is connected to the fifth end point;
an orthographic projection of the fourth connecting rod on the fourth plane is overlapped with an orthographic projection of the fifth connecting rod on the fourth plane, an orthographic projection of the fourth endpoint on the fourth plane is overlapped with an orthographic projection of the fifth endpoint on the fourth plane, and the fourth plane and the fifth plane are parallel along the second direction;
along a third direction, the unit cell structure further comprises a sixth subsection and a seventh subsection which are oppositely arranged;
the sixth branch comprises four sixth connecting rods which are respectively a sixth connecting rod A, a sixth connecting rod B, a sixth connecting rod C and a sixth connecting rod D, first ends of the four sixth connecting rods are connected to a sixth end point, and the sixth end point and second ends of the four sixth connecting rods are located in a sixth plane;
A second end of the sixth A connecting rod is connected to the first node, a second end of the sixth B connecting rod is connected to the fifth node, a second end of the sixth C connecting rod is connected to the eighth node, a second end of the sixth D connecting rod is connected to the fourth node, and a second end of the second D connecting rod is connected to the sixth endpoint;
the seventh branch comprises four seventh connecting rods which are respectively a seventh first connecting rod, a seventh second connecting rod, a seventh third connecting rod and a seventh third connecting rod, first ends of the four seventh connecting rods are connected to a seventh end point, and the seventh end point and second ends of the four seventh connecting rods are all located in a seventh plane;
a second end of the seventh a connecting rod is connected to the second node, a second end of the seventh b connecting rod is connected to the sixth node, a second end of the seventh c connecting rod is connected to the seventh node, a second end of the seventh d connecting rod is connected to the third node, and a second end of the second d connecting rod is connected to the seventh end point;
an orthographic projection of the sixth connecting rod on the sixth plane is overlapped with an orthographic projection of the seventh connecting rod on the sixth plane, and an orthographic projection of the sixth end point on the sixth plane is overlapped with an orthographic projection of the seventh end point on the sixth plane, and the sixth plane and the seventh plane are parallel along the third direction;
Wherein the first plane and the fourth plane are perpendicular, the sixth plane is perpendicular to the first plane, and the sixth plane is perpendicular to the fourth plane; and the first direction, the second direction and the third direction intersect pairwise.
2. The non-reciprocal flexural mechanics metamaterial according to claim 1, wherein the non-reciprocal flexural mechanics metamaterial is a material having asymmetric positive and negative flexural stiffness characteristics.
3. The non-reciprocal flexural mechanical metamaterial according to claim 1, wherein the first node, the second node, the third node, the fourth node, the fifth node, the sixth node, the seventh node, and the eighth node are each eight vertices of a cuboid, and the second endpoint is a center of the cuboid.
4. The non-reciprocal flexural mechanical metamaterial according to claim 3, wherein the first end point, the second end point, and the third end point in the non-reciprocal flexural mechanical metamaterial are the centers of the first plane, the second plane, and the third plane by the displacement amount moving up or downδThe fourth end point, the fifth end point, the sixth end point and the seventh end point are the upward or upward and downward displacement of the centers of the fourth plane, the fifth plane, the sixth plane and the seventh plane δ；
The first, second and third pitches are all equal toδ；
The height of the cuboid is the distance between the first node and the fourth nodelAnd 0 <δ＜0.5l。
5. The non-reciprocal flexural mechanical metamaterial according to claim 3, wherein the unit cell structure is rotated 180 degrees around a connecting line of the first end point, the second end point and the third end point to coincide with itself.
6. The non-reciprocal flexural mechanical metamaterial according to claim 1, wherein adjacent unit cell structures share the first or third sections along the first direction;
along the second direction, adjacent unit cell structures share the fourth or fifth subsection;
and/or adjacent unit cell structures share the sixth or seventh division in the third direction.
7. The non-reciprocal, flexural mechanical metamaterial according to claim 1, wherein the cross-sectional shapes of the first, second, third, fourth, fifth, sixth, and seventh connecting rods are circular, rectangular, or annular.
8. The non-reciprocal flexural mechanics metamaterial according to claim 1, wherein the non-reciprocal flexural mechanics metamaterial is prepared by a three-dimensional additive manufacturing method;
the preparation material of the non-reciprocal bending mechanical metamaterial is polymer or metal.
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