Metamaterials for shock absorption applications and methods of making the same

Abstract

This invention relates to metamaterials for vibration damping and load-bearing applications and methods for their preparation, wherein the essence of metamaterial design lies in creating materials through artificially manufactured structural units with specific properties and functions.

Description

Technical Field

[0001] This invention relates to metamaterials for vibration damping applications and methods for their preparation. Background Technology

[0002] Vibration damping is a crucial function designed to protect objects, structures, or living organisms from damage caused by sudden impacts or vibrations. It acts as a buffer, absorbing and dissipating the energy generated in such events. In mechanical systems, damping helps prevent excessive stress, wear, and damage by reducing the intensity and duration of impacts. A car crash is an example of an impact with potentially devastating consequences. The impact of a collision needs to be mitigated to protect items inside the vehicle, and most importantly, the passengers. Ideal damping materials are those that exhibit superior energy absorption capabilities during events such as high-impact events. They should possess properties such as high strength, controlled deformation, progressive collapse, and effective energy dissipation to mitigate forces and protect occupants or structures from severe damage during a collision or impact.

[0003] Furthermore, crash bars rapidly dissipate collision energy, resulting in very sudden deceleration, which can cause equipment damage and / or adverse health effects on passengers. Ideally, shock-absorbing materials should be lightweight and absorb / dissipate the maximum amount of energy in a stable manner while maintaining strength and stiffness after impact.

[0004] Existing materials and structures (such as impact-absorbing boxes or metallic foams) are either highly rigid and strong before impact, or stable energy-absorbing materials with low stiffness and low strength, but cannot possess both. Therefore, the challenge lies in creating lightweight structures that provide both high stiffness and stable energy damping. Hyperelastic metallic alloys (such as NiTi alloys) are also known to possess dissipative and stiffness properties. However, these materials are more expensive and difficult to mass-produce.

[0005] Existing methods for enhancing shock absorption use polymer materials such as plastics, foams, and rubber. These materials are soft and therefore unsuitable for applications requiring rigidity to avoid vibration and deformation (automotive, aerospace). In these industries, the use of such materials, which allow for good energy dissipation, must be combined with rigid components that provide strength. This means that plastics and rubber must be used in conjunction with metals or other rigid materials, which inherently increases the vehicle's overall weight and cost. For metal shock absorbers, impact energy-absorbing boxes or honeycomb grids are used, but their buckling is "catastrophic." This means that after the initial collapse, the structure loses its initial stiffness and strength and cannot be reused for the same function after an impact. Summary of the Invention

[0006] Purpose of the invention One object of the present invention is to provide a shock-absorbing metamaterial that combines stiffness and energy absorption functions, and can maintain its initial stiffness and strength after being subjected to impact.

[0007] Another object of the present invention is to provide a vibration damping structure including the aforementioned vibration damping metamaterial.

[0008] Another objective of this invention is to demonstrate that the aforementioned damping metamaterial or damping structure can be manufactured using additive manufacturing technology.

[0009] Another objective of this invention is to demonstrate that the aforementioned damping metamaterial or damping structure can be manufactured from bulk metallic materials.

[0010] An ideal shock absorber combines high stiffness with high energy absorption while maintaining structural integrity (stiffness) after impact and should be scalable to practical applications. The inventors have demonstrated an industrially viable metamaterial that combines high stiffness with high dissipation capacity before and after impact. This is achieved by striking a balance between plastic deformation and buckling (which the inventors call "yield buckling").

[0011] One or more objectives are achieved by a metamaterial for load-bearing and damping applications, wherein the metamaterial is made of an elastic-plastic material and comprises multiple unit cells (the multiple unit cells are arranged, for example, in a periodic or non-periodic pattern), wherein the unit cells include rigid portions connected by ligaments that act as plastic hinges when subjected to critical buckling loads, and wherein the metamaterial is capable of absorbing impact / deformation through the sequential yielding buckling of the unit cells, thereby enabling the material to collapse gradually and in a controlled manner.

[0012] This metamaterial can be constructed using artificially designed structural units with specific properties and functions. These structural units, called unit volumes, can be customized in terms of shape, size, and lattice constant, while the interactions between them can also be designed.

[0013] In one specific embodiment, the metamaterial unit cell is planar, for example, having a uniform thickness, and the ligaments bend within the plane of the unit cell. The metamaterial unit cells can be coplanar, i.e., extending within the same plane or curved surface.

[0014] Sequential buckling is achieved when one or more sets of unit cells buckle sequentially. For this purpose, the metamaterial may, for example, comprise multiple parallel strips, and each unit cell has a top and a bottom end aligned with a ligament in the load direction, the top end connecting to the first strip and the bottom end connecting to the second strip. More specifically, the metamaterial may contain multiple rows of parallel unit cells between the parallel strips. For example, these rigid portions may be connected to adjacent strips by one or more additional ligaments, these additional ligaments being the same size and shape as the ligaments connecting the rigid portions.

[0015] In one embodiment, each unit cell includes two rigid portions. In one embodiment, the rigid portion is square, with one diagonal extending along the load direction, i.e., perpendicular to the adjacent strip, along the longitudinal axis of the unit cell. Thus, when the ligament between the two rigid portions buckles, the edges of the two rigid portions abut against each other.

[0016] Once a ligament flexes, the rigid parts it connects rotate with the ligament, eventually causing the rigid parts to come into contact with each other (see [link]). Figure 4 (ac), after which the force begins to increase again upon further compression. The material must exhibit elastic-plastic mechanical behavior. Only materials exhibiting elastic-plastic behavior, such as plastics or metals, will buckle under the yield-buckling mechanism. The direction in which the ligament begins to deform (refer to...) Figure 1 The direction (left or right, as shown in the figure) is random, depends on local instability, and the direction is not important to the result.

[0017] The tangent modulus Et is the slope of the stress-strain curve at any given stress or strain. The tangent modulus Et varies with strain. In the context of this disclosure, the tangent modulus refers to the tangent modulus Et at or slightly above the yield point in the true stress-strain curve, particularly the tangent modulus Et at the 0.2% true plastic strain point.

[0018] Based on the relationship between the ligament's thin length and tangential modulus Et relative to its elastic modulus, three mechanisms can be observed.

[0019] For slender unit cells, the structure will buckle in the first stage, and in the second stage, the ligaments will eventually undergo plastic deformation. For unit cells with thicker ligaments, the ligaments will undergo plastic deformation but remain straight in the first stage and eventually buckle in the second stage. In both cases, the post-buckling load continues to increase.

[0020] Yielding and buckling occur when ligaments are of moderately slender length: the ligament undergoes plastic deformation, and if the yield load exceeds the reduced modulus load, the structure immediately loses stability and buckles. In this context, the reduced modulus load is the critical buckling load derived from Euler's formula, replacing the elastic modulus E with the reduced modulus Er, according to the following formula: Where Et is the tangent modulus at 0.2% plastic strain, and E is the elastic modulus. Therefore, the load decreases sharply during buckling.

[0021] The sharp drop in load at the buckling point makes it possible to design metamaterials composed of one or more clusters or rows of elements that buckle sequentially. Robust sequential buckling can only be achieved using yield buckling.

[0022] Metamaterials used in load-bearing and / or damping applications exhibit sequential yielding buckling and provide high specific energy absorption, high stiffness, load-bearing capacity, controlled collapse, and controlled and smooth deceleration. Metamaterials must be elasto-plastic materials. Preferably, the material is a metal, as metals are elasto-plastic materials that strengthen upon deformation and have higher yield strength compared to polymers and similar materials. Suitable metals include steel, aluminum, and aluminum alloys.

[0023] Metamaterials are specially designed materials with unique structural properties that enable them to effectively bear and distribute mechanical loads. Unlike traditional materials, load-bearing metamaterials are designed with specific internal structures or patterns that endow them with extraordinary mechanical properties.

[0024] Examples of metamaterials according to the invention have unit cells arranged in a periodic pattern, i.e., including repeating unit cells (unit cells having, for example, equal dimensions, shapes, spacing, and orientations), which are the fundamental building blocks of the metamaterial structure. The arrangement and geometry of these unit cells are designed to achieve desired mechanical properties, such as a high strength-to-weight ratio, enhanced stiffness, or excellent energy absorption capacity. By optimizing the internal structure, load-bearing metamaterials can exhibit superior load-bearing capacity while maintaining lightweight design. These materials are commonly used in applications where weight reduction, strength, and structural integrity are critical factors. Examples include aerospace components, automotive parts, and civil engineering structures.

[0025] In metamaterials, a unit cell refers to the smallest repeating structural element that constitutes the material. Unit cells in metamaterials can include rigid portions and ligaments that interconnect these rigid portions. These ligaments act as plastic hinges during plastic deformation of the metamaterial, designed to effectively distribute and manage mechanical loads. The arrangement and geometry of the unit cells determine the overall strength, stiffness, and load-bearing capacity of the metamaterial. By optimizing the unit cell design, load-bearing metamaterials can exhibit enhanced mechanical properties, such as a high strength-to-weight ratio, adjustable elasticity, or impact resistance, making them suitable for applications requiring lightweight yet robust structures.

[0026] To utilize metamaterials as dampers, yield buckling can be combined with the use of sequential buckling strips or unit clusters. Prior to buckling, deformation of the metamaterial primarily occurs within the ligaments. If the ligaments are parallel to the load direction, the initial stiffness is high. With ligament buckling, the compressed metamaterial loses its stability and begins to collapse, with a corresponding decrease in load. Essentially, yield buckling occurs because the stress distribution on the ligaments is asymmetrical. The compression side of the ligament experiences a plastic load with a tangential modulus of Et. In contrast, the tension side of the ligament experiences elastic unloading (see...). Figure 10Its elastic modulus E > Et. The resulting load is primarily tensile, leading to a reduction in the total reaction force. This yield-buckling property, combined with the geometry of the metamaterial, enables a continuous process of any number of buckling steps.

[0027] This combination causes the metamaterial to gradually collapse along well-defined strips of unit cells (line mode). As the ligaments in each of these strips buckle, the force-displacement ratio reaches a local maximum. With increasing compression, the strips deform further and the force decreases. The geometry of the strips limits the amount of deformation they can withstand, and the force reaches a local minimum. The force-displacement curve formed by a series of such buckling events is initially very stiff, then enters a plateau phase. This plateau phase consists of a cyclical series of local maximums and minimums (waves). Sequential yield buckling is characterized by the cascading or sequential failure of individual subwavelength unit cells within the metamaterial structure, leading to a gradual and controlled collapse under load. This sequential buckling behavior is a result of the specific arrangement and connection of the unit cells and their mechanical properties. When one unit cell buckles and collapses, it transfers the load to adjacent unit cells, causing a chain reaction propagating through the structure. In summary, this "wave-plateau" characteristic enables optimal energy absorption and multi-stage / multi-purpose dampers. Figure 6 This indicates that the maximum force remains constant until the last line pattern (the last of the six in this example) also collapses.

[0028] The ligament-block geometry of the unit cells and the sequential discrete buckling of the individual strips or rows of unit cells enable metamaterials to simultaneously achieve two objectives: providing structural stiffness and strength before impact, and enhancing energy absorption and dissipation during impact. Furthermore, sequential yield buckling leads to a gradual and predictable collapse of the structure. This controlled failure behavior is beneficial in applications where structural integrity and safety are critical, as it provides warning signals or visual cues before complete failure, allowing for potential mitigation or intervention.

[0029] Another advantage is their potential to be used as "reusable" shock absorbers: as long as there is another row or cluster of elements to buckle, the residual stiffness will not compromise the structural integrity of the component to which it belongs. For example, in vehicles, shock absorbers are often part of the chassis and drivetrain, and a loss of stiffness would result in a loss of steering function. The amount of deformation that a second load can withstand will, of course, be reduced by the amount of deformation absorbed in the previous load cycle.

[0030] In summary, these metamaterials possess ideal shock absorption properties, are reusable, adjustable, and can be mass-produced using metals. They are ideal because the impact force does not decrease after impact but remains stable, resulting in less abrupt deceleration. They are reusable because the structure retains its stiffness characteristics after impact. They are adjustable because their stiffness, strength, and energy absorption can be independently adjusted through the geometry and plasticity of the metamaterial. They are robust because sequential buckling functions effectively even at high impact velocities and when the impact direction is at an angle to the longitudinal direction of the unit cell. By incorporating metamaterials into the design of impact-absorbing components such as bumpers, frames, or protective barriers, enhanced impact resistance can be achieved while minimizing weight and size.

[0031] Metamaterial-based impact absorption systems can also be designed to exhibit unique responses to impact forces. By manipulating the internal structure and composition of metamaterials, it is possible to create systems that exhibit negative stiffness (i.e., a local slope of the force-displacement curve that is negative). Figure 2 c) or other nonlinear mechanical behaviors of materials. These unconventional mechanical properties allow metamaterials to deform or undergo structural changes upon impact, effectively dissipating and redistributing collision energy.

[0032] Furthermore, metamaterials can be used to design impact-absorbing structures with tunable properties. By adjusting the geometry or composition of metamaterials, their response to impact forces can be customized to meet specific requirements. This adaptability enables the design of impact-absorbing systems to effectively mitigate different types of impacts, from low-velocity collisions to high-energy impacts.

[0033] To achieve negative stiffness characteristics after buckling and utilize them to achieve sequential buckling, we propose design rules for metamaterial dampers that combine high stiffness and stable damping.

[0034] The metamaterials according to the present invention can conform to a set of design rules. Elastic-plastic columns can fail under compression due to a combination of geometric buckling and plastic deformation of the material.

[0035] There are three potential buckling mechanisms, see [link to relevant documentation] Figure 3 : i. Elastic buckling ( Figure 3 Region i): When the column is slender, it will begin to buckle before plastic deformation: F e = F cr < F y F e For the elastic (Euler) buckling load of the element, F cr F is the critical buckling load of the element. y This represents the yield load of the element. Therefore, the post-buckling stiffness will remain positive, causing the force to continue to increase.

[0036] ii. Plastic buckling ( Figure 3 Region ii): When the column cross-section is large enough, it will no longer elastically deflect, and buckling will occur at the onset of plastic deformation: F e > F cr = F r > F y .

[0037] iii. Yield and buckling ( Figure 3 (Region iii): When the column cross-section is sufficiently large and the column's tangent modulus is sufficiently low, buckling occurs at the yield point. This leads to a sharp drop in load, accompanied by buckling.

[0038] These general rules i-iii can be transformed into a set of specific design rules: Design Rule 1: Yield buckling induces negative post-buckling stiffness. Since the reduced modulus load depends only on the slenderness of the structure and the ratio between the elastic modulus and the tangent modulus, it is independent of the initial yield load. The structure can yield at loads higher than the buckling load defined by the reduced modulus, where the reduced modulus load is lower than the yield load. Because the formula for the reduced modulus load Fr only applies above the yield point, buckling will not occur before reaching the yield point. This ensures an asymmetric load distribution (the compressed portion of the beam experiences plastic loading, while the tension portion of the ligament experiences elastic unloading).

[0039] Yielding buckling is achieved if the slenderness ratio Λ of some or all of the unit cells satisfies the following formula: Where E is the elastic modulus, Er is the reduced modulus (calculated based on the tangent modulus Et at 0.2% plastic strain), and σy is the yield strength at 0.2% strain.

[0040] The slenderness ratio is a widely used and known concept in the field of buckling theory, and it can be easily and directly calculated, as explained in https: / / en.wikipedia.org / wiki / Slenderness_ratio.

[0041] This formula can also be expressed as: F r < F cr = F y < F e Where Fr is the reduced modulus load, F cr For the critical buckling load, F y For , is the yield load, and Fe is the elastic buckling load.

[0042] For example, if a unit cell has two rigid square sections, each with a diagonal aligned with the ligament (parallel to the load direction), then the slenderness ratio of the unit cell is Λ = t. 2 / 2hl, where l is the length of the unit cell, and the ligament has a length h, a width t, and a thickness b > t. In this case, the load F r F cr F y and F e It can be calculated as follows: in: t represents the width of the ligament connecting the rigid parts, in mm. h represents the height of the ligament connecting the rigid parts, in mm. b represents the thickness of the unit cell and ligament, in mm. l represents the length of the unit structure, in mm. E is the elastic modulus of the material, measured in GPa. E t This is the highest tangential modulus of the material above its yield point, expressed in GPa. σ y The yield strength of the material is expressed in GPa, specifically the yield strength σ at 0.2% strain. 0,2 .

[0043] Design Rule 2: The load reduction at the buckling point allows for the design of metamaterials with sequentially buckling unit clusters. This load reduction ensures that buckling of subsequent clusters is not activated before the unit elements in the first cluster self-contact, for example, as shown in... Figure 4 As shown in bc. Both sequential buckling and high stiffness can only be achieved under a yield-buckling mechanism and when buckling occurs within the plane of the unit cell. This can be achieved if the thickness b is greater than the ligament width t.

[0044] Design Rule 3: To achieve good damping characteristics and high structural stability, it is desirable to limit the load drop before self-contact without affecting the damping stroke. This is achieved by introducing a specific metamaterial geometry that includes both vertical ligaments and additional ligaments not in the load path. These stabilizing ligaments help delay the buckling load beyond the reduced modulus load, allowing the structure to buckle together at negative stiffness beyond the yield buckling region. This ensures that Design Rule 1 is always satisfied; by controlling the critical buckling load F... cr Pushing to the point where the load exceeds the reduced modulus Fr, equation F r <F cr < F e The inequality on the left side is satisfied.

[0045] As a demonstration of how these design rules are used, refer to metamaterials in CN111341395A (Prior Art (PA)). It describes a metamaterial composed of a very open structure. In this structure, the angle between the inclined struts and the compression direction is greater than 70°, approaching a bending-dominated structure. Therefore, these structures are very flexible in the first stage, making them unsuitable for damping. The first stage of deformation in the PA metamaterial exhibits elastic buckling behavior. The PA arch is made of an elastic material, while the design rules state that yield buckling requires an elastic-plastic material. However, even if the PA arch were made of an elastic-plastic material, it would still not exhibit yield buckling. This metamaterial uses the jump buckling of a pre-bent arch instead of the Euler buckling of a straight column (loaded along its axial direction). The pre-bent beam is more compliant in compression, resulting in lower strength, stiffness, and ultimately, lower energy absorption. Therefore, the PA metamaterial does not meet any of the three design rules. Energy absorption only occurs when the array elements begin to collide with each other (the holes in the lines close), and its behavior is not significantly different from that of a bulk material.

[0046] The metamaterials according to the invention can be produced in the form of plates or sheets, which can be considered as two-dimensional applications (see the Production Methods section). However, such plates or sheets can be transformed into three-dimensional applications, for example, by forming them into cylinders or prisms and welding the edges together. Other three-dimensional shapes that cannot be made from sheets or plates can be produced by more expensive and complex methods, such as additive manufacturing or casting techniques, such as the lost-wax casting process.

[0047] In one embodiment, the metamaterial comprises repeating unit cells arranged in a geometric pattern that, under load (e.g., during compression), results in a desired sequential collapse mechanism.

[0048] By arranging element bodies into geometric patterns, the deformation of metamaterials becomes easier to predict and reproduce. One example of a geometric pattern is arranging element bodies in rows. By stacking multiple rows of element bodies, deformation under load will result in sequential buckling of each row.

[0049] In one embodiment, the rigid portion of the metamaterial connected by ligaments rotates under load (e.g., during compression) due to the buckling of the ligaments.

[0050] Due to rotation, the initiation of metamaterial deformation is gradual and controlled, rather than sudden and unpredictable. The force required for further deformation remains relatively constant until the rigid sections connected by ligaments come into contact. At that moment, the force required for further deformation of the metamaterial increases again, potentially leading to buckling of the next set of ligaments in another unit cell or multiple unit cells.

[0051] In one implementation, yield buckling results in negative post-buckling stiffness, which causes the metamaterial to collapse sequentially when subjected to loading (e.g., compression).

[0052] If all elements in a metamaterial have the same geometry and buckling load, any non-negative post-buckling stiffness will trigger simultaneous buckling of elements in all layers. Only negative post-buckling stiffness can separate the buckling modes of elements in the same layer of the metamaterial and achieve a multi-step sequential collapse.

[0053] In one implementation, the compressive plastic deformation of the metamaterial occurs only in the following unit cells: when the metamaterial is loaded (e.g., under compression), the rigid portion connected by the plastic hinge has begun to rotate around the plastic hinge until the rigid portion collides, and under further loading, the stress causes the next row of unit cells to plastically deform due to yield buckling.

[0054] If metamaterials are used as shock absorbers, the metamaterials will not deform as a whole due to increasing forces (which is normal in classical technical materials). Instead, the energy of the impact is absorbed and the forces acting on the structure do not increase significantly, and therefore do not increase the forces acting on the contents of the structure or the passengers.

[0055] In a preferred embodiment, when the critical buckling load F of the unit cell cr Yielding and buckling occur when the following inequality applies: F r < F cr < F e Where F r For the reduced modulus load of the element, F e Let be the elastic buckling load of the element, where the ligament in the element is parallel to the load direction. If the metamaterial comprises elements of length l and thickness b, and ligaments of length h and width t, then the load is as follows: as well as in: t represents the width of the ligament connecting the rigid parts, in mm. h represents the height of the ligament connecting the rigid parts, in mm. b represents the thickness of the metamaterial, in mm. l represents the length of the unit structure, in mm. E is the elastic modulus of the material, measured in GPa. E t Tangent modulus of the material, in GPa σy is the yield strength of the material, in GPa.

[0056] F y This represents the yield load at the ligament, expressed in kN.

[0057] The inventors discovered that if metamaterials meet these criteria, metamaterials suitable for vibration damping or load-bearing applications can be obtained.

[0058] In one embodiment, the metamaterial unit cell also includes stabilizing ligaments that are not directly in the load path. For example, such stabilizing ligaments can connect the unit cell to adjacent unit cells or other parts of the metamaterial.

[0059] To further stabilize the metamaterial and prevent accidental or uncontrollable lateral deformation, stabilizing ligaments can be applied. For example, if the first set of ligaments is oriented along the Y-direction, a second set of ligaments at an angle to the Y-direction will stabilize the structure against loads not in or close to the Y-direction. The inventors have found that sequential buckling can occur under non-axial loads with off-axis angles up to 10°, so load angles up to 10° can be mitigated by ligaments in the Y-direction (=load direction) alone. However, for larger angles between the load angle and the ligament orientation, additional stabilizing ligaments are recommended. The most extreme case is a 90° angle between the second set of ligaments and the first set, but other angles are also effective.

[0060] In one embodiment, the metamaterial has a specific stiffness or specific modulus of at least 2 GPa·g-1.cm³, and a specific energy absorption greater than 5 kJ / kg in the first 20% of the travel, and / or the stress ratio between the average stress after impact and the highest stress after buckling can be greater than 80%, preferably greater than 90%, more preferably greater than 95%. This means the stress curve exhibits a plateau, thus resulting in more efficient energy absorption and requiring less strain to absorb the impact. For the same deceleration, a shorter travel is achieved. This is suitable for future vehicles with shorter front crumple zones—which is very useful for cars without large engine packs at the front. In a more specific embodiment, the specific energy absorption is 8 to 11 kJ / kg, the equivalent specific stiffness is 2 GPa·g-1.cm³, and the effective travel range is up to 75%. This is suitable for conventional vehicles with longer crumple zones.

[0061] Specific modulus (https: / / en.wikipedia.org / wiki / Specific_modulus) or specific stiffness is the ratio of a material's elastic modulus (or stiffness) to its mass density. Specific energy absorption is defined as the energy absorbed per unit mass of a material, and therefore its unit is kJ / kg. The post-impact stress ratio is the ratio between the mean stress and the highest post-buckling stress.

[0062] In one implementation, sequential yielding buckling occurs at 1 x 10-3 s -1 up to 150 s- 1 This is achieved at a strain rate of [specific value].

[0063] In one embodiment, the metamaterial comprises a three-dimensional unit body, wherein the ligament extends in three directions and contains at least first-order rotational symmetry and / or reflection symmetry.

[0064] Planar metamaterials can be transformed into three-dimensional shapes, for example, by bending them into tubes with circular or other cross-sections, or by stacking them together. However, this implementation involves truly three-dimensional structures where ligaments exist outside the two-dimensional plane of the planar metamaterial. This allows for the production of metamaterials that exhibit unique structural properties in all three directions.

[0065] In one embodiment, a shock absorber or load-bearing component manufactured using the metamaterial is provided.

[0066] According to a second aspect, a method for producing the metamaterial according to the invention is provided, wherein... i. Removing material from an initial solid elastoplastic strip, sheet, or tube using one or more of the following techniques to produce a plurality of unit cells arranged in a periodic or non-periodic pattern, wherein the unit cells include rigid portions connected by ligaments that are capable of acting as plastic hinges during loading: a. Milling b. Cutting c. Stamping d. Waterjet cutting e. Laser cutting f. EDM g. Electrochemical processing h. Plasma processing, or ii. To prepare metamaterials by additive manufacturing to fabricate, for example, multiple unit cells arranged in a periodic or aperiodic pattern, wherein the unit cells include rigid portions connected by ligaments that act as plastic hinges under load, or iii. Preparation of metamaterials by lost-wax casting.

[0067] Metamaterials can be produced using conventional techniques as described above.

[0068] 3D metamaterials can be produced through additive manufacturing.

[0069] In one embodiment, the initial solid elasto-plastic strip, sheet, or tube material is metal, preferably steel, aluminum, or an aluminum alloy.

[0070] Using the above techniques, solid strips, sheets, or tubes can be transformed into metamaterials by cutting holes and retaining rigid parts and plastic hinges.

[0071] In one implementation, the metamaterial is then subjected to forming operations, such as rolling, roll forming, or bending.

[0072] Planar two-dimensional metamaterials can be made into quasi-three-dimensional metamaterials, for example, by rolling them into a tubular shape and joining the edges together to form a closed tube.

[0073] In one implementation, the metamaterial is attached to itself by mechanical, adhesive, or welding methods to form a tubular shape or to another component.

[0074] The concept of this invention has proven effective, as demonstrated by uniaxial and multiaxial loading conditions. Even at very high impact velocities (50 km / h, which is a realistic impact condition), and even when the impact direction is not aligned with the structure, the invention works effectively. Furthermore, the deceleration of the impacted structure is less severe. Attached Figure Description

[0075] The invention will now be described with reference to the following non-limiting drawings.

[0076] Figure 1 This illustrates one of the simplest forms of a metamaterial unit. The two rhomboid sections are rigid, and the connection between them acts as a ligament, functioning as a plastic hinge during buckling. The connection at the top and bottom also acts as a ligament, serving as a plastic hinge. The ratio between the dimensions of the central ligament and the dimensions of the top and bottom ligaments will influence the area where yielding and buckling may occur.

[0077] Figure 1 The width t of the ligament in the middle a is the factor that determines the elastic flexion the ligament will undergo. Figure 2 a) Plastic buckling ( Figure 2 b) or the expected yielding and buckling ( Figure 2 c) The relevant parameters. The buckling mode determines the critical force (F). cr Furthermore, it determines whether the material exhibits positive stiffness S>0 (the force increases for further deformation) or negative stiffness S<0 after buckling. Note that the u / l ratio is compressive strain, since u is displacement and l is element length.

[0078] Figure 1 The length l in the design is also a relevant parameter, as it, together with the width t, determines the t / l ratio, which constitutes an important part of the design criteria and determines which buckling mode is applicable. Figure 3 It shows Figure 2 The three regions (i, ii, and iii), and the equation that determines Fr.

[0079] Figure 4 It shows Figure 1 The application of elemental units in metamaterial structures. The figure shows four rows of elemental units (line modes) stacked on top of each other, each row containing four side-by-side elemental units. Figure 'b' illustrates what happens during loading. One line mode exhibits yield buckling (b) and collapses until the rigid portion abuts (c). Under further loading, subsequent line modes collapse. As long as undeformed line modes exist, residual stiffness does not compromise the structural integrity of the component to which it belongs. It should be noted that the direction of plastic hinge deformation is random based on local instability and is not significant to the outcome.

[0080] Figure 5 a shows a unit cell that includes not only vertical ligaments (width t) but also horizontal ligaments (*). Figure 5 b shows the deformation of the unit during compressive loading.

[0081] Figure 6 It shows the use of Figure 5 Figure a shows a cylinder made from a unit cell and its force-displacement curve, which clearly illustrates sequential buckling, where the maximum force exhibits a plateau period, after which the force tends to level off, only increasing again after the buckling potential is fully realized. The shape and function of the component remain intact, as shown in the force-displacement curve and Figure b. The inventors found that this structure can absorb impact loads at angles up to 10° to the longitudinal axis of the structure.

[0082] Figure 7 a illustrates the application of this concept in 3D shapes. Figure 7 b shows the deformation after compression along the z-direction. The result is the same when compression is performed along the y or x-direction (not shown).

[0083] Figure 8 It shows the basis Figure 5 The metamaterial is a cylinder with a diameter of 144 mm, in its undeformed state (a), at the onset of yielding buckling (b), and with the ligament almost fully rotated. The metamaterial was fabricated by milling holes in a steel tube.

[0084] Figure 9 A schematic diagram of a method for producing metamaterials from strips by stamping openings is shown.

[0085] Figure 10 The stress distribution on the ligament during buckling (dashed line) and after buckling (solid line) is shown, indicating that the tension side (negative stress) has higher stress than the compression side (normal stress). Note that compressive stress and strain are usually defined as positive values.

[0086] Figure 11The buckling loads during sequential yielding buckling of metamaterials are shown: (a) without additional ligaments, and (b) with additional ligaments but not on the load path.

[0087] Figure 12 An alternative embodiment of the impact energy absorption box 1 is shown, which is made of metamaterial 2, which is made of an elastic-plastic material (such as steel). The impact energy absorption box 1 in Figure 13 It is shown in perspective section, while Figure 14 The unit cell 3 is shown in cross-section. The metamaterial 3 comprises a tubular stack of annular unit cells 3, each annular unit cell 3 including annular rigid portions or flanges 4A, 4B connected by annular ligaments 5, which plastically hinge upon being subjected to a critical buckling load. In the illustrated embodiment, the tubular stack of the impact energy-absorbing box 1 is cylindrical, but other shapes are also possible. The metamaterial 2 is capable of absorbing impact and collision loads through the sequential yielding and buckling of each unit cell 3, thereby enabling the progressive and controlled collapse of the impact energy-absorbing box 1.

[0088] Except for the flanges 4A and 4B at the outer ends of the tubular stack, each flange 4 is part of two adjacent unit bodies 3. In the illustrated embodiment, the flange 4 is reinforced by two concentric ribs 6A and 6B, the length of which is twice the ligament thickness t. The radial distance between the two concentric ribs 6A and 6B is equal to the length l of the ligament, i.e., the distance between the two adjacent flanges 4.

[0089] Metamaterials have the following aspect ratios: The geometry of metamaterials should satisfy: Where Er is the reduced modulus calculated using Et, Et is the tangent modulus at 0.2% strain, and σ is the yield strength. y The stress at 0.2% strain, σ 0,2 In this situation, the ligament responds to the critical buckling load F through buckling. cr Hinging occurs. The combination of slenderness ratio, cross-section, elastic modulus E, and tangent modulus Et leads to the critical buckling load F. cr Under the action of force, yielding and buckling occur, in which the ligament has an asymmetric stress distribution. The compression side of the ligament is subjected to plastic loading with a tangential modulus of Et, and the tension side of the ligament is subjected to elastic unloading with an elastic modulus E > Et. Figure 10 As shown. Therefore, the ligaments flex sequentially.

[0090] In this embodiment, the specific energy absorption is in the range of 8 to 11 kJ / kg, the equivalent specific stiffness is 2 GPa.g-1.cm3, and the effective stroke range is as high as 75%.

Claims

1. A metamaterial for load-bearing and shock-absorbing applications, wherein the metamaterial is made of an elastic-plastic material, and wherein the metamaterial comprises a plurality of unit cells, wherein each unit cell includes a rigid portion connected by ligaments that act as plastic hinges during loading, and wherein the metamaterial is capable of absorbing impact / deformation through sequential yielding buckling of the unit cells, thereby enabling the metamaterial to collapse gradually and in a controlled manner.

2. The metamaterial according to claim 1, wherein the ligament responds to the critical buckling load F cr When the articulation occurs, the ligament has a critical buckling load F that induces a response. cr The yield buckling section, elastic modulus E, and tangent modulus Et of the ligament, wherein there is an asymmetric stress distribution on the ligament, the compression side of the ligament is subjected to a plastic load with a tangent modulus of Et, and the tension side of the ligament is subjected to an elastic unloading with an elastic modulus E > Et.

3. The metamaterial according to claim 1 or 2, comprising repeating unit cells arranged in a geometric pattern that causes a sequential collapse mechanism under load.

4. The metamaterial according to claim 1, 2 or 3, wherein the rigid portion connected by ligaments rotates under load due to plastic deformation of the plastic hinge.

5. The metamaterial according to any one of claims 1 to 4, wherein yielding buckling results in a negative post-buckling stiffness, which causes the collapse of the material to occur sequentially under material loading.

6. The metamaterial according to any one of the preceding claims, wherein at least a portion of the unit cell has an elongation ratio Λ that conforms to the following formula: Where E is the elastic modulus, Er is the reduced modulus, and σy is the yield strength.

7. The metamaterial of claim 6, wherein the unit cell has two rigid portions, both of which are square and have diagonals aligned with the ligament, the unit cell has a length l, the ligament has a length h, a width t, and a thickness b > t, and wherein Λ = t 2 / 2hl.

8. The metamaterial according to claim 6 or 7, wherein when the critical buckling load F of the unit cell cr Yielding and buckling occur when constrained by the following inequalities: F r < F cr < F e Where F r For the reduced modulus load of the element, F e Let be the elastic buckling load of the element, and wherein the ligaments in the element are parallel to the load direction, wherein as well as Where A is the cross-sectional area of ​​the ligament and Λ is the slenderness ratio.

9. The metamaterial of claim 8, wherein the ligament has a width t, a height h, and a thickness b, the unit cell has a length l, and wherein as well as 。 10. The metamaterial according to any one of the preceding claims, wherein the unit cell further comprises a stabilizing ligament not in the load path.

11. The metamaterial according to any one of the preceding claims, wherein the specific stiffness or specific modulus is at least 2 GPa.g. - 1 .cm 3 The specific energy absorption is greater than 5 kJ / kg and / or the stress ratio between the average stress after impact and the highest stress after buckling is greater than 80%, preferably greater than 90%, more preferably greater than 95% and / or the effective compression stroke can be adjusted from 20% to 75%.

12. The metamaterial according to claim 11, wherein the specific energy absorption is 8 to 11 kJ / kg and the equivalent specific stiffness is 2 GPa.g -1 .cm 3 .

13. The metamaterial according to any one of the preceding claims, wherein the sequential yielding buckling is within 1 x 10⁻⁶. -3 s -1 up to 150s- 1 This is achieved at a strain rate of [specific value].

14. The metamaterial according to any one of the preceding claims, wherein the unit cell is three-dimensional, and wherein the ligament extends in three directions and contains at least one order of rotational symmetry and / or reflection symmetry.

15. The metamaterial according to any one of the preceding claims, wherein the unit cells can be arranged in a periodic or non-periodic pattern.

16. The metamaterial according to any one of the preceding claims, comprising a tubular stack of annular units.

17. The metamaterial of claim 16, wherein the unit cell comprises a rigid portion or flange connected by annular ligaments.

18. The metamaterial according to claim 17, having the following aspect ratio: 。 19. A shock absorber or load-bearing component made using the metamaterial of any one of claims 1 to 18.

20. A method for preparing metamaterials according to any one of claims 1 to 18, wherein: i. To prepare a plurality of unit cells arranged in a periodic or non-periodic pattern by removing material from an initial solid elastoplastic strip, sheet, or tube using one or more of the following techniques: The unit cells include rigid portions connected by ligaments capable of acting as plastic hinges during loading. a. Milling b. Cutting c. Stamping d. Waterjet cutting e. Laser cutting f. EDM g. Electrochemical processing h. Plasma processing, or ii. Fabricating metamaterials by additive manufacturing to prepare multiple unit cells arranged in a periodic or non-periodic pattern, wherein the unit cells include rigid portions connected by ligaments that are capable of acting as plastic hinges during loading via one or more of the following techniques, or iii. Preparation of metamaterials by lost-wax casting.

21. The method of claim 20, wherein the initial solid elasto-plastic strip, sheet or tube material is a metal, preferably steel, aluminum or aluminum alloy.

22. The method of claim 20 or 21, wherein the metamaterial is subsequently subjected to a forming operation, such as rolling, roll forming, or bending.

23. The method according to any one of claims 20 to 22, wherein the metamaterial is attached to itself by mechanical, adhesive or welding connection methods to form a tubular shape or to another component.

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