Metamaterials for shock absorption applications and methods for producing said metamaterials

Abstract

This invention relates to metamaterials for shock absorption and load bearing applications and to the methods for producing said metamaterials, wherein the essence of the metamaterial design lies in creating materials through artificially crafted structural units with specific properties and functions.

Description

[0001] METAMATERIALS FOR SHOCK ABSORPTION APPLICATIONS AND METHODS FOR

[0002] PRODUCING SAID METAMATERIALS

[0003] Field of the invention

[0004] The invention relates to metamaterials for shock absorption applications and to methods for producing said metamaterials.

[0005] Background of the invention

[0006] Shock absorption is a crucial function designed to protect objects, structures, or living organisms from the damaging effects of sudden impacts or vibrations. It acts as a buffer, absorbing and dissipating the energy generated during such events. In mechanical systems, shock absorption helps to prevent excessive stress, wear, and damage by reducing the intensity and duration of the impact. A car crash is an example of a shock with potentially devastating consequences. The impact of the crash needs to be mitigated to protect the contents and, most importantly, the passengers in the vehicle. An ideal shock-absorbing material is one that exhibits exceptional energy absorption capabilities during such as high impact events. It should possess properties such as high strength, controlled deformation, progressive collapse, and effective energy dissipation to mitigate the forces and to protect occupants or structures from severe damage during crashes or collisions.

[0007] Also a crash bar dissipates the crash energy very quickly causing a very sudden deceleration that potentially causes damage to equipment and / or physical health implications for passengers. An ideal shock absorbing material should be light-weight and absorb / dissipate a maximum of energy in a stable way as well as remain strong and stiff after impact.

[0008] Existing materials and structures such as crash cans or metallic foams are either stiff and strong before impacting or stable energy-absorbing with a low stiffness and strength but not both. The challenge is hence to create lightweight structures that can both provide high stiffness as well as stable energy damping at the same time. Superelastic metallic alloys such as NiTi are also known to be dissipative and stiff. But these materials are much more expensive and hard to manufacture at the large scale.

[0009] Existing methods to enhance shock absorption use polymeric materials such as plastic, foams and rubbers. These materials are soft and therefore cannot be used in applications where one needs to be stiff to avoid vibrations and deformations (cars, aerospace). The use of such materials which allow good energy dissipation must be combined in these industries with a stiff component that provides strength. This means that plastics and rubbers necessarily must be used in combination with metals or other stiff materials, which inherently increase the overall weight and cost of the vehicles. For metallic shock absorption one uses crash cans or honeycomb lattices, but there the buckling is “catastrophic”. This means that after the initial collapse, the structures lose their initial stiffness and strength, and cannot be reused as the same function after impact.

[0010] Objectives of the invention

[0011] It is an objective of the invention to provide a shock absorbing metamaterial that combines stiffness and energy absorption and that retains can its initial stiffness and strength after having been subjected to a shock.

[0012] It is also an objective of the invention to provide a shock absorbing structure comprising said shock absorbing metamaterial.

[0013] It is also an objective of the invention to demonstrate that said shock absorbing metamaterial or shock absorbing structure can be fabricated by additive manufacturing techniques.

[0014] It is also an objective of the invention to demonstrate that said shock absorbing metamaterial or shock absorbing structure can be fabricated from bulk metallic materials.

[0015] Description of the invention

[0016] The ideal shock absorber combines high stiffness with high energy absorption whilst retaining structural integrity (stiffness) after impact and should be scalable to real world applications. The inventors demonstrate an industrially feasible metamaterial combining high stiffness before and after impact with high dissipative capacity. This is achieved by striking a balance between plastic deformation and buckling which they termed “yield buckling”.

[0017] One or more of the objectives are reached with a metamaterial for load-bearing and shock absorbing applications wherein the metamaterial is made of an elastoplastic material and wherein the metamaterial comprises a plurality of unit cells, e.g., arranged in a periodic or nonperiodic pattern, wherein the unit cells comprise rigid parts connected by ligaments which ligaments act as plastic hinges during loading by a critical buckling load, and wherein the metamaterial is able to absorb shocks / deformation through sequential yield buckling of the unit cells thereby enabling a progressive and controlled collapse of the material.

[0018] The metamaterial can be created with artificially crafted structural units with specific properties and functions. The structural units, referred to as unit cells, can be customized in terms of shape, size, and lattice constant, while interactions between them can be engineered.

[0019] In a specific embodiment, the unit cells of the metamaterial are planar, e,g., having an even thickness, and the ligaments buckle in the plane of the unit cell. The unit cells of the metamaterial can be coplanar, i.e. , extend in a same flat or curved plane.

[0020] Sequential buckling is achieved if groups of one or more unit cells buckle sequentially. To this end, the metamaterial may for example comprise a plurality of parallel strips and the unit cells have a top end and a lower end aligned with the ligament in a loading direction, the top end being connected to a first one of the strips and the lower end being connected to a second one of the strips. More specifically, the metamaterial may comprise rows of parallel unit cells between the parallel strips. The rigid parts can for example be connected to an adjacent one of the strips by one or more further ligaments, e.g., having the same size and shape as the ligament connecting the rigid parts.

[0021] In a specific embodiment, each unit cell comprises two rigid parts. In a specific embodiment, the rigid parts are square with one diagonal extending in the loading direction, i.e. under right angles with the adjacent strips, along a longitudinal axis of the unit cell. This way, the edges of the two rigid parts abut against each other when the ligament between the two rigid parts buckles.

[0022] Once the ligaments buckle, the rigid parts to which the ligaments are attached rotate with the ligament and finally the rigid parts abut each other (see figure 4, a-c) after which the force starts increasing again upon further compression. The material must exhibit elastoplastic mechanical behaviour. Only materials exhibiting elastoplastic behaviour, e.g., plastics or metals, will buckle in the yield buckling regime. The direction to which the ligament starts to deform (cf. figure 1 : to the left or to the right (as depicted) is random, based on local instabilities and the direction is unimportant to the result.

[0023] The tangent modulus Et is the slope of the stress-strain curve at any specified 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 just above the yield point in the true stress - true strain curve, in particular at the point of 0,2% true plastic strain.

[0024] Three regimes can be observed depending on the slenderness of the ligament and the tangent modulus Et relative to its elastic modulus.

[0025] For slender unit cells, the structure will buckle in a first stage, and in a second stage the ligament eventually deforms plastically. For unit cells with thicker ligaments, the ligament will plastically deform, yet will remain straight in a first stage and in a second stage it will eventually buckle. In both these cases, the load continues to increase after buckling.

[0026] Yield buckling emerges when the ligament has intermediate slenderness: the ligament deforms plastically and if the yield load is larger than the reduced modulus load, this immediately makes the structure lose its stability and buckle. In this context, the reduced modulus load is the critical buckling load derived from Eulers’ formula replacing the elastic modulus E with the reduced modulus Er, in accordance with the following formula: wherein Et is the tangent modulus at a plastic strain of 0,2 % and E is the elastic modulus. As a result, the load sharply decreases right at buckling.

[0027] This stark decrease of the load right at the point of buckling enables the design of metamaterials with clusters or rows of one or more unit cells that buckle sequentially. Robust sequential buckling can only be achieved when using yield buckling.

[0028] The metamaterial for load bearing and / or shock absorption applications shows sequential yield buckling and provides high specific energy absorption, high stiffness, load bearing, controlled collapse, controlled and smooth deceleration. The metamaterial must be an elastoplastic material. Preferably, the material is a metal as this is an elastoplastic material that strengthens upon deforming and has a high yield strength as compared to polymers and similar materials. Suitable metals include steel, aluminium and aluminium alloys.

[0029] A metamaterial is a specially designed material that possesses unique structural properties, enabling it to carry and distribute mechanical loads effectively. Unlike traditional materials, load-bearing metamaterials are engineered with specific internal architectures or patterns that provide them with extraordinary mechanical characteristics.

[0030] Examples of metamaterials according to the invention have unit cells arranged in a periodic pattern, i.e., comprising repeating unit cells, e.g., of equal size, shape, spacing and orientation, which are the basic building blocks of the metamaterial's structure. The arrangement and geometry of these unit cells are designed to achieve desired mechanical properties such as high strength-to-weight ratios, enhanced stiffness, or superior energy absorption capabilities. By optimizing the internal structure, load-bearing metamaterials can exhibit exceptional load-bearing capacities while maintaining lightweight construction. These materials are typically used in applications where weight reduction, strength, and structural integrity are critical factors. Examples include aerospace components, automotive parts and civil engineering structures.

[0031] In the metamaterial, a unit cell refers to the smallest repeating structural element that makes up the material. The unit cell in a metamaterial may comprise rigid parts and ligaments interconnecting the rigid parts and acting as plastic hinges during plastic deformation of the metamaterial, which are designed to distribute and manage mechanical loads efficiently. The arrangement and geometry of the unit cells determine the overall strength, stiffness, and loadbearing capacity of the metamaterial. By optimizing the unit cell design, load-bearing metamaterials can exhibit enhanced mechanical properties such as high strength-to-weight ratios, tuneable elasticity, or impact resistance, making them suitable for applications that require lightweight yet robust structures.

[0032] To use the metamaterial as a shock absorber the phenomenon of yield buckling can be used in combination with the use of sequentially buckling strips or clusters of unit cells.. Before buckling, the deformation of the metamaterial mainly takes place in the ligaments. If the ligaments are parallel to the loading direction, then there is an initially high stiffness. Concurrent with buckling of the ligaments, the metamaterial under compression loses its stability and starts to collapse with a corresponding decrease in load. In essence, yield buckling emerges because the stress distribution across the ligament is asymmetric. The compressed side of the ligament undergoes plastic loading with a tangent modulus Et. In contrast the tensile side of the ligament undergoes elastic unloading (see figure 10) with an elastic modulus E >Et. The resultant load is dominantly tensile, which leads to a reduction in the total reaction force. This feature of yield buckling in combination with a metamaterial geometry allows a sequence of an arbitrarily large number of buckling steps.

[0033] This combination allows step-by-step collapse of the metamaterial along well-defined strips of unit cells (line modes). When the ligaments in each of these strips buckle, the forcedisplacement achieves a local maximum. As the compression is increased, the strips further deform and the force decreases. The geometrical design of the strips limits the amount of deformation they can undergo, and the force achieves a local minimum. The sequence of multiple such buckling events produces a force-displacement curve that is initially very stiff, followed by a plateau. The plateau consists of a cyclic series of local maxima and minima (waves). Sequential yield buckling is characterized by a cascading or sequential failure of individual subwavelength unit cells within the metamaterial structure, leading to a progressive and controlled collapse under load. This sequential buckling behaviour is a result of the specific arrangement and connectivity of the unit cells, as well as their mechanical properties. As one unit cell buckles and collapses, it transfers the load to neighbouring cells, causing a chain reaction that propagates through the structure. Altogether, this ‘wave-plateau’ property is what enables optimal energy absorption and the potential for a multi-stage / multi-use shock absorber. Figure 6 shows that the maximum force stays constant, until the last line mode (of the 6 in this example) has also collapsed.

[0034] The ligament-block geometry of the unit cells and the sequential discrete buckling of respective strips or rows of unit cells allows the metamaterial to fulfil two purposes at the same time: they provide structural stiffness and strength before impact and provide enhanced energy absorption and dissipation capabilities during impact. Additionally, sequential yield buckling leads to a gradual and predictable collapse of the structure. This controlled failure behaviour is beneficial in applications where structural integrity and safety are critical, as it provides warning signs or visual cues before complete failure, allowing for potential mitigation or intervention.

[0035] Another advantage is that they could potentially be used as “multiple-use” shock absorbers: as long as there are next rows or clusters of unit cells to buckle, the residual stiffness will not compromise the structural integrity of the assembly of which it is a part e.g. in a vehicle , the shock absorption elements are usually part of the chassis and drive train structure where loss of stiffness would result in loss of steering function. The amount of deformation that can be taken up by a second loading is of course reduced by the amount of deformation absorbed during the previous load cycle.

[0036] In conclusion, this metamaterial has ideal shock absorbing properties that are multiuse, tuneable and possible to mass-manufacture in metals. They are ideal because the force does not drop after the impact, but plateaus. Hence the deceleration is less violent. They are multiuse because the structure retains its stiffness properties after the impact. They are tuneable because their stiffness, strength, and energy absorption can be independently tuned via the geometry and plasticity of the metamaterial. They are robust because the sequential buckling also works at large impact speeds and also when the impact occurs at an oblique angle to the longitudinal direction of the unit cells. By incorporating metamaterials into the design of crashabsorbing components like bumpers, frames, or protective barriers, it is possible to achieve enhanced impact resistance while minimizing weight and size.

[0037] Metamaterial-based crash 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 materials that exhibit negative stiffness (i.e. the local slope of the force-displacement curve is negative (see Figure 2c)) or other non-linear mechanical behaviour. These unconventional mechanical properties allow metamaterials to deform or undergo structural changes upon impact, effectively dissipating and redistributing the energy of the collision.

[0038] Furthermore, metamaterials can be used to design crash-absorbing structures with tuneable properties. By adjusting the geometrical parameters or composition of the metamaterial, its response to impact forces can be customized to match specific requirements. This adaptability enables the design of crash-absorbing systems that can effectively mitigate different types of impacts, ranging from low-speed collisions to high-energy impacts.

[0039] To achieve the negative stiffness feature after buckling and use it to achieve the sequential buckling, here we propose rules for the design of metamaterial shock absorbers which combine high stiffness and stable shock absorption.

[0040] The metamaterials according to the invention may comply with a set of design rules. An elastoplastic column under compression can fail due to the combination of the geometry buckling and the plastic deformation of the material.

[0041] There are three potential buckling regimes, see Figure 3: i. Elastic buckling (Figure 3, region i): when the column is slender, it will start to buckle prior to plastic deformation: Fe= Fcr< Fy, where Feis the elastic (Euler) buckling load of the unit cell, Fcris the critical buckling load of the unit cell and Fyis the yield load of the unit cell. As a result the post-buckling stiffness will remain positive leading to a continuing rise in force. ii. Plastic buckling (Figure 3, region ii): when the column cross-section is sufficiently large, it will no longer deflect elastically and buckling occurs at the onset of plastic deformation: Fe> Fcr= Fr> Fy. iii. Yield buckling (Figure 3, region iii): when the column cross-section is sufficiently large AND the tangent modulus of the column is sufficiently low then buckling occurs at the yield point. This results in a sharp load decrease concomitant with buckling.

[0042] These general rules i-iii can be translated into a set of specific design rules:

[0043] Design rule 1 : yield buckling triggers negative post-buckling stiffness. Since the reduced modulus load only depends on the slenderness of the structure and on the ratio between elastic modulus and tangent modulus, it is independent of the initial yield load. The structure can be made to yield at a load that is higher than the buckling load defined by the reduced modulus, in which case the reduced modulus load is lower than the yield load. Since the formula for reduced modulus load Fr only applies above the yield point, buckling cannot occur until the yield point is reached. This ensures an asymmetric load distribution (the compressive part of the beam is undergoing plastic loading, whereas the tensile part of the ligament is undergoing elastic unloading.

[0044] Yield buckling is achieved if some or all of the unit cells have a slenderness ratio A in accordance with the following formula: wherein E is the elastic modulus, Er is the reduced modulus (calculated on basis of the tangent module Et at 0,2 % plastic strain), and oy is the yield strength at 0,2 % strain.

[0045] Slenderness ratio is a concept widely used and known in the field of buckling theory and can readily and straightforwardly be calculated, as explained in htps: / / en.wikipedia.org / wiki / Slenderness ratio.

[0046] The formula can also be formulated as:

[0047] Fr ^ Fcr - Fy ^ Fi wherein Fr is the reduced modulus load, Fcris the critical buckling load, Fyis the yield load and Fe is the elastic buckling load.

[0048] If for example the unit cells have two square rigid parts, both having a diagonal in line with the ligament (parallel to the loading direction), the unit cells have a slenderness ratio A = t2 / 2hl, wherein I is the length of the unit cell, the ligaments having a length h, a width t and a thickness b > t. In that case, the loads Fr, Fcr, Fyand Fecan be calculated as follows: wherein:

[0049] - t is the width of the ligament connecting the rigid parts in mm

[0050] - h is the height of the ligament connecting the rigid parts in mm

[0051] - b is the thickness of the unit cell and the ligament in mm

[0052] - I is the length of the unit cell structure in mm

[0053] E is the elastic modulus of the material in GPa

[0054] Etis the highest tangent modulus of the material in GPa beyond the yield point

[0055] - oyis the yield strength of the material in GPa, in particular the yield strength 00,2 at 0,2 % strain.

[0056] Design rule 2: The decrease in load right at the point of buckling enables the design of metamaterials having sequentially buckling clusters of unit cells. This load decrease ensures that buckling of subsequent clusters is not activated before unit cell elements in the first cluster have made self-contact, e.g. as shown in Figure 4 b-c. Sequential buckling combined with high stiffness can only be achieved in the yield buckling regime and where the buckling is in the plane of the unit cell. This can be achieved if the thickness b is larger than the ligament width t.

[0057] Design rule 3: To obtain good shock absorption properties in combination with high structural stability, it is desirable to limit the decrease in load prior to self-contact without adversely affecting the stroke of the shock absorption. This is achieved by introducing a specific metamaterial geometry which comprises both vertical ligaments and additional ligaments which are not in the loading path. These stabilising ligaments help to delay the buckling load beyond the reduced modulus load, making the structure buckle together with a negative stiffness beyond the yield buckling region. This guarantees that design rule 1 is always achieved; by pushing the critical buckling load Fcrbeyond the reduced modulus load Fr, the left-hand inequality of the equation Fr< Fcr< Feis satisfied.

[0058] By means of a demonstration of how to use these design rules, reference is made to the metamaterial in CN111341395A. Here, a metamaterial (Prior Art (PA)) is described consisting of a very open structure. The structures have a large angle between the inclined strut and the compression direction of larger than 70° which is close to the bending dominant structures. As a result, the structures are very soft in the first stage, so these structures cannot be used for shock absorbing. The first stage of deformation in the PA metamaterial exhibits elastic buckling behaviour. The PA arch is made of an elastic material and the design rule states that an elastoplastic is required for yield buckling. However, even if the PA arch would be made of elastoplastic material it would still not exhibit yield buckling. The metamaterial uses snap- through buckling of a pre-bent arch as opposed to Euler buckling (loading column along its axis) of a straight column. The pre-bent beams are more compliant in compression which results in lower strength, stiffness and ultimately energy absorption. As a consequence, the PA metamaterial does not comply with any of the 3 design rules. The energy absorption only occurs once the elements of the array begin to impinge upon one another (the holes in the line become closed) and do not behave significantly differently to a bulk material.

[0059] The metamaterial according to the invention can be produced in plate or sheet form, which can be considered a 2D application (see the section on production methods). However, such a plate or sheet can be transformed into a 3D application, e.g. by making a cylinder or a prism and welding the edges together. Other 3D-shapes, which cannot be made from sheet or plate can be produced by more costly and elaborate methods like additive manufacturing or by casting techniques such as the lost wax method.

[0060] In an embodiment the metamaterial comprises repeating unit cells which are arranged in a geometric pattern that leads to a desired sequential collapse mechanism when loaded, e.g. in compression.

[0061] By arranging the unit cells in a geometric pattern the deformation of the metamaterial is easier to predict and reproduce. An example of a geometrical pattern is to arrange the unit cells in rows. By stacking a number of rows of unit cells the deformation under loading will result in a sequential buckling of the rows.

[0062] In an embodiment the rigid parts of the metamaterial that are connected by the ligaments rotate as a result of the buckling by the ligaments when loaded, e.g. in compression.

[0063] Because of the rotation, the onset of deformation of the metamaterial is gradual and controlled, not sudden and unpredictable. The force needed for further deformation remains relatively constant until the moment that the rigid parts that are connected by the ligaments abut. At that moment, the force needed for further deformation of the metamaterial rises again, potentially leading to the buckling of the next series of ligaments in another unit cell or cells.

[0064] In an embodiment yield buckling leads to negative post-buckling stiffness which enables the collapse of the metamaterial to occur in sequence when the material is loaded, e.g. in compression.

[0065] If all unit cells in the metamaterial have the same geometry and buckling load, any nonnegative stiffness after buckling will trigger all layers of unit cells to buckle simultaneously. Only the negative post-buckling stiffness can separate the buckling modes from the same layers of the unit cells in the metamaterial and enable the collapse in a multistep sequential way.

[0066] In an embodiment the compressive plastic deformation of the metamaterial only occurs in the unit cells wherein the rigid parts that are connected by the plastic hinges have started to rotate around the plastic hinges until the rigid parts collide when the metamaterial is loaded, e.g. in compression, and wherein upon further loading the stress causes the next row of unit cells to plastically deform as a result of yield buckling.

[0067] If the metamaterial is used as a shock absorber the metamaterial does not deform as a whole by an ever increasing force, which is normal in a classical technical material, but on the contrary, the energy of the shock is absorbed without a significant increase in force acting on the structure, and thus also on the contents or passengers of the structure.

[0068] In a preferred embodiment yield buckling occurs when the critical buckling load of the unit cell Fcr, is constrained by the following inequality:

[0069] Fr< Fcr Fe where Fris the reduced-modulus load of the unit cell, and Feis the elastic buckling load of the unit cell, and wherein the ligament in the unit cells is parallel to the loading direction. If the metamaterial comprises unit cells, with a length I, a thickness b, and ligaments with a length h, and a width t, the loads are as follows:

[0070] And

[0071] F =Ebt3e~ 2hl wherein:

[0072] - t is the width of the ligament connecting the rigid parts in mm

[0073] - h is the height of the ligament connecting the rigid parts in mm

[0074] - b is the thickness of the metamaterial in mm

[0075] - I is the length of the unit cell structure in mm

[0076] E is the elastic modulus of the material in GPa

[0077] Etis the tangent modulus of the material in GPa

[0078] - oy is the yield strength of the material in GPa.

[0079] Fyis the yield load at the ligament in kN.

[0080] The inventors found that a suitable metamaterial for shock absorbing or load bearing applications is obtained if the metamaterial satisfies these criteria.

[0081] In an embodiment the unit cells of the metamaterial also comprise stabilising ligaments that are not directly in the loading path. Such stabilising ligaments may for example connect the unit cell with adjacent unit cells or other parts of the metamaterial.

[0082] To further stabilise the metamaterial and to prevent unexpected or uncontrolled sideways deformation stabilising ligaments can be applied. For example, if a first set of ligaments are oriented in the Y-direction , then a second set with a direction at an angle to the Y-direction will stabilise the structure against loading that is not in, or close to, the Y directions. The inventors found that sequential buckling may occur at non-axial loads at out-of-axis angles up to 10°, so that angles of loading of up to 10° can be mitigated with ligaments in the Y- direction only (= loading direction), but for larger angles between loading angle and ligament orientation additional stabilising ligaments are advisable. The most extreme case is when the second set is at a 90°-angle to the first set, but other angles also work.

[0083] In an embodiment the metamaterial has a specific stiffness or specific modulus of at least 2 GPa.g-1 .cm3 and a specific energy absorption of above 5 kJ / kg in the first 20% of the stroke and / or the post-impact stress ratio between the mean stress and the highest stress after buckling can be larger than 80%, preferably larger than 90% and more preferably larger than 95%. This means that the stress curve shows a plateaus, so the energy absorption is more efficient and less strain is needed to absorb an impact. For the same deceleration, a shorter stroke is obtained. This has applications for future vehicles which have a shorter front end crumple zone - useful for cars without a huge motor block in front. In a more specific embodiment, the specific energy absorption is from 8 to 11 kJ / kg with an equivalent specific stiffness of 2 GPa.g-1 .cm3 and a large range of effective stroke up to 75%. This has applications for traditional vehicles, which have a long crumple zone.

[0084] The specific modulus (https: / / en.wikipedia.org / wiki / Specific_modulus) or specific stiffness is the elastic modulus (or stiffness) per mass density of a material. Specific energy absorption is defined as the energy absorbed per unit mass of material, hence the unit kJ / kg. The post-impact stress ratio is the ratio between the mean stress and the highest stress after buckling.

[0085] In an embodiment sequential yield buckling is enabled at strain rates from 1 x 10'3s-1up to 150 s--1.

[0086] In an embodiment the metamaterial comprises three-dimensional unit cells wherein ligaments extend in three directions and contains at least one order of rotational and / or reflection symmetry.

[0087] A flat metamaterial may be converted into a three-dimensional shape, for instance by bending a flat metamaterial into a tube with a circular or other cross-section, or by stacking flat metamaterials together. However, this embodiment involves a real 3D structure wherein there are ligaments also outside of the 2D-plane of a flat metamaterial. This way a metamaterial can be produced that exhibits its unique structural properties, in three directions.

[0088] In an embodiment a shock absorber or load bearing part produced using the metamaterial is provided.

[0089] According to a second aspect a method of producing the metamaterial according to the invention is provided wherein

[0090] I . from an initially solid elastoplastic strip, sheet or tube, material is removed to produce a plurality of unit cells arranged in a periodic or non-periodic pattern, wherein the unit cells comprise rigid parts connected by ligaments that, when loaded, can act as plastic hinges during loading, the material being removed by means of one or more of the following techniques: a. milling b. cutting c. stamping d. water jet cutting e. laser cutting f. EDM g. Electrochemical machining h. Plasma machining, or ii. the metamaterial is produced by additive manufacturing to produce a plurality of unit cells, e.g., arranged in a periodic or non-periodic pattern, wherein the unit cells comprise rigid parts connected by ligaments that, when loaded, act as plastic hinges during loading, or iii. The metamaterial is produced by the lost wax method casting.

[0091] The metamaterial can be produced using conventional techniques as indicated above.

[0092] 3D metamaterials could be produced by additive manufacturing. In an embodiment initially solid elastoplastic strip, sheet or tube material is a metal, preferably steel, aluminium or an aluminium alloy.

[0093] Using the techniques referred to above, a solid strip, sheet or tube can be converted in a metamaterial by cutting out the holes and leaving the rigid parts and the plastic hinges.

[0094] In an embodiment the metamaterial is subsequently subjected to a shaping operation such as rolling, roll-forming or bending.

[0095] The flat 2D-metamaterial can be made into a quasi 3D-metamaterial by, for instance, roll-forming it into a tube shape and joining the edges together to form a closed tube.

[0096] In an embodiment the metamaterial is joined either to itself to form a tube or to another assembly using a mechanical, adhesive or welding joining method.

[0097] The concept of the present invention proved to work, which was demonstrated with uniaxial as well as multi-axial loading conditions. It also works at very high impact speeds (50 km / h), which are realistic impact conditions, and even when the direction of impact is not aligned with the structure. Also, deceleration of the impacted structure is less violent.

[0098] Brief description of the figures

[0099] The invention will now be explained by means of the following, non-limiting figures.

[0100] Figure 1 shows one of the simplest forms for a unit cell for a metamaterial. The two diamond shaped parts are the rigid parts and the connection between them is the ligament which acts as a plastic hinge upon buckling. The connections at the top and bottom are also ligaments which serve as plastic hinges. The ratios between the dimensions of the centre ligament and the dimensions of the top and bottom ligament will affect the region in which yield buckling can take place.

[0101] The width t of the ligament in Figure 1 a is a relevant parameter for determining whether the ligament will be subjected to elastic buckling (Figure 2a), plastic buckling (Figure 2b) or the desired yielding buckling (figure 2c). The buckling mode determines the critical force (Fcr) and it also determines whether the material after buckling shows a positive stiffness S>0 (the force for further deformation increases) or a negative stiffness S<0. Note that the ratio of u / l is the compressing strain since u is the displacement and I is the unit length.

[0102] The length I in Figure 1 also is a relevant parameter because together with the width, t, it determines the ratio of t / l which forms an important part of the design criteria and which buckling mode applies. Figure 3 shows the three regions (i, ii and iii) of figure 2, as well as the equation to determine Fr.

[0103] Figure 4 shows an application of the unit cell of figure 1 in a metamaterial structure. There are 4 rows of unit cells (line modes) on top of each other each containing 4 unit cells side by side. Figures b-e shows what happens during loading. One line mode shows yield bucking (b) and collapses until the rigid parts abut (c). Upon further loading subsequent line modes collapse. As long as there are undeformed line modes present, the residual stiffness will not compromise the structural integrity of the assembly of which it is a part. It should be noted that the direction to which the plastic hinges deform is random based on local instabilities and the direction is unimportant to the result.

[0104] Figure 5a shows a unit cell that comprises not only vertical ligaments (with width t), but also horizontal ligaments (*). Figure 5b shows the deformation of this cell during compressive loading.

[0105] Figure 6 shows a cylinder made using the unit cell of figure 5a and its force displacement curve that clearly shows the sequential buckling where the maximum force shows a plateau where the forces level off and only after using the full buckling potential the force increases. The shape and function of the part stays intact as shown by the force displacement curve and figure b. The inventors found that the structure can absorb impact loads at an angle up to 10° to the longitudinal axis of the structure.

[0106] Figure 7a shows the application of the concept in a 3D shape. Figure 7b shows the deformation after a compression in the z direction. When the compression is in the y or x direction the results are the same (not shown).

[0107] Figure 8 shows a cylinder with a diameter of 144 mm based on the unit cell of figure 5a in the undeformed state (a), the onset of yield buckling (b) and at nearly full rotation of the ligaments. This metamaterial was produced by cutting the openings in a steel tube by milling.

[0108] Figure 9 shows a schematic representation of a method that can be used to produce metamaterials from a strip by punching the openings.

[0109] Figure 10 shows the stress distribution across the ligament at buckling (dashed line) and in post-buckling (solid line) showing higher stress on the tensile side (negative stress) than the compressive side (positive stress). Note the convention of defining compressive stresses and strains as being positive.

[0110] Figure 11 shows the buckling load during the sequential yield buckling of metamaterials (a) without and (b) with additional ligaments not in loading path.

[0111] Figure 12 shows an alterative embodiment of a crash can 1 of a metamaterial 2, made of an elastoplastic material, such as steel. The crash can 1 is shown in a perspective cross section in Figure 13, while Figure 14 shows a unit cell 3 in cross section. The metamaterial 3 comprises a tubular stack of annular unit cells 3 comprising annular rigid parts or flanges 4A, 4B connected by annular ligaments 5 that hinge plastically when loaded by a critical buckling load. In the shown embodiment the tubular stack of the crash can 1 is cylindrical but alternative outlines can also be used. The metamaterial 2 is able to absorb shocks and impact loads through sequential yield buckling by the respective unit cells 3, thereby enabling a progressive and controlled collapse of the crash can 1 . Each flange 4 is part of two adjacent unit cells 3, except the flanges 4A, 4B at the outer ends of the tubular stack. In the shown embodiment, the flanges 4 are stiffened by two concentric ribs 6A, 6B having a length that is twice the thickness t of the ligaments. The radial distance between the two concentric ribs 6A, 6B is equal to the length I of the ligament, i.e. the distance between two adjacent flanges 4.

[0112] The metamaterial has the following slenderness ratio:

[0113] The geometry of the metamaterial, should be such that: with Er being the reduced modulus calculated with Et being the tangent modulus at 0,2 % strain and the yield strength oybeing the stress at 0,2 % strain, 00,2. In that case, the ligaments hinge by buckling in response to a critical buckling load Fcr.. The combination of slenderness ratio, cross section, elastic modulus E and tangent modulus Et, cause yield buckling in response to the critical buckling load Fcrwith an asymmetric stress distribution across the ligament with a compressed side of the ligament undergoing plastic loading with a tangent modulus Et, and a tensile side of the ligament undergoing elastic unloading with an elastic modulus E > Et, as shown in Figure 10. As a result, the ligaments buckle sequentially.

[0114] With this embodiment, the specific energy absorption was found to be in the range of 8 to 11 kJ / kg with an equivalent specific stiffness of 2 GPa.g-1 .cm3 and a large range of effective stroke up to 75%..

Claims

CLAIMS1 . Metamaterial for load-bearing and shock absorbing applications wherein the metamaterial is made of an elastoplastic material and wherein the metamaterial comprises a plurality of unit cells, wherein the unit cells comprise rigid parts connected by ligaments that act as plastic hinges during loading, and wherein the metamaterial is able to absorb shocks / deformation through sequential yield buckling of the unit cells thereby enabling a progressive and controlled collapse of the metamaterial.

2. Metamaterial according to claim 1 wherein the ligaments hinge in response to a critical buckling load Fcr, the ligaments having a cross section, an elastic modulus E and a tangent modulus Et, causing yield buckling in response to the critical buckling load Fcrwith an asymmetric stress distribution across the ligament with a compressed side of the ligament undergoing plastic loading with a tangent modulus Et, and a tensile side of the ligament undergoing elastic unloading with an elastic modulus E > Et.

3. Metamaterial according to claim 1 or 2, comprising repeating unit cells which are arranged in a geometric pattern that leads to a sequential collapse mechanism when loaded.

4. Metamaterial according to claim 1 , 2 or 3, wherein the rigid parts that are connected by the ligaments rotate as a result of the plastic deformation of the plastic hinges when loaded.

5. Metamaterial according to any one of the claims 1 to 4 wherein yield buckling leads to negative post-buckling stiffness which enables the collapse of the material to occur in sequence when the material is loaded.

6. Metamaterial according to any one of the preceding claims wherein at least part of the unit cells have a slenderness ratio A in accordance with the following formula:wherein E is the elastic modulus, Er is the reduced modulus, and oy is the yield strength.

7. Metamaterial according to claim 6, wherein the unit cells have two of said rigid parts, both rigid parts being square having a diagonal in line with the ligament, the unit cells having a length I, the ligaments having a length h, a width t and a thickness b > t, and wherein A = t2 / 2hl.

8. Metamaterial according to claim 6 or 7, wherein yield buckling occurs when the critical buckling load of the unit cell Fcr, is constrained by the following inequality:Fr < Fcr Fi where Fris the reduced-modulus load of the unit cell, and Feis the elastic buckling load of the unit cell, and wherein the ligament in the unit cells is parallel to the loading direction, whereinFr= ErAA andFe= EAA with A being the cross sectional area of the ligament and A being the slenderness ratio.

9. Meta mate ria I according to claim 8, wherein, the ligaments have a width t, a height h and a thickness b, and the unit cells have a length I, and whereinandF =Ebt3e~ 2hl10. Metamaterial according to any one of the preceding claims wherein the unit cells also comprise stabilising ligaments that are not in the loading path.

11. Metamaterial according to any one of the preceding claims wherein the specific stiffness or specific modulus is at least 2 GPa. g-1. cm3, a specific energy absorption above 5 kJ / kg and / or wherein the post-impact stress ratio between the mean stress and the highest stress after buckling is larger than 80%, preferably larger than 90% and more preferably larger than 95% and / or wherein the effective compressive strokes can be tuned from 20% to 75%.

12. Metamaterial according to claim 11 , wherein the specific energy absorption is from 8 to 11 kJ / kg with an equivalent specific stiffness of 2 GPa. g-1. cm3.

13. Metamaterial according to any one of the preceding claims wherein sequential yield buckling is enabled at strain rates from 1 x 10'3s-1up to 150 s-’1.

14. Metamaterial according to any one of the preceding claims wherein the unit cells are three- dimensional, and wherein ligaments extend in three directions and contain at least one order of rotational and / or reflection symmetry.

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

16. Metamaterial according to any one of the preceding claims, comprising a tubular stack of annular unit cells.

17. Metamaterial according to claim 16, wherein the unit cells comprise rigid parts or flanges connected by annular ligaments.

18. Metamaterial according to claim 17, having a slenderness ratio of19. Shock absorber or load bearing part produced using the metamaterial of any one of claims 1 to 18.

20. Method of producing the metamaterial according to any one of claims 1 to 18 wherein: i. from an initially solid elastoplastic strip, sheet or tube material is removed to produce a plurality of unit cells arranged in a periodic or non-periodic pattern, wherein the unit cells comprise rigid parts connected by ligaments that can act as plastic hinges during loading by means of one or more of the following techniques: a. milling b. cutting c. stamping d. water jet cutting e. laser cutting f. EDM g. Electrochemical machining h. Plasma machining, or ii. the metamaterial is produced by additive manufacturing to produce a plurality of unit cells arranged in a periodic or non-periodic pattern, wherein the unit cells comprise rigid parts connected by ligaments that, when loaded, can act as plastic hinges during loading by means of one or more of the following techniques, or iii. The metamaterial is produced by the lost wax method casting.

21. Method according to claim 20, wherein the initially solid elastoplastic strip, sheet or tube material is a metal, preferably steel, aluminium or an aluminium alloy.

22. Method according to claim 20 or 21, wherein the metamaterial is subsequently subjected to a shaping operation such as rolling, roll-forming or bending.

23. Method according to any one of claims 20 to 22 wherein the metamaterial is joined either to itself to form a tube or to another assembly using mechanical, adhesive or welding joining method.

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