Auxetics and FEA: Modern Materials Driven by Modern Simulation Methods.

Auxetics are materials, metamaterials or structures which expand laterally in at least one cross-sectional plane when uniaxially stretched, that is, have a negative Poisson's ratio. Over these last decades, these systems have been studied through various methods, including simulations through finite elements analysis (FEA). This simulation tool is playing an increasingly significant role in the study of materials and structures as a result of the availability of more advanced and user-friendly commercially available software and higher computational power at more reachable costs. This review shows how, in the last three decades, FEA proved to be an essential key tool for studying auxetics, their properties, potential uses and applications. It focuses on the use of FEA in recent years for the design and optimisation of auxetic systems, for the simulation of how they behave when subjected to uniaxial stretching or compression, typically with a focus on identifying the deformation mechanism which leads to auxetic behaviour, and/or, for the simulation of their characteristics and behaviour under different circumstances such as impacts.

Micro-Scale Mechanical Metamaterial with a Controllable Transition in the Poisson's Ratio and Band Gap Formation.

The ability to significantly change the mechanical and wave propagation properties of a structure without rebuilding it is currently one of the main challenges in the field of mechanical metamaterials. This stems from the enormous appeal that such tunable behavior may offer from the perspective of applications ranging from biomedical to protective devices, particularly in the case of micro-scale systems. In this work, a novel micro-scale mechanical metamaterial is proposed that can undergo a transition from one type of configuration to another, with one configuration having a very negative Poisson's ratio, corresponding to strong auxeticity, and the other having a highly positive Poisson's ratio. The formation of phononic band gaps can also be controlled concurrently which can be very useful for the design of vibration dampers and sensors. Finally, it is experimentally shown that the reconfiguration process can be induced and controlled remotely through application of a magnetic field by using appropriately distributed magnetic inclusions.

3D Auxetic Metamaterials with Elastically-Stable Continuous Phase Transition.

In solid state physics, phase transitions can influence material functionality and alter their properties. In mechanical metamaterials, structural-phase transitions can be achieved through instability or buckling of certain structural elements. However, these fast transitions in one mechanical parameter typically affect significantly the remaining parameters, hence, limiting their applications. Here, this limitation is addressed by designing a novel 3D mechanical metamaterial that is capable of undergoing a phase transition from positive to negative Poisson's ratio under compression, without significant degradation of Young's modulus (i.e. the phase transition is elastically-stable). The metamaterial is fabricated by two-photon lithography at the micro-scale and its mechanical behavior is assessed experimentally. For another choice of structural parameters, it is then shown that the auxetic behavior of the considered 3D metamaterial class can be maintained over a wide range of applied compressive strain.

Micro-Scale Auxetic Hierarchical Mechanical Metamaterials for Shape Morphing.

Shape morphing and the possibility of having control over mechanical properties via designed deformations have attracted a lot of attention in the materials community and led to a variety of applications with an emphasis on the space industry. However, current materials normally do not allow to have a full control over the deformation pattern and often fail to replicate such behavior at low scales which is essential in flexible electronics. Thus, in this paper, novel 2D and 3D microscopic hierarchical mechanical metamaterials using mutually-competing substructures within the system that are capable of exhibiting a broad range of the highly unusual auxetic behavior are proposed. Using experiments (3D microprinted polymers) supported by computer simulations, it is shown that such ability can be controlled through geometric design parameters. Finally it is demonstrated that the considered structure can form a composite capable of shape morphing allowing it to deform to a predefined shape.

Controllable Hierarchical Mechanical Metamaterials Guided by the Hinge Design.

In this work, we use computer simulations (Molecular Dynamics) to analyse the behaviour of a specific auxetic hierarchical mechanical metamaterial composed of square-like elements. We show that, depending on the design of hinges connecting structural elements, the system can exhibit a controllable behaviour where different hierarchical levels can deform to the desired extent. We also show that the use of different hinges within the same structure can enhance the control over its deformation and mechanical properties, whose results can be applied to other mechanical metamaterials. In addition, we analyse the effect of the size of the system as well as the variation in the stiffness of its hinges on the range of the exhibited auxetic behaviour (negative Poisson's ratio). Finally, it is discussed that the concept presented in this work can be used amongst others in the design of highly efficient protective devices capable of adjusting their response to a specific application.

The Multidirectional Auxeticity and Negative Linear Compressibility of a 3D Mechanical Metamaterial.

In this work, through the use of a theoretical model, we analyse the potential of a specific three-dimensional mechanical metamaterial composed of arrowhead-like structural units to exhibit a negative Poisson's ratio for an arbitrary loading direction. Said analysis allows us to assess its suitability for use in applications where materials must be able to respond in a desired manner to a stimulus applied in multiple directions. As a result of our studies, we show that the analysed system is capable of exhibiting auxetic behaviour for a broad range of loading directions, with isotropic behaviour being shown in some planes. In addition to that, we show that there are also certain loading directions in which the system manifests negative linear compressibility. This enhances its versatility and suitability for a number of applications where materials exhibiting auxetic behaviour or negative linear compressibility are normally implemented.

Impact resistance of composite magnetic metamaterials.

In this work, through numerical studies, we show the possibility of designing composites in a form of magneto-mechanical metamaterials which are capable of exhibiting an enhanced impact resistance in comparison to their non-magnetic counterparts. We also show that it is possible to control the impact resistance of the system solely by means of the magnitude of the magnetic moment associated with magnetic inclusions inserted into the system as well as through the way how magnetic inclusions are distributed within the structure. The latter result is particularly interesting as in this work we show that through the appropriate distribution of magnetic inclusions it is possible to minimise the force that is being transferred to an object through the protective mechanical metamaterial. It is also suggested that the concept proposed in this work can be implemented in the case of already existing protective devices such as military-related protective devices and car bumpers in order to increase their efficiency.

On the dynamics and control of mechanical properties of hierarchical rotating rigid unit auxetics.

In this work, we investigate the deformation mechanism of auxetic hierarchical rotating square systems through a dynamics approach. We show how their deformation behaviour, hence their mechanical properties and final configuration for a given applied load, can be manipulated solely by altering the resistance to rotational motion of the hinges within the system. This provides enhanced tunability without necessarily changing the geometry of the system, a phenomenon which is not typically observed in other non-hierarchical unimode auxetic systems. This gives this hierarchical system increased versatility and tunability thus making it more amenable to be employed in practical application which may range from smart filtration to smart dressings.