Non-affinity in multi-material mechanical metamaterials

Abstract

Non-affine deformations enable mechanical metamaterials to achieve their unusual properties while imposing implications for their structural integrity. The presence of multiple phases with different mechanical properties results in additional non-affinity of the deformations, a phenomenon that has never been studied before in the area of extremal mechanical metamaterials. Here, we studied the degree of non-affinity, Ŵ , resulting from the random substitution of a fraction of the struts,ρ h , that make up a lattice structure and are printed using a soft material (elastic modulus = E s) by those printed using a hard material (E h). Depending on the unit cell angle (i.e., θ = 60°, 90°, or 120°), the lattice structures exhibited negative, near-zero, or positive values of the Poisson's ratio, respectively. We found that the auxetic structures exhibit the highest levels of non-affinity, followed by the structures with positive and near-zero values of the Poisson's ratio. We also observed an increase in Ŵ with E h E s and ρ h until E h E s =10 4 and ρ h = 75%-90% after which Ŵ saturated. The dependency of Ŵ upon ρ h was therefore found to be highly asymmetric. The positive and negative values of the Poisson's ratio were strongly correlated with Ŵ. Interestingly, achieving extremely high or extremely low values of the Poisson's ratio required highly affine deformations. In conclusion, our results clearly show the importance of considering non-affinity when trying to achieve a specific set of mechanical properties and underscore the structural integrity implications in multi-material mechanical metamaterials. A simple mechanical load (e.g., uniaxial compression, tension, or shear) applied to a geometrically simple (e.g., square-shaped) piece of what is traditionally considered a material (e.g., metals, polymers) leads to a simple deformation that is highly predictable at large enough length scales and is homogeneously distributed within the material. Such a homogenous deformation is formally called an 'affine' deformation and can be fully described using an affine transformation (i.e., a linear transformation plus a rigid body translation) applied to the coordinates of the points constituting the material 1,2. All this simplicity, predictability, and homogeneity may be lost when a simple mechanical load is applied to an architected material. Architected materials 3 , which are sometimes referred to as mechanical metamaterials 4-6 , possess complex small-scale geometries that are engineered to give rise to unusual mechanical properties at the macroscale. In a way, the whole point of rationally designing 7 the small-scale geometry of architected materials, may be to break the affinity of the deformations in an exact way so as to achieve unusual macroscale properties. Non-affine deformations can, for example, be exploited to achieve negative values of the Poisson's ratio 8,9 , action-at-a-distance actuation behaviors 10 , and independent tailoring of the elastic properties 11. Some other functionalities of mechanical metamat...

Analysis of additively manufactured (3D printed) dual-material auxetic structures under compression

“…The use of multiple materials in auxetic structures is an area receiving attention [25][26][27][28][29][30][31]. Wang et al…”

“…[25] designed a collection of dual-material auxetic materials and they investigated the influence of design parameters on auxeticity and equivalent Young's modulus. Mirzaali et al [26,27] showed that a multi-material design could lead a wide range of elastic properties. Su et al [28] investigated a unique dual-material auxetic structure with reinforcement arches which increase the structure stiffness significantly.…”

Energy Absorption and Mechanical Performance of Functionally Graded Soft–Hard Lattice Structures

“…Mechanical meta-materials demonstrate unprecedented mechanical properties that directly originate in their geometrical designs at different scales, in particular, small scales that are engineered to achieve unusual properties at the bulk (or macroscale) [ 1 , 2 , 3 ]. Some of these unique dimensionless properties are multi-stability [ 4 , 5 ], zero shear modulus [ 6 ], variable softening/hardening [ 7 ], snapping deformations [ 8 ] and a negative Poisson’s ratio (auxetics) [ 5 , 9 ].…”

“…Some of these unique dimensionless properties are multi-stability [ 4 , 5 ], zero shear modulus [ 6 ], variable softening/hardening [ 7 ], snapping deformations [ 8 ] and a negative Poisson’s ratio (auxetics) [ 5 , 9 ]. It has been recently shown that the elastic stiffness and Poisson’s ratio of mechanical meta-materials can independently be tailored by rational design of not only the microarchitecture but also introducing bi-materials (i.e., hard and soft) [ 1 ]. Therefore, material properties of the solid constituent of meta-materials can also add a new level of design freedom in the design process of meta-materials.…”

“…From the design point of view, there are various architectures with different cell topology such as auxetic and honeycomb, which already are being used in the literature [ 1 , 15 , 28 , 29 , 30 , 31 , 32 , 33 ]. Among them, honeycomb cells are the most common topology used to study the quasi-static and dynamic behavior of such structures [ 34 , 35 , 36 ].…”