Homogenized mechanical properties of auxetic composite materials in finite-strain elasticity

Abstract

Careful microstructural design can result in materials with counterintuitive effective (macroscale) mechanical properties such as a negative Poisson's ratio, commonly referred to as auxetic behavior. One specific approach to achieving auxetic behavior is to elastically connect structural elements with rotational degrees of freedom to result in elastic structures that unfold under uniaxial loading in specific directions, thereby giving rise to bi-or triaxial expansion, i.e. auxetic behavior (transverse expansion under uniaxial extension). This concept has been applied successfully to elastically coupled two-dimensional rigid rotational elements (such as rotating rectangles and triangles) which exhibit a negative effective in-plane Poisson's ratio under uniaxial (ex)tension. Here, we adopt this fundamental design principle but take it to the next level by achieving auxetic behavior in finitely strained composites made of stiff inclusions in a hyperelastic matrix, and we study the resulting elastic properties under in-plane strain by numerical homogenization. Our results highlight the emergence of auxetic behavior based on geometric arrangement and properties of the base material and demonstrate a path towards simple inclusion-matrix composites with auxetic behavior.

Buckling and Vibration of Circular Auxetic Plates

“…Due to their counter-intuitive properties, auxetic materials have been investigated as smart materials for potential applications including cushion materials [9], stents [10,11], pressure vessels [12], sensors [13], morphing airfoils [14,15], smart folding structures [16], smart metamaterials [17], aeroengine fan blades [18], and vibration dampers [19], to name a few. Arising from their unique properties, the mechanical performance of auxetic solids has been investigated [20][21][22][23][24][25][26][27][28][29][30][31][32][33], including their elastic stabilities [34][35][36]. Additionally, investigations in the dynamic behavior of auxetic solids and structures have also been performed [37][38][39][40][41][42][43][44][45].…”

Orthotropic Laminated Open-cell Frameworks Retaining Strong Auxeticity under Large Uniaxial Loading

“…For example, an array of rotating rigid units can induce auxetic behavior, and this is one of the fundamental auxetic mechanisms according to some background on geometry3031323334353637. Many auxetic cellular and laminated composite solids can be designed from considerations of geometry and rotation3738394041424344.…”

Low Porosity Metallic Periodic Structures with Negative Poisson's Ratio

“…In particular, it has been shown that auxetic behavior can be achieved in a variety of highly porous materials [10], including foams with re-entrant [11][12][13][14][15] and chiral [16,17] microstructure, microporous polymeric materials [18], networks of rigid units [19] and skeletal structures [20]. Moreover, negative Poisson's ratio has also been shown in non-porous systems, such as laminates [21,22], sheets assemblies of carbon nanotubes [23], composites [24] and polycrystalline thin films [25].…”