Deformation mechanism of innovative 3D chiral metamaterials

www.nature.com/scientificreports OPEN Deformation mechanism of innovative 3D chiral metamaterials Wenwang Wu1,2, Dexing Qi1,2, Haitao Liao1,2, Guian Qian3, Luchao Geng4, Yinghao Niu1,2 & Jun Liang1,2 Received: 25 January 2018 Accepted: 31 July 2018 Published: xx xx xxxx Rational design of artificial microstructured metamaterials with advanced mechanical and physical properties that are not accessible in nature materials is very important. Making use of node rotation and ligament bending deformation features of chiral materials, two types of innovative 3D chiral metamaterials are proposed, namely chiral- chiral- antichiral and chiral- antichiral- antichiral metamaterials. In-situ compression and uniaxial tensile tests are performed for studying the mechanical properties and deformation mechanisms of these two types of 3D chiral metamaterials. Novel deformation mechanisms along different directions are explored and analyzed, such as: uniform spatial rotation deformation, tensile-shearing directed (compression-shearing directed), tensile-expansion directed (compression-shrinkage directed) deformation mechanisms of 3D chiral metamaterials, and competitions between different types of deformation mechanisms are discussed. The proposed 3D chiral metamaterials represents a series of metamaterials with robust microstructures design feasibilities. Rational design of artificial micro architected metamaterials with advanced mechanical and physical properties that are not accessible in nature materials is challenging and important. Artificially designed metamaterials are usually arranged in repeating patterns, at scales that are smaller than the wavelengths of the phenomena they influence. The smart properties of metamaterials origin from artificially designed structures at sub-wavelength scales, and can be tailored and tuned precisely with their architected shape, geometry, size, orientation and arrangements. The interactions between architected microstructures of metamaterials and electromagnetic, sound and optical waves will result in blocking, absorbing, enhancing, or bending of waves. It has been demonstrated that rationally designed metamaterials have promising multifunctional applications, such as ultralow mass densities and ultrastrong metamaterials1–5, sound and vibration attenuation metamaterials6,7, electromagnetic cloaking metamaterials8,9, negative thermal expansion metamaterials10,11, subwave length optical metamaterials12–15, etc. As a special type of mechanical metamaterials, auxetic metamaterials with negative Poisson ratio can expand its volume when stretched, and the concept of auxetic materials with negative Poisson ratio was firstly described by Love in 1944 for the first time16. Auxetic metamaterials exhibit enhanced mechanical properties over conventional materials, such as higher shearing modulus, increased indentation resistance, good absorption properties and higher fracture toughness. Auxetic materials can be applied for designing innovative multifunctional structures, such as: body armor, packing material, knee and elbow pads, robust shock absorbing material and sponge mops. According to the geometrical relations of auxetic unit cell, there are mainly three types of auxetic materials: reentrant materials, rigid square rotation materials and chiral structures17. Chiral structures stands for a series of structures which cannot be mapped onto its mirror image by rotations and translations alone18, and various types of chiral structures exist commonly in nature, such as: DNA, RNA, chiral carbon nanotube, twisting flower petals and stems, plant climbing tendrils and twisted leaves, chiral cellulose19–21. Besides these chiral materials in nature, various types of multifunctional artificial chiral metamaterials are designed and fabricated as well. Because of their lack of mirror symmetry, chiral metamaterials22,23 have recently enabled several remarkable phenomena, such as negative refractive index24, superchiral light25, and use as broadband circular polarizers26,27 or detectors28. 1 Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing, 100081, China. 2Beijing Key Laboratory of Lightweight Multi-functional Composite Materials and Structures, Beijing, 100081, China. 3Laboratory for Nuclear Materials, Paul Scherrer Institute, Villigen PSI, 5232, Switzerland. 4State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, 100871, China. Correspondence and requests for materials should be addressed to W.W. (email: ) or H.L. (email: ) or G.Q. (email: ) ScienTific REPOrts | (2018) 8:12575 | DOI:10.1038/s41598-018-30737-7 1 www.nature.com/scientificreports/ 3D chiral metamaterials No. Chiral-chiral-antichiral Chiral-antichiral-antichiral L(mm) d(mm) t(mm) Nx Ny Nz A 10 5 1 6 6 6 B 10 6 1.5 5 5 5 A 12 5 1 6 6 6 B 10 6 1.5 6 6 6 Table 1. Geometrical parameters for the two types of 3D chiral metamaterials samples (ligament length L; node width d; ligament thickness t; Number of nodes along x direction Nx; Number of nodes along y direction Ny; Number of nodes along z direction Nz). Figure 1. The x-y, y-z, z-x and stereo views of the architected 3D chiral matamaterials (a,b,c) and (d) chiralchiral- antichiral metamaterials; (e,f,g) and (h) chiral- antichiral- antichiral metamaterials. The mechanical properties of chiral structures can be investigated with different theoretical approaches, such as: strain energy homogenization method, internal external force equilibrium of unit cell, Cosserat (micro-polar) elasticity, etc29–34. In the classical theory of elasticity, the degrees of freedom are not included for describing the mechanical behaviors of microstructured solid where the microstructure characteristic length is comparable to the solid structure35. Due to the additional degrees of freedom allowed by internal microstructures, chiral Cosserat solids have different mechanical behaviors from solids with a center of symmetry35–37, The Cosserat (also called micropolar) elasticity theory of Eringen37 demonstrated robust efficiency and reliability in the modeling of materials with microstructures, such as: granular or fibrous materials, bone microstructure, or 3D lattice structures, etc. For example, based on the micropolar theory and tensor analysis, Liu et al.38 developed a continuum theory for describing the dilatation–rotation coupling and shear–rotation coupling deformation mechanism of 2D chiral lattice structures. Chen et al.39 proposed a micropolar continuum model for describing the constitutive relation for tetrachiral lattice structure, where 13 independent material constants are employed. Spadoni et al.40 proposed a micropolar continuum model for analyzing the in-plane properties of hexachiral structures, where deformable-ring node model are employed. Recently, Kang et al.41 exploited the buckling introduced mechanical instabilities in surfa (...truncated)