2021/11/11 by Michele Brun, Brun, Michele, Sébastien Guenneau +1
Engineering · Materials Science · #Advanced Antenna and Metasurface Technologies #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Metamaterials and Metasurfaces Applications #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.2111.06424
openalex publication_date 2021/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyse the elastic properties of a class of cylindrical cloaks deduced\nfrom linear geometric transforms bf x \→ bf x' in the framework of the\nMilton-Briane- Willis cloaking theory [New Journal of Physics 8, 248, 2006].\nMore precisely, we assume that the mapping between displacement fields bfν( bf x) \→ bf u'( bf x') is such that bf u'( bf x') = bf\nA-t bf u( bf x), where bf A is either the transformation gradient\nFij = \∂ x'i/ \∂ xj or the second order identity tensor\n bf I. The nature of the cloaks under review can be three-fold: some of\nthem are neutral for a source located a couple of wavelengths away; other lead\nto either a mirage effect or a field confinement when the source is located\ninside the concealment region or within their coated region (some act as\nelastic concentrators squeezing the wavelength of a pressure or shear polarized\nincident plane wave in their core); a last category of cloaks is classified as\nan elastic counterpart of electromagnetic perfect cylindrical lenses. The\nformer two categories require either rank-4 elastic tensor and rank-2 density\ntensor and additional rank-3 and 2 positive definite tensors ( bf A = bf\nF) or a rank 4 elasticity tensor and a scalar density ( bf A = bf I)\nwith spatially varying positive values. However, the latter example further\nrequires that all rank-4, 3 and 2 tensors be negative definite ( bf A = bf\nF) or that the elasticity tensor be negative definite (and non fully\nsymmetric) as well as a negative scalar density ( bf A = bf I). We\nprovide some illustrative numerical examples with the Finite Element package\nComsol Multiphysics when bf A is the identity.\n