Euler-Rodrigues and Cayley Formulae for Rotation of Elasticity Tensors

Norris, Andrew N.

doi:10.1177/1081286507077982

Cited by 24 publications

(14 citation statements)

References 22 publications

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“…Furthermore, the anisotropic Poisson response of materials were investigated through the calculation of the directional Poisson ratios, ν ij , determined from the coefficients of the Voigt compliance tensor (inverse of the elastic tensor), S , as: where the value for ν ij represents the ratio of deformation in the principal direction j to a uniaxial strain applied along the orthogonal principal direction i in the basis frame of the elastic tensor 26 . The global minimum and maximum directional Poisson’s ratios were found by rotating the original elastic tensor through the range of possible orientations via the Euler–Rodriguez and Cayley method and Euler angle rotations around the z , x ʹ, and z ʹʹ axes at a resolution of π /30 radians 49 .…”

Section: Methodsmentioning

confidence: 99%

Computational prediction of new auxetic materials

et al. 2017

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Auxetics comprise a rare family of materials that manifest negative Poisson’s ratio, which causes an expansion instead of contraction under tension. Most known homogeneously auxetic materials are porous foams or artificial macrostructures and there are few examples of inorganic materials that exhibit this behavior as polycrystalline solids. It is now possible to accelerate the discovery of materials with target properties, such as auxetics, using high-throughput computations, open databases, and efficient search algorithms. Candidates exhibiting features correlating with auxetic behavior were chosen from the set of more than 67 000 materials in the Materials Project database. Poisson’s ratios were derived from the calculated elastic tensor of each material in this reduced set of compounds. We report that this strategy results in the prediction of three previously unidentified homogeneously auxetic materials as well as a number of compounds with a near-zero homogeneous Poisson’s ratio, which are here denoted “anepirretic materials”.

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Section: Methodsmentioning

confidence: 99%

Computational prediction of new auxetic materials

et al. 2017

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“…where Q is any symmetric, invertible and divergence free (div Q = 0) second order tensor. The increased degrees of freedom afforded by the arbitrary nature of Q means that (21) is equivalent to the generalized scalar wave equation…”

Section: Pentamode Materialsmentioning

confidence: 99%

Acoustic metafluids

Norris

2009

The Journal of the Acoustical Society of America

194

109

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Acoustic metafluids are defined as the class of fluids that allow one domain of fluid to acoustically mimic another, as exemplified by acoustic cloaks. It is shown that the most general class of acoustic metafluids are materials with anisotropic inertia and the elastic properties of what are known as pentamode materials. The derivation uses the notion of finite deformation to define the transformation of one region to another. The main result is found by considering energy density in the original and transformed regions. Properties of acoustic metafluids are discussed, and general conditions are found which ensure that the mapped fluid has isotropic inertia, which potentially opens up the possibility of achieving broadband cloaking.

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“…The origin of the coordinate system is set at a point on the body which may not coincide with the center of gravity of the model. The image data from the reflective balls is transformed from the body coordinate system to the inertial coordinate system [25].…”

Section: Data Acquisition and Processingmentioning

confidence: 99%

Aerodynamic Analysis of a Flapping Wing Aircraft for Short Landing

Zhu

Guo

et al. 2020

Applied Sciences

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An investigation into the aerodynamic characteristics has been presented for a bio-inspired flapping wing aircraft. Firstly, a mechanism has been developed to transform the usual rotation powered by a motor to a combined flapping and pitching motion of the flapping wing. Secondly, an experimental model of the flapping wing aircraft has been built and tested to measure the motion and aerodynamic forces produced by the flapping wing. Thirdly, aerodynamic analysis is carried out based on the measured motion of the flapping wing model using an unsteady aerodynamic model (UAM) and validated by a computational fluid dynamics (CFD) method. The difference of the average lift force between the UAM and CFD method is 1.3%, and the difference between the UAM and experimental results is 18%. In addition, a parametric study is carried out by employing the UAM method to analyze the effect of variations of the pitching angle on the aerodynamic lift and drag forces. According to the study, the pitching amplitude for maximum lift is in the range of 60°~70° as the flight velocity decreases from 5 m/s to 1 m/s during landing.

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Euler-Rodrigues and Cayley Formulae for Rotation of Elasticity Tensors

Cited by 24 publications

References 22 publications

Computational prediction of new auxetic materials

Computational prediction of new auxetic materials

Acoustic metafluids

Aerodynamic Analysis of a Flapping Wing Aircraft for Short Landing

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