Gourgiotis Panos A, Bigoni Davide
School of Engineering and Computing Sciences, Durham University, South Road, Durham DH1 3LE, UK.
DICAM, University of Trento, via Mesiano 77, 38123 Trento, Italy
Philos Trans A Math Phys Eng Sci. 2017 May 13;375(2093). doi: 10.1098/rsta.2016.0159.
Different from Cauchy elastic materials, generalized continua, and in particular constrained Cosserat materials, can be designed to possess extreme (near a failure of ellipticity) orthotropy properties and in this way to model folding in a three-dimensional solid. Following this approach, folding, which is a narrow zone of highly localized bending, spontaneously emerges as a deformation pattern occurring in a strongly anisotropic solid. How this peculiar pattern interacts with wave propagation in the time-harmonic domain is revealed through the derivation of an antiplane, infinite-body Green's function, which opens the way to integral techniques for anisotropic constrained Cosserat continua. Viewed as a perturbing agent, the Green's function shows that folding, emerging near a steadily pulsating source in the limit of failure of ellipticity, is transformed into a disturbance with wavefronts parallel to the folding itself. The results of the presented study introduce the possibility of exploiting constrained Cosserat solids for propagating waves in materials displaying origami patterns of deformation.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'
与柯西弹性材料不同，广义连续体，特别是约束科塞尔材料，可以设计成具有极端（接近椭圆性失效）的正交各向异性特性，从而以这种方式对三维固体中的折叠进行建模。按照这种方法，折叠作为高度局部化弯曲的狭窄区域，会自发地作为一种出现在强各向异性固体中的变形模式而出现。通过推导一个反平面无限体格林函数，揭示了这种特殊模式在时谐域中与波传播的相互作用，这为各向异性约束科塞尔连续体的积分技术开辟了道路。格林函数被视为一种扰动因素，它表明在椭圆性失效极限下靠近稳定脉动源出现的折叠会转变为波前与折叠本身平行的扰动。本研究结果介绍了利用约束科塞尔固体在呈现折纸变形模式的材料中传播波的可能性。本文是主题为“复杂介质中通过不稳定性进行图案化：理论与应用”的特刊的一部分。
