Continuum theory for mechanical metamaterials with a cubic lattice substructure

IF 1 Q4 MECHANICS

Mathematics and Mechanics of Complex Systems Pub Date : 2019-04-22 DOI:10.2140/MEMOCS.2019.7.75

S. Eugster, F. dell’Isola, D. Steigmann

引用次数: 66

Abstract

A three-dimensional continuum theory for fibrous mechanical metamaterials is proposed, in which the fibers are assumed to be spatial Kirchhoff rods whose mechanical response is controlled by a deformation field and a rotation field, the former accounting for strain of the rod and the latter for flexure and twist of the rod as it deforms. This leads naturally to a model based on Cosserat elasticity. Rigidity constraints are introduced that effectively reduce the model to a variant of second-gradient elasticity theory.

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具有立方晶格子结构的机械超材料的连续统理论

提出了纤维力学超材料的三维连续介质理论，将纤维视为空间基尔霍夫棒，其力学响应由变形场和旋转场控制，变形场负责杆的应变，旋转场负责杆变形时的挠曲和扭转。这自然导致了基于Cosserat弹性的模型。引入刚性约束，有效地将模型简化为二次梯度弹性理论的一种变体。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematics and Mechanics of Complex Systems MECHANICS-

CiteScore

3.00

自引率

5.30%

发文量

期刊介绍： MEMOCS is a publication of the International Research Center for the Mathematics and Mechanics of Complex Systems. It publishes articles from diverse scientific fields with a specific emphasis on mechanics. Articles must rely on the application or development of rigorous mathematical methods. The journal intends to foster a multidisciplinary approach to knowledge firmly based on mathematical foundations. It will serve as a forum where scientists from different disciplines meet to share a common, rational vision of science and technology. It intends to support and divulge research whose primary goal is to develop mathematical methods and tools for the study of complexity. The journal will also foster and publish original research in related areas of mathematics of proven applicability, such as variational methods, numerical methods, and optimization techniques. Besides their intrinsic interest, such treatments can become heuristic and epistemological tools for further investigations, and provide methods for deriving predictions from postulated theories. Papers focusing on and clarifying aspects of the history of mathematics and science are also welcome. All methodologies and points of view, if rigorously applied, will be considered.