Design of two-dimensional extremal material based on truss lattices

Extremal materials with rank-deficient elastic tensor are classified by counting the soft deformation modes, while their elasticity is assigned by hard modes. To date, only pentamode materials with a single hard mode have been studied in depth, and a broader space of extremal materials is left almos...

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Bibliographic Details
Published in:Acta mechanica Sinica 2023-07, Vol.39 (7), Article 723044
Main Authors: Wang, Kun, Lv, Haiyu, Liu, Xiaoning, Zhang, Anfu, Hu, Gengkai
Format: Article
Language:English
Subjects:
Analytic functions
Classical and Continuum Physics
Computational Intelligence
Elastic deformation
Elasticity
Engineering
Engineering Fluid Dynamics
Lattice vibration
Lattices
Mathematical analysis
Research Paper
Singular value decomposition
Tensors
Theoretical and Applied Mechanics
Trusses
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Summary:Extremal materials with rank-deficient elastic tensor are classified by counting the soft deformation modes, while their elasticity is assigned by hard modes. To date, only pentamode materials with a single hard mode have been studied in depth, and a broader space of extremal materials is left almost unexplored. In this work, basic ingredients and design schemes aiming to more general extremal materials are studied based on truss lattices. To homogenize periodic lattices with nonaffine deformation induced by local mechanisms, we revisited the matrix formulation with singular value decomposition and derived the effective elastic tensor in compact form of Kelvin-like decomposition, with which we are able to outline the origin and design logic of extremal materials. The method is then applied to design two-dimensional extremal materials on demand of arbitrarily prescribed elasticity tensor. The unique static responses in two-dimensional unimode continua which is closely related to complex analytic functions are confirmed by our designed lattice material. The proposed method is also applicable for more general extremal materials in three-dimensional cases.
ISSN:0567-7718
1614-3116
DOI:10.1007/s10409-023-23044-x