Abstract
The study focuses on the identification of extreme mechanical properties of 3D lattice metamaterials based on regular tensegrity modules: 4-strut simplex, 3-strut simplex, expanded octahedron, truncated tetrahedron and X-module. The basis of the analysis is a continuum model which is used to find the equivalent elasticity matrices of the unit cells. For each examined tensegrity module a line of extreme properties is determined, which indicates the occurrence of the soft mode of deformation. Moreover, the eigenvectors corresponding to soft and stiff deformation modes are calculated and presented graphically. The obtained results are promising from the point of view of future creation of tensegrity lattices and metamaterials with extreme mechanical properties. One of the analysed materials is identified as quasi bimode, two as quasi trimodes, another one as a trimode and one more as a unimode.
Highlights
The idea of extreme materials was developed in 1995 by Milton and Cherkayev [1]
The continuum model proposed in [20] and analysed in [21] is based on the equivalence of the strain energy of an unsupported tensegrity structure defined with the use of the finite element method (FEM) [23,24,25,26] and the strain energy of a solid determined using the symmetric linear 3D elasticity theory (LTE) [27]
The main focus of the present paper is put on the identification of extreme mechanical properties of five regular tensegrity modules
Summary
The idea of extreme materials was developed in 1995 by Milton and Cherkayev [1]. The term extreme implies that the material is extremely stiff under certain stresses or extremely compliant in other orthogonal cases of stresses. The original results presented in this paper, which include determination of the parameters that assure occurrence of extreme properties and identification of stiff and soft modes, are based on the previously published results [21] on the continuum description of tensegrity modules. The applied continuum model can be used for the analysis of both tensegrity unit cells and lattice structures or materials composed of these cells As it is proved of this paper, under certain assumptions (compliance of infinitesimal mechanisms) the properties of the cellular metamaterial are the same as the properties of its single cell. In order to identify extreme mechanical properties of 3D lattice metamaterials, the author examines single tensegrity modules that can be applied as unit cells in mechanical metamaterials. As the results obtained for single modules correspond to the properties of materials constructed from them, the conclusions can be drawn in regard to whole lattice metamaterials
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