Abstract
The present paper is dedicated to an evaluation of novel cellular metamaterials based on a tensegrity pattern. The materials are constructed from supercells, each of which consists of a number of simplex modules with different geometrical proportions. Mechanical properties of the metamaterial can be controlled by adjusting the level of self-equilibrated forces or by changing the properties of structural members. A continuum model based on the equivalence of strain energy of the 3D theory of elasticity with a discrete formulation is used to identify the qualitative properties of the considered metamaterials. The model allows the inclusion of nonlinearities related to the equations of equilibrium in actual configuration of the structure with self-equilibrated set of normal forces typical for tensegrities. The lattices are recognised as extreme metamaterials according to the eigensolution of the equivalent elasticity matrices of the continuum model. The six representative deformation modes are defined and discussed: stiff, soft and medium extensional modes and high (double) as well as low shear modes. The lattices are identified as unimode or nearly bimode according to the classification of extreme materials.
Highlights
Identification of unusual mechanical properties of tensegrity structures is one of the interesting challenges of exploring the mechanics of engineering metamaterials
The lattices are identified as unimode or nearly bimode according to the classification of extreme materials
Metamaterials are usually defined as man-made composites that do not exist in nature and have atypical or unusual properties [1,2]
Summary
Identification of unusual mechanical properties of tensegrity structures is one of the interesting challenges of exploring the mechanics of engineering metamaterials. Tensegrities exhibit some special features, which are a result of the occurrence of infinitesimal mechanisms that are stabilized by the system of normal forces in self-equilibrium One can control their static and dynamic characteristics with an adjustment of the pre-stressing forces [13,14]. Smart properties as well as a negative Poisson’s ratio were observed in reference [28] for the orthotropic metamaterial based on the simplex tensegrity pattern. The study of extreme properties of materials is based on the analysis of elasticity tensor As is known, it must be positive definite and in the theory of elasticity it shows certain types of symmetries. Its extreme characteristics can be controlled with the self-stress state and cable to strut properties ratio, following the features of smart metamaterials. According to the best knowledge of the authors there are no papers in this field in the available literature
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