Effect of variation of coefficient of thermal expansion on thermomechanical deformation of cylindrical in-plane auxetics based on re-entrant cells

Active development of mechanical metamaterials has currently led to the widespread application of auxetic structures in various applications with differing loading conditions. This research explores thermomechanical behaviour of novel in-plane cylindrical auxetic lattice structures by studying the correlation between their deformational characteristics and the coefficient of thermal expansion (CTE) of the material. Unlike traditional auxetic cylinders, the plane of auxeticity in the developed models is oriented perpendicular to the cylinder axis, which defines their specific behavior. To understand the behavior of auxetic lattices under combined thermal and mechanical loads, computational experiments were conducted based on the finite element method (FEM). Deformations of both rectangular and cylindrical lattice structures were investigated. The relationships between transverse deformation and CTE were obtained and compared. The influence of CTE on the structural Poisson's ratio of rectangular auxetic lattices was assessed, which is a key parameter characterizing the auxetic behavior of the structure under thermomechanical loading. The feasibility of modeling the mechanical behavior of auxetic cylinders using an orthotropic mechanical model with effective material properties was verified. The constants for defining such a material model were obtained by simulating a numerical experiment on tensile and shear testing of the rectangular auxetic lattices along coordinate axes. Using an example with artificial material properties, it was demonstrated that the predominant deformation mechanism, caused by the opposing effects of mechanical and thermal loads, can be controlled by selecting a material with an appropriate CTE. This allows for regulating the structural response to changes in temperature and mechanical load. Such results can be utilized for creating cylindrical auxetic lattice structures subjected to mechanical and thermal deformations in applications requiring controlled thermomechanical responses.