Simultaneously program thermal expansion and Poisson's ratio in three dimensional mechanical metamaterial

The engineering materials and structures, which usually suffer both temperature variation and mechanical loading, motivate the urgent need of the multifunctional metamaterials with simultaneously programmable coefficient of thermal expansion (CTE) and Poisson's ratio (PR). Whereas, the current 3D metamaterials can not continuously program the CTE and PR. Herein, a class of 3D metamaterial is originally devised by an exclusive geometrical methodology. The explicit expressions of the CTE and PR are theoretically established and are also verified by the numerical modeling. The analysis confirms that the CTE can be widely tailored by varying the geometrical parameters and selection of the constituents. Besides, the controllable PR can be also easily obtained by adjusting the geometrical parameters. Moreover, the devised 3D metamaterial gives paired tailorable CTE and controllable PR, including especially negative CTE + negative PR. An arrangement rule is developed to construct a series of hierarchical cells which can program CTE and PR in multi principle axes and can be periodically arrayed for obtaining the 3D cellular metamaterials. The devised 3D metamaterials are capable of realizing the widely coupled programmability of both CTE and PR and provide a strategy of shape morphing stimulated both by temperature variation and mechanical loading.