A New Metamaterial Plate With Tunable Thermal Expansion

Homogeneous materials typically expand when heated, leading to dimensional changes and often significant thermal stresses in structures subject to temperature variations. Microstructured periodic materials, also called metamaterials, offer a promising solution for achieving zero, negative, and in general tunable equivalent thermal expansion which is needed to mitigate unwanted mechanical effects of temperature changes. To obtain zero or negative equivalent thermal expansion coefficient at least two different materials must be combined and typically the unit cell is designed in two dimensions, with different parts made of the two constituent materials, and then it is extruded in the out-of-plane direction. In this work, we propose a novel geometry, with a non-symmetric layered unit cell, that is fully compatible with fabrication processes employed for micro-electro-mechanical systems. Parametric studies show that a proper design of the unit cell allows to achieve the desired coefficient of thermal expansion and to tune (or even cancel) the global thermal-induced deflection due to the asymmetrical layers configuration in the metamaterial plate.