A series of auxetic metamaterials with negative thermal expansion based on L-shaped microstructures

Abstract

Mechanical metamaterials are facing various multi-functional requirements. In this study, a series of auxetic metamaterials with enhanced negative thermal expansion and improved stiffness are proposed. These metamaterials consist of four novel L-shaped microstructures connected in various clockwise or counterclockwise directions. Two length ratios and four angle parameters are utilized to define the geometry of these metamaterials. Both analytical analysis and validated numerical homogenization methods are employed to determine their effective thermoelastic properties, including effective Young's modulus, Poisson's ratio, and coefficient of thermal expansion. It is demonstrated that tailoring these microstructural geometries can modulate the effective thermoelastic properties of these metamaterials accordingly. By appropriately tailoring the geometric parameters, these metamaterials exhibit increased effective stiffness as well as more pronounced auxeticity and negative thermal expansion compared to traditional triangle and trapezoid microstructures. Notably, the in-plane effective anisotropic or isotropic Poisson's ratio and coefficient of thermal expansion can be adjustable over a broader range from negative to positive values. High stiffness, High strength, and near-zero thermal expansion can be achieved concurrently in these metamaterials, which is very conducive for structural designing in thermal environments. These metamaterials with a coupled design of stiffness, thermal expansion, and Poisson's ratio hold significant potential for advancing applications in satellite platforms, space structures, composite sandwiches, and precision equipment.