On the anisotropic and negative thermal expansion from dual-material re-entrant-type cellular metamaterials

Negative thermal expansion (NTE) and negative Poisson's ratio (NPR) are counterintuitive material properties that have gained popularity as the focus of many recent works. However, most of the structures previously studied only exhibit NTE or NPR exclusively. One important structure that has already been shown to exhibit NPR is the re-entrant triangle. In this work, the property of NTE in re-entrant triangular cellular structure composed of welded/bonded/brazed ribs of two different materials is investigated via analytical and finite element (FE) modelling. Based on analytical and FE analysis, the geometrical and material parameters for attaining NTE in the re-entrant metamaterial are established. The analysis and simulations reveal the dependence of NTE on the inclination of the longer chevron strut, the dimensionless rod coefficient of thermal expansion (CTE), the ratio of thermal expansion coefficients of constituent struts but independent of scale and temperature. The extent of this property becomes more negative for higher values of the angle of the longer chevron strut with the vertical, higher ratios of CTE of the base to chevron strut material and for lower values of the non-dimensional re-entrant base material thermal expansion coefficient. The anisotropic and NTE behaviour is stretch-dominated. Effectively, combined with previous knowledge of NPR in the re-entrant triangle, NTE leads to further significance of such structures for many thermal and mechanical applications, such as composite materials, sensors and electronic components industries in both thermal and mechanical applications.