A finite element analysis on the potential for negative thermal expansion and negative compressibility of triangular building blocks

Abstract

The thermal expansion and compressibility of a two dimensional basic unit in the form of a triangular system made up of three beams welded together were studied by a finite element method, where the base of the triangular construct has different properties (thermal expansion and Young’s moduli) than those of the sides. The results show that this triangular system is capable of exhibiting both negative thermal expansions in one dimension when the base of the triangle has a larger thermal expansion than that of the sides (as in the case of the triangular shortening effect, where the beams making up the triangles are pin-jointed together) and negative compressibility. More interestingly, the degree of linear thermal expansion is dependent on the relative stiffness (Young’s moduli) of the materials that make up the base and sides of the triangular construct. The effect of pressure change on such constructs is discussed and it show how the linear compressibility varies as a function of the rigidity of the base as compared to the rigidity of the sides.