Auxeticity windows for composites

Materials with negative Poisson ratios are known to have high shear rigidities – a useful property for many types of structural and functional materials. To improve upon relatively low Young’s modulus of existing auxetics, one may consider embedding such components in an elastic material with sufficiently high modulus. We show theoretically that such composite materials do exhibit auxeticity when the inclusion volume fraction exceeds a critical value and the ratio of Young’s modulus of inclusion to that of a matrix falls within a definite interval. The existence of these auxeticity windows, once verified experimentally, opens up a new avenue of auxetics research.