Partially Auxetic Structure of Rotating Rectangles

The subject of the analysis is a modified auxetic structure in the form of rotating rectangles, which exhibit large negative Poisson’s ratio values. The structure modification consisted of introducing rotational axes on the surfaces of structural units near the corners of the rectangles. Such a system had previously unknown relationships between Poisson’s coefficient and parameters in the form of the quotient of the lengths of the sides of the rectangle, the position of the axis of rotation, and the degree of opening of the structure. Poisson’s coefficient is always −1 for square units, while it takes numerical values in a wide range of negative and positive values for rectangular units. Based on geometric relationships, formulas were determined to calculate the linear size of the structure and the values of Poisson’s ratio. It is shown that depending on the quotient of the lengths of the sides of the rectangle, the structures can lose their auxetic properties. For elongated rectangles (structures with a/b = 2.5), extremely high negative values of Poisson’s ratio are obtained but only for small changes in linear dimensions, and with greater stretching, the structure loses auxetic properties. Such a tendency occurs for a large group of structures of systems composed of rotating rectangles. The physical structures built provide an experimental complement to the research conducted.