Aspetti fisico-matematici dei Materiali Auxetici con Memoria di Forma

The Poisson coefficient, or Poisson’s Ratio, plays a fundamental role in the Continuum Mechanics theory, which represents the relationship between lateral contraction and longitudinal elongation of a material subjected to tensile stress; in almost all materials this coefficient, commonly indicated by the letter ! , has a positive value and very close to 1/3, for common materials used in construction, and to 1/2, for rubber materials. In auxetic materials this ratio takes on negative values, in fact the mentioned materials are often referred to by the acronym NPR (negative Poisson's ratio); this entails remarkable features such as high energy absorption capacity, fracture resistance, bending stiffness and shear strength and is due to the particular microscopic structure of the molecules. We will then see a modeling of these materials through the study of the fundamental cells that compose it and with different geometries of the microstructure (hexagonal chiral, rotation of polygons) which adequately describe the auxetic behavior. Moreover, from the study of the constitutive equations, we are faced with phenomena such as phase transitions and shape memory, which highlight further capacities of NPR materials; through the use of the fractional derivative a particular strain-strain relationship was analyzed, following by numerical simulations, which adequately reproduces what we call auxetic deformation. [edited by Author]