Poisson's ratio bounds in orthotropic materials. Application to natural composites: wood, bamboo and Arundo donax

The paper discusses the restrictions the positive definite character of the strain energy imposes to the values of the Poisson's ratios in a linear elastic orthotropic constitutive law. By exploiting the reciprocity principle and the conservation of energy, non-trivial constraints arise, leading to a particularly expressive form of the domain of existence, named Tetrahedron-Ellipsoid locus, in the space of three independent Poisson's ratios.