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. The presented analysis establishes several notable restrictions for the elastic behavior of orthotropic composite materials, in all the cases in which there are great differences in the Young's moduli. For instance, near the edge of this locus, some Poisson ratios may belong to an interval not including the zero value; a very interesting peculiarity, perhaps not yet figured out in literature. In order to assess the coerciveness of the formulation, the results are applied to common wood essences, to several Italian growing species of bamboo and Arundo donax, natural composite functionally graded orthotropic materials. In the latter cases, an extensive experimental investigation is carried out to detect several Poisson's ratios, not studied in literature. Poisson ratios are obtained directly by strains measured by means of both physical strain gauges and Digital Image Correlation (DIC).