Effective elastic moduli of a soft medium with hard polygonal inclusions and extremal behavior of effective Poisson's ratio
The authors study effective elastic moduli of a soft medium with hard polygonal inclusions. For that, they consider two-dimensional two-phase elastic composites consisting of a soft isotropic medium into which hard elastic inclusions have been placed, requiring that the inclusions are interconnected only at corner points. Denoting the ratio of soft and hard Young moduli of phases by \(\delta\), the authors show that the leading term in the asymptotic expansion as \(\delta\to 0\) for effective modulus can be calculated from a finite dimensional algebraic minimization problem. They explicitely solve this algebraic problem for several composites with either hexagonal or orthotropic symmetry. In particular, from the above constituents the authors construct an isotropic material with maximal positive Poisson ratio, as well as an orthotropic material with Poisson ratio less than \(-1\). They also recover, in a simple way, Miltons isotropic composite with Poisson ratio close to \(-1\). This work is quite interesting and may find several readers working in the are of composite materials.
two-dimensional two-phase elastic composites
finite dimensional algebraic minimization problem
scientific article; zbMATH DE number 829849
scientific article