Modeling deformation of auxetic and non-auxetic polymer gels

Abstract

• The responsive-behavior of auxetic and non-auxetic polymer gels to mechanical loads is modeled. • Elastic deformation patterns of gels with different structural and mechanical properties are depicted. • The first strain gradient theory is employed. • Equilibrium equations of polymer gels under finite strain gradient and infinitesimal strain gradient regimes are derived. • Effects of Poisson's ratio and strain gradient on plane strain deformation of gels are analytically investigated. In this study, the responsive-behavior of auxetic and non-auxetic polymer gels to mechanical loads is modeled. The elastic deformation patterns of gels with different structural and mechanical properties are depicted. The first strain gradient theory is employed to model the random structure of crosslinked polymer gels. The applicability of the first strain gradient theory to model the mechanics of polymer gels is demonstrated. The equations governing the elastostatic equilibrium of polymer gels under finite strain gradient and infinitesimal strain gradient regimes are derived depending on the strain and its first-order gradient. An analytical solution for the plane strain deformation is derived. This solution is harnessed to investigate effects of Poisson's ratio and the strain gradient on the plane strain deformation of auxetic and non-auxetic polymer gels. The results revealed that Poisson's ratio and the micro-strain field significantly influence the elastic extensibility and elastic compressibility of polymer gels. Depending on its Poisson's ratio and the nature of its microstructure, a polymer gel may exhibit homogeneous/inhomogeneous deformation, and its rigidity may be enhanced/degraded.