Auxetic effects in the large deflection bending characteristics of FG GRMMC shallow arches

Abstract

Shallow arches are ubiquitous in long-span buildings, bridge structures, and tunnels. Uniform loading can cause large deflections characterized by snap-through, which can ultimately lead to structural failure. In this work, nonlinear bending of functional graded graphene reinforced metal matrix composite (GRMMC) shallow arches with auxetic properties is studied using higher order shear constitutive equations based on the von Kármán nonlinear theory of beam. Asymptotic solutions for an arch with simply and clamped supported ends are derived using a two-perturbation approach. The results show that the the initial thermal stress-induced deformation of the members increases with increasing environmental temperature. The generated auxetic effect in the structures due to Negative Poisson's Ratio (NPR) will act to resist bending deformation. This strengthening effect is more noticeable with increase in the deflection, especially in the first snap-through. In addition, the elastic foundation increases the global stiffness of the arch, thus enhancing its bending stiffness. The current work not only provides a theoretical foundation for understanding the interrelationship between the auxetic effect and mechanical performance of structures but also offers guidance for designing metamaterial structures.