Nonlinear Analysis of Snapping Hyperelastic Prestressed Arches

Resumo

Over the past decades, a variety of applications of multistable structures has appeared in different
branches of engineering. Among the structures exhibiting multistability, metamaterials, formed by a sequence of
structures able to undergo large displacements and deformations without presenting damage, thus being able to
assume different equilibrium positions, are investigated in the current literature. Many of these structures display
a nonlinear behavior with limit point instability, allowing the structure to jump between various stable equilibrium
positions and thus present a reversible hysteretic behavior. Among the materials used in this type of structure are

hyperelastic materials. In this work, the behavior of hyperelastic arches obtained from buckled columns in a post-
buckling configuration, under transversal loads, is studied; a bistable structural unit typical of metamaterials. To

understand the nonlinear behavior of these structures, a finite element model is used by means of the Abaqus

software that allows specifying several constitutive laws commonly used for hyperelastic materials. To obtain non-
linear equilibrium paths, the Riks method is applied. A parametric analysis of the nonlinear behavior of the arch

shows the influence of the geometry of the arch (height-to-span ratio and thickness), self-weight and load
imperfections on the nonlinear equilibrium paths, load capacity (critical load) and stored energy of the structure.