Experimental and numerical analysis of hyperelastic prestressed arches

Abstract

In recent decades, there has been an increasing number of researches and applications involving hyperelastic structures, integrating different areas of engineering structures and materials, driven by technological advances in the manufacturing process, many involving multistability and the practical use of snap-through buckling. However, there is little information on the stability of hyperelastic multistable structural elements. The objective of this work is, therefore, to study experimentally and numerically the stability of hyperelastic arches, a structural form found in many applications. The arches are made of rubber-like material (polyvinyl siloxane), an elastomer that closely conforms to the incompressible hyperelastic ideal, which is described by the constitutive polynomial model. Uniaxial tests are used to determine the material constants. The aid of a digital image record during the tests allows an in-depth analysis of the deformation field. Several specimens are tested, covering a large range of rise-to-span ratios and two cross-section geometries, thus allowing for an in-depth understanding of the multistable behavior of pre-compressed hyperelastic arches. The tests are conducted under displacement control, allowing the determination of load and displacement limit points. Excellent correlation is obtained between the experiments and the nonlinear equilibrium paths obtained using three-dimensional finite element models. The results obtained show that the arches, due to the flexibility of hyperelastic materials, can undergo large displacements and rotations without damage, giving them great potential for energy absorption and storage. Density is a crucial property of rubber, significantly influencing its structural response. The important role of self-weight on bifurcation loads and nonlinear equilibrium paths is demonstrated here. Understanding the non-linear behavior and stability of these structures is important in practical applications such as vibration control, energy absorption and harvesting, metamaterials development, bioengineering, medicine, and flexible robots, among others.