A Finite Strain Analytical Solution for Stress-Softening of Hyperelastic Materials Under Cyclic Bending

Abstract

In this paper, a new approach for stress-softening of an isotropic, incompressible, hyperelastic and rectangular beam that undergoes cyclic bending-unbending deformation, is presented. Employing an exponential softening function, damage response of the hyperelastic beam due to cyclic finite bending is investigated. The stress-softening phenomenon occurs in elastomeric materials when they deform for the first time. Under the same deformation, the stress required in reloading is smaller than the initial loading stage. This is known as the Mullins effect. To verify the accuracy of the proposed solution, finite element analysis of the same problem is carried out. In this study, a principal stretch-based strain energy function i.e., Ogden model and an invariant-based function such as a newly introduced Exp–Exp model are used for all bending, unbending and re-bending procedures. The proposed method needs a much shorter time compared to FEM simulations. Thus, in design and optimization of the structures under bending that requires a large number of analyses, the proposed semi-analytical solution can be considered as an efficient tool for studying the effects of different material and geometrical parameters.

Finite Bending of Fiber-Reinforced Visco-Hyperelastic Material: Analytical Approach and FEM

“…In the absence of body forces, the simplified form of the first equilibrium equation in the current cylindrical configuration is as follows [ 28 ]: …”

“…where the shear stress σ ∞ rθ is generated by the presence of reinforcing fibers. In the absence of body forces, the simplified form of the first equilibrium equation in the current cylindrical configuration is as follows [28]:…”

“…Later, Shojaeifard, Sheikhi, Baniassadi, and Baghani [ 27 ] suggested a constitutive framework to represent the time-dependent behavior of visco-hyperelastic rectangular materials under finite bending. In our previous work, a new model was proposed for the stress-softening of an incompressible hyperelastic rectangular bar under cyclic bending and unbending deformation [ 28 ]. In addition, Bakhtiyari, Baniasadi, and Baghani [ 29 ] proposed a thermo-visco-hyperelastic approach for shape memory polymers under large bending deformations and temperature changes.…”

Transient swelling of cylindrical hydrogels under coupled extension-torsion: Analytical and 3D FEM solutions

“…There are several standard deformation regimes used for material characterization (Pashazadeh et al, 2021; Xolin et al, 2020), and one of the most important is coupled extension and torsion. This is due to the fact that this deformation regime involves both the tensile and shear modes of deformation simultaneously.…”