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

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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.