On finite bending of visco-hyperelastic materials: a novel analytical solution and FEM

In this paper, an analytical approach is proposed to examine the finite strain time-dependent behavior of incompressible, isotropic visco-hyperelastic elastomeric material under bending. Phenomenological hyperelastic invariant-based strain energy density function, Yeoh model, and N-termed Prony series are utilized to define the strain-dependent and time-dependent parts of the visco-hyperelastic constitutive model, respectively. 3D finite element analysis of the problem is carried out using ABAQUS/Visco to verify the analytical solution results. Material parameters of polyurea are calibrated using an optimization framework for experimental results under five different strain rates, simultaneously. Two well-known tests of viscoelastic materials, stress relaxation and creep tests, are investigated both analytically and numerically. Distribution of the Cauchy stress components and the resultant bending moment versus time, and the variation of the mentioned results with different rise times and ultimate bent angles are provided for the stress relaxation test. Moreover, the strain and bending angle results are plotted in a creep test for different rise times and applied moments. Besides, a multi-step relaxation test and creep recovery test are performed for different loading conditions. Finite element method results confirm the analytical approach with great compatibility.