On the coupling of rectilinear shear and stretching in a slab made of incompressible elastic neo-Hookean materials: analytic formulation and finite element validation

• Published in: Meccanica (Milan) 2023-08, Vol.58 (8), p.1657-1669
• Main Authors: Bechir, Hocine, Djema, Amar, Yaya, Kamel, Methia, Mounir
• Format: Article
• Language: English
• Subjects: Automotive Engineering; Boundary conditions; Civil Engineering; Classical Mechanics; Constitutive equations; Constitutive relationships; Coupling; Differential equations; Elastic analysis; Elastomers; Engineering; Equilibrium equations; Finite element method; Mechanical Engineering; Ordinary differential equations; Parameter identification; Shear tests; Stretching; Test procedures
• ISSN: 0025-6455; 1572-9648
• DOI: 10.1007/s11012-023-01671-4

In this paper, a novel concept test is proposed in order to characterize multi-axial behavior of elastomeric materials. It consists to coupling the deformations of rectilinear shear and of axial-stretching, to this end; a testing protocol is conceived and analyzed. As result, the constitutive equation depends on both the stretching-direction, i.e. Θ and magnitude of displacement, i.e. γ prescribed on the sample edge. Using simplifying assumptions, the system of equilibrium equations is transformed into an ordinary differential equation (ODE) of the third order. In order to obtain the displacement field, the ODE is solved on the basis of novel boundary conditions. Besides, this new testing is studied by Finite element method (FEM). At large strains, i.e. γ ≥ 0.5 and Θ ∈ 0 , π / 2 ; we have shown that, the analytic predictions of the displacement field are consistent with FE-simulation results. Thereby, the experimental data arising from this novel-shear test could be used for both parameter identification and/or validation of hyperelastic models.