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| Bond-based peridynamics simulation for tensile large deformation and fracture behavior of incompressible Neo-Hookean hyperelastic membrane |
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Abstract Two-dimensional(2D) bond-based peridynamics (BBPD) model based on the incompressible Neo-Hookean (NH) constitutive model is studied for the simulation of the tensile large deformation and failure behavior of incompressible hyperelastic membrane. First, the force density vector and micropotential function of PD bond are derived by equating the strain energy density of 2D BBPD model to that of NH hyperelastic constitutive model. The model parameters is found to be related to the ratio of the principal stretches within the neighborhood of PD bond. Then a bond-associated horizon is introduced, and the principal stretches are calculated based on the calculation of the deformation gradient within the horizon. Thus a 2D BBPD model for NH hyperelastic material is established. In order to verify the established 2D BBPD model, the nominal stress-stretch curves of a square hyperelastic membrane under uniaxial tension and biaxial tension with different biaxial tension speed ratios are calculated by using the proposed BBPD model, and compared with the theoretical curves. The deformation and load-displacement curves of a hyperelastic membrane with a central circular hole under uniaxial and biaxial tensile loadings are also calculated, and compared with the FEM predictions. Finally, the deformation and failure processes of the hyperelastic membrane with a central circular hole under different tensile loadings are calculated, and the influence mechanisms of loading conditions on the mechanical properties and failure behavior of NH hyperelastic membrane are analyzed based on the evolution analysis of strain energy density and damage of the material points at the crack tip. It is found that the error of calculation results of the proposed BBPD model is less than 10%. The failure load of the hyperelastic membrane with a central circular hole decreases and the failure displacement increases with the increasing of the biaxial tension speed ratio. Crack bifurcation occurs in the hyperelastic membrane with a central circular hole, and the bifurcation angle of the cracks increases with the increasing of the biaxial tension speed ratio.
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Received: 31 July 2024
Published: 28 February 2025
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2025, Vol. 46 
