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This study presents a two-dimensional (2D) bond-based peridynamics (BBPD) model based on the incompressible neo-Hookean (NH) constitutive model for simulating the tensile large deformation and failure behavior of incompressible hyperelastic membranes. First, the force density vector and micropotential function of the PD bond are derived by equating the strain energy density of the 2D BBPD model with that of the NH hyperelastic constitutive model. The model parameters are found to be related to the ratio of principal stretches in the neighborhood of the PD bond. Then a bond-associated horizon is introduced, and principal stretches are calculated based on the calculation of the deformation gradient within this horizon. A 2D BBPD model for NH hyperelastic materials is thus established. To validate the model, the nominal stress-stretch curves for a square hyperelastic membrane under uniaxial tension and biaxial tension with different biaxial tension speed ratios are calculated using the proposed BBPD model, and compared with theoretical curves. The deformation and load-displacement curves of a hyperelastic membrane with a central circular hole under uniaxial and biaxial tensile loads are also calculated and compared with finite element method (FEM) predictions. Finally, the deformation and failure processes of the hyperelastic membrane with a central circular hole under different tensile loads are calculated, and the influences of loading conditions on the mechanical properties and failure behavior of the NH hyperelastic membrane are analyzed based on the evolution analysis of strain energy density and damage of material points at the crack tip. It is found that the proposed BBPD model achieves less than 10% error in calculations. The failure load of the hyperelastic membrane with a central circular hole decreases while the failure displacement increases with rising biaxial tension speed ratios. Crack bifurcation occurs in the hyperelastic membrane with a central circular hole, with the bifurcation angle increasing alongside the biaxial tension speed ratio.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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