Closing up a hole in neo-Hookean membrane. (English) Zbl 0780.73035
Summary: The hole in a nonlinearly elastic membrane of infinite extent is sutured. The membrane is then loaded with sufficient stretching. A model of complex variable for the general suturing process is developed in the context of finite plane stress theory. Neo-Hookean material is assumed in this membrane. The undeformed shape of the hole may be simulated by a family of conformal mappings. The one-to-one correspondence between complex conjugates on a unit circle mapped from the hole is employed for the suturing process. A second approximation closed form solution is obtained from successive substitutions. Graphical results are demonstrated.
MSC:
| 74K20 | Plates |
| 74B20 | Nonlinear elasticity |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
Keywords:
suturing process; finite plane stress theory; family of conformal mappings; second approximation closed form solutionReferences:
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