Effects of multiple families of nonlinear fibers on finite deformation near a crack tip in a neo-Hookean sheet. (English) Zbl 1475.74110
Summary: In this paper, we investigate the asymptotic crack tip fields in a neo-Hookean sheet reinforced by two families of nonlinear fibers, where the fibers are characterized by the standard reinforcing model. In the asymptotic analysis, the fibers with stronger stiffening compared to the matrix dominate the mechanical behavior at the crack tip, which simplifies the analysis. A hodograph transformation is used to solve for the leading and higher order eigenmodes for the nonlinear eigenvalue problem derived from the model. Asymptotic path-independent \(J\)-integrals are constructed to evaluate the leading order parameters separately. The asymptotic crack tip fields agree well with finite element results for different combinations of fiber orientation angles and modulus ratios. We find that the peak value of stress for the case with two families of fibers decreases significantly compared to the case for a single family of fibers.
MSC:
| 74R10 | Brittle fracture |
| 74G70 | Stress concentrations, singularities in solid mechanics |
| 74E30 | Composite and mixture properties |
| 74B20 | Nonlinear elasticity |
| 74G10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics |
Keywords:
crack tip field; hyperelastic material; hodograph transformation; asymptotic method; nonlinear eigenvalue problemReferences:
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