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Cavitation in elastic and hyperelastic sheets. (English) Zbl 1213.74224

Summary: Plane stress, axially symmetric, cavitation patterns are examined for large sheets with an embedded central circular hole. Both (radially-uniform) remote tension and internal pressure loads are considered. Material behavior is modeled by finite strain Hookean-type elastic and hyperelastic constitutive relations with logarithmic strains.
Governing field equations are reduced to a single ordinary differential equation with the principal stress difference as the independent variable. Calculations reveal that under internal pressure the usual definition of cavitation state does not apply as load increases monotonously along the deformation path.
Introducing the specific cavitation energy, as a practical measure in cavitation analysis, provides a unified framework for assessment of cavitation phenomena. Comparison with related patterns of spherical and cylindrical cavitation fields supports the main findings of this study.

MSC:

74L15 Biomechanical solid mechanics
74G70 Stress concentrations, singularities in solid mechanics
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