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Void nucleation and growth for a class of incompressible nonlinearly elastic materials. (English) Zbl 0703.73025

Summary: In this paper, a bifurcation problem for a solid sphere subjected to uniform tensile dead-loading \(p_ 0\) at its boundary is examined within the framework of finite elastostatics. The sphere is composed of a particular class of homogeneous isotropic incompressible nonlinearly elastic materials, namely those of power-law type. One solution to the problem, for all values of \(p_ 0\), corresponds to a homogeneous state in which the sphere remains undeformed while stressed. However, for sufficiently large values of \(p_ 0\), there is in addition a second possible configuration involving an internal traction-free spherical cavity. The dependence on constitutive parameters of the critical load at which bifurcation occurs is examined as well as the subsequent void growth. The stress distribution after cavitation occurs is also described. The results are obtained in closed analytic form.

MSC:

74B20 Nonlinear elasticity
74E05 Inhomogeneity in solid mechanics
74G70 Stress concentrations, singularities in solid mechanics
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