Discontinuous energy minimizers in nonlinear elastostatics: An example of J. Ball revisited
[Compare \textit{J. M. Ball}, Philos. Trans. R. Soc. London, A 306, 557-611 (1982; Zbl 0513.73020).] Simple direct methods of the calculus of variations, together with mild a priori restrictions of a constitutive nature, are exploited to show that a uniform radial displacement at the boundary fails to induce a homogeneous radial expansion of a compressible elastic ball when the boundary displacement reaches a critical value (of which an explicit lower bound is offered): rather, above the critical value, energy minimizers are radial deformations with a hole at the center, and are accompanied by a stress field with radial stress vanishing, and circumferential stress unbounded, at the surface of the hole.
boundary value problem replaced by minimization problem
existence of singular equilibrium solutions
everywhere smooth radial equilibrium solutions with finite energy
a priori restrictions of a constitutive nature
uniform radial displacement at the boundary
fails to induce a homogeneous radial expansion
boundary displacement reaches a critical value
energy minimizers are radial deformations
scientific article; zbMATH DE number 3919920