For a linear elastic, incompressible disc with an inextensible rim, non-trivial plane-strain solutions exist in the linear theory; the nonlinear theory rules them out, and the linear solutions are still useful design tools.
Some annular disk inclusion problems in elasticity
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The circular disc made of linear elastic incompressible material and the 'bathyscaphe lesson'
For a linear elastic, incompressible disc with an inextensible rim, non-trivial plane-strain solutions exist in the linear theory; the nonlinear theory rules them out, and the linear solutions are still useful design tools.