Fourier series and finite element solutions are given for stresses in a cylindrical case filled with an annulus of elastomeric material. The Fourier series solutions are for membrane stresses, which dominate at early time, and are given for three case-elastomer models: (1) a slide boundary model in which the case wall moves as a unit with the elastomer in radial motion but, with a weak bond between the case and elastomer, is free to slide relative to the elastomer in tangential motion, (2) a unit motion model for a well-bonded elastomer in which the case wall and elastomer are assumed to move together as a unit in both radial and tangential motion, and (3) a radiation boundary model in which tangential motion of the case wall radiates energy into a well-bonded elastomer. For typical case, elastomer and bond mechanical properties, the radiation boundary model gives the most appropriate solution, which differs substantially from the other solutions even for very soft elastomers. Finite element solutions agree closely with and support the validity of all three analytical models, which were used to guide the finite element “experiments” and interpret and generalize their results.

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