Benchmark analytic solution of the dynamic sphere problem for Bodner–Partom elastic–viscoplastic materials

• We give analytic solution for elastic–viscoplastic spherical shell.
• We examine computational convergence of analytic solution.
• Converged analytic solution has error of less than 0.01%.

Developing benchmark analytic solutions for problems in solid and fluid mechanics is important for the purpose of testing and verifying computational physics codes. In order to test the numerical results of physics codes that predict the response of elastic–viscoplastic materials, we consider the geometrically linear dynamic sphere problem. We present an exact solution for the dynamic response of a spherical shell composed of a linearly elastic–viscoplastic material exhibiting isotropic symmetry. The solution takes the form of an infinite series of eigenfunctions. We demonstrate, both qualitatively and quantitatively, the convergence of the computed benchmark solution under spatial, temporal, and eigenmode refinement. We also use our computational benchmark solution to compute viscoplastic strains on a spherical shell composed of titanium.