An extension of the Eulerian-Lagrangian kinematic description (Haber, 1984) to elastodynamic problems is presented. Expressions are derived for field variables and material time derivatives using the new kinematic description. The variational equation of motion is written in a weak form suitable for use with isoparametric finite elements. The new kinematic model allows a finite element mesh to continuously adjust for changes in the structural geometry, material interfaces, or the domain of the boundary conditions without a discrete remeshing process. Applications of the new model to mode I dynamic crack propagation demonstrates its advantages over moving mesh methods based on conventional Lagrangian kinematic models. Numerical results show excellent agreement with analytic predictions.

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