A three-dimensional analysis is presented for high velocity impact problems. A Lagrangian finite-element technique is formulated for tetrahedron elements subjected to large strains and displacements. The effects of material strength and compressibility are included to account for elastic-plastic flow and wave propagation. The strains and strain rates in each element are determined from the displacements and velocities of the nodes. The strains, strain rates, and material properties are used to determine the elastic stresses, plastic deviator stresses, hydrostatic pressure, and artificial viscosity. The stresses are equated to concentrated forces acting on concentrated masses at the nodes, and the nodal equations of motion are numerically integrated. Illustrative examples are also included.

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