The user manual lists 12 pages of technical papers associated
with the formulation of LS-DYNA.
For a general overview of explicit finite element methods in hydrocodes,
such as the public domain version of DYNA3D, see Benson, D. J., “Computational
Methods in Lagrangian and Eulerian Hydrocodes,” Computer Methods in
Applied Mechanics and Engineering, Elsevier, Amsterdam, The Netherlands, 1992,
Vol. 99, 1992, pp. 235-394.

The following finite element textbooks are the personal favorites of David
Benson and are listed from least to most expensive (and comprehensive):

- Hughes, T. J. R. “The Finite Element Method: Linear Static and Dynamic
Finite Element Analysis” Dover Publications, (2000).
- Belytschko, T., Liu, W. K., and Moran, B. “Nonlinear Finite Elements
for Continua and Structures,” John Wiley and Sons, (Sept. 12, 2000).
- Zienkiewicz, O. C., and Taylor, R. L. “The Finite Element Method,
3 Volume Set” Butterworth-Heinemann; 5th edition (August 25, 2000).