This is an introductory course on nonlinear finite element analysis of solid mechanics and heat transfer problems. Nonlinearities can be caused by changes in geometry or be due to nonlinear material behavior. Both types of nonlinearities are covered in this course.
O. C. Zienkiewicz and R. L. Taylor (2000), The Finite Element Method: Volume 2 Solid Mechanics, Butterworth-Heinemann. Another excellent repository of information of nonlinear finite elements geared toward the Civil Engineers.
J. Bonet and R. Wood (2008), Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press. This is a particularly good reference for the general continuum mechanics and kinematics involved, with a detailed discussion on material nonlinearities.
S. C. Brenner and L. R. Scott (2007), The mathematical theory of finite element methods, vol. 15 of Texts in Applied Mathematics, Springer-Verlag, Classical book on the mathematics foundation of finite element methods.
R. M. Brannon (2004), Rotation.Almost everything you ever wanted to know about rotations.
A.J.M Spencer (2004), Continuum Mechanics, Dover Publications. An excellent introduction to continuum mechanics. You should own a copy for your personal library.
Taylor, R.L., Simo, J.C., Zienkiewicz, O.C., and Chan, A.C.H, 1986, The patch test - a condition for assessing FEM convergence, International Journal for Numerical Methods in Engineering, 22, pp. 39-62.
Simo, J.C. and Vu-Quoc, L., 1986, A three-dimensional finite strain rod model. Part II: Computational Aspects,Computer Methods in Applied Mechanics and Engineering,58, pp. 79-116.
Ibrahimbegovic, A., 1995, On finite element implementation of geometrically nonlinear Reissner's beam theory: Three-dimensional curved beam elements,Computer Methods in Applied Mechanics and Engineering,122, pp. 11-26.
Buchter, N., Ramm, E., and Roehl, D., 1994, Three-dimensional extension of non-linear shell formulation based on the enhanced assumed strain concept,Int. J. Numer. Meth. Engng., 37, pp. 2551-2568.
Rouainia, M. and Peric, D., 1998, A computational model for elasto-viscoplastic solids at finite strain with reference to thin shell applications,Int. J. Numer. Meth. Engng., 42, pp. 289-311.