ABSTRACT
Chapters 2 through 12 addressed linear solid mechanics and heat transfer, and corresponding finite element methods for linear problems. Applications that linear methods serve to analyze include structures under mild loads, disks and rotors spinning at modest angular velocities, and heated plates. However, a large number of problems of interest are nonlinear. For one example, plasticity is a nonlinear materials theory suited for metals in metal forming, vehicle crash, and ballistics applications. In problems with high levels of heat input, mechanical properties such as the elastic modulus, and thermal properties such as the coefficient of specific heat, may be strongly temperature dependent. Rubber seals and gaskets commonly experience strains exceeding 50%. Soft biological tissues typically are modeled as rubberlike. Many problems involve variable contact, for example, meshing gear teeth. Heat conducted across electrical contacts may be strongly dependent on normal pressures. Fortunately, much of the linear finite element method can be extended to nonlinear problems, as explained in this chapter.
