ABSTRACT
The previous section addressed 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 are nonlinear. 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, can 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 can be strongly dependent on normal pressures. Fortunately, much of the linear finite-element method can be adapted to nonlinear problems, as explained in this chapter. The next chapter focuses on isothermal problems. The extension to thermomechanical problems will be presented in a subsequent chapter.
