Nonlinear Models and Plasticity

In mechanics, linear models have been well developed and received wide acceptance. They are based on linear elasticity, incompressibility of fluids and ideal gas properties. At the present stage of scientific and technical advances very exacting requirements are imposed upon materials and structures. The necessity to take into account their properties in nonlinear area of the mechanical behavior has given rise to the development of models both for theoretical description and prediction of nonlinear characteristics. Solutions involving the resulting complex mathematical expressions are made possible through the use of numerical solution programs on powerful computers. The nonlinear behavior in the mechanics of a deformable solid body is considered in the theories of plasticity, creep, and viscoelasticity. Although theory of plasticity is well developed, it must be noted that it is still far from being complete.