Because of its low cost and outstanding properties, steel is by far the most common and versatile material, with a wide range of applications such as in mechanical, civil and architectural engineering. With numerous combinations of alloying elements and microstructures, the spectrum of achievable mechanical properties, e.g., strength, ductility, toughness and durability, is unparalleled. However, the production of steel is not environmentally friendly due to the large amounts of carbon dioxide generated by the inherent reduction of iron oxide by carbon. New processes, such as hydrogen reduction, and better recycling solutions are at different stages of research but will take decades before full implementation and production.

Nevertheless, to reduce the impact of steel on the environment, much progress can be achieved in the near future through the optimization of steel products, which is the focus of this course. The mechanical properties of steel are dominated by its elasto-viscoplastic behavior and limited by its fracture modes. Since the plastic behavior is highly sensitive to the material considered, and fracture even more, it is impossible to synthetize the broad diversity of mechanical responses in just a few scenarios but there are some commonalities within the steel family as well as with other metals. In addition, these aspects highly depend on the manufacturing processes and service conditions of the products, in particular temperature.

Because product design optimization relies ever more on numerical simulations, it is essential to develop modeling techniques that account for the important aspects above. The solutions of a boundary value (BV) problem, whether a forming process or the fatigue behavior of a structural component, is guided by the laws of mechanics and numerically obtained by discretization of space and time, generally through finite element (FE) analyses. For better time efficiency, only a discrete number of finite element simulations with limited sets of process or performance parameters may be executed, the results of which providing the necessary data to train a neural network. Subsequently, this meta-model is employed to provide the simulation result of a complex BV problem in seconds for any interpolated set of parameters, which renders an optimization very simple and time-efficient to conduct. It is clear that the accuracy of the FE model, which may be used directly or provide the input for the meta-model based on neural network, is essential for the success of an optimization procedure. This is the reason why the relationships between stress, strain and other variables, i.e., the constitutive description, must be as accurate as possible. The plastic behavior must be experimentally characterized accurately and represented by constitutive equations. Although a number of failure mechanisms result directly from the solution of such BV problem, others such as fracture are not predictable without specific criteria as well as specific implementations into numerical tools. Therefore, the objective of this course is to demonstrate the importance of the description of the constitutive and fracture modeling of steel and other selected metals with applications to forming, cyclic loading and fatigue, crack propagation and toughness. Although many of these models are developed at a continuum mechanics scale, they are based on the understanding of deformation mechanisms. Moreover, this course underline that modern identification approaches of the mechanical behavior such as the virtual fields method, which is particularly suitable for constitutive model calibration, are introduced. Finally, since temperature is an important variable, specific aspects relevant to the resistance to high temperature creep and the cryogenic application of stainless steel to superconductors, are introduced.