This article provides a summary of the overall development of the finite element method (FEM) and its contribution to the materials forming industry. It focuses on the overall philosophy and evolution of the FEM for solving bulk forming issues. A number of applications of FEM are presented in the order they would be used in a typical manufacturing process sequence: primary materials processing, hot forging and cold forming, and product assembly. The article discusses four FEM modules: the deformation model, the heat-transfer model, the microstructural model, and the carbon diffusion model. The article also covers material fracture and die stress analysis and reviews optimization of the design of forming processes.

This article focuses on the modeling and simulation of diffusion-controlled processes related to both materials processing such as heat treatments, and materials degradation from a practical perspective by using the one-dimensional (1-D) sharp interface approach. It describes various diffusion simulation models, such as one-phase simulations, moving phase-boundary simulations, and dispersed system simulations. The article presents case studies that illustrate some examples where diffusion simulations have been applied to industrial-based problems, with an emphasis on the approaches used and the lessons learned from performing such simulations.

Diffusion is the process by which molecules, atoms, ions, point defects, or other particle types migrate from a region of higher concentration to one of lower concentration. This article focuses on the diffusivity data and modeling of lattice diffusion in solid-state materials, presenting their diffusion equations. It discusses different methods for evaluating the diffusivity of a material, including the measurement of diffusion coefficients, composition profiles, and layer growth widths. The article reviews the various types of direct and indirect diffusion experiments to extract tracer, intrinsic, and chemical diffusivities. It provides information on the applications of single-phase and multiphase diffusion.

This article focuses on the analyzing and modeling of stress-strain behavior of polycrystals of pure face-centered cubic (fcc) metals in the range of temperatures and strain rates where diffusion is not important. It presents a phenomenological description of stress-strain behavior and provides information on the physical background, alternative interpretations, and directions of research. The quantitative description of strain hardening of fcc polycrystals is provided. The article also discusses the modeling of stress-strain behavior in body-centered cubic metals, hexagonal metals, stage IV work hardening, and the various classes of single-phase alloys.

This article presents a mechanical description of superplasticity and discusses constitutive equations that are essential for simulating superplastic forming processes, applicable to structural superplasticity. It presents the phenomenological constitutive equations of superplasticity and classical physical constitutive equations. The article also reviews the accommodation mechanisms that are divided into two major groups, namely, diffusional accommodation and accommodation by dislocations.

Dealloying is a corrosion process in which one or more elements are selectively dissolved, leaving behind a porous residue of the remaining elements. This article describes the dealloying in various systems, namely, dezincification, graphitic corrosion, dealuminification, and noble metal alloys dealloying. The current-potential behavior of a binary alloy undergoing selective dissolution is reviewed. The article highlights the four mechanisms required for the formation of porous metals: ionization-redeposition, surface diffusion, volume diffusion, and percolation model of selective dissolution.