Electronic structure methods based on the density functional theory (DFT) are used as a powerful tool for assessing the mechanical thermodynamic and defect properties of metal alloys. This article presents the origins of the electronic structure methods and their strengths and limitations. It describes the basic procedures for calculating essential structural properties in metal alloys. The article reviews the approximations and computational details of the pseudopotential plane wave methods used in metal systems. It provides information on the applications of DFT methods in metal alloy systems. The article discusses the calculations of a variety of structural, thermodynamic, and defect properties, with particular emphasis on structural metal alloys and their derivatives.

This article assesses the evolution of martensite modeling in the changing materials engineering environment. It describes the physics of displacive transformations using Ginzburg-Landau theory, microstructure representation, dynamics and simulations, density functional theory, and shuffle transitions. The article reviews the application of the Ginzburg-Landau approach to rigorous solutions for issues in the structure of a martensitic nucleus based on the martensitic nucleation theory. The three basic behavior modes of martensitic growth, such as elastic, elastic/plastic, and fully plastic are discussed. The article also reviews the overall kinetics of martensitic transformations.

This article demonstrates the depth and breadth of commercial and third-party software packages available to simulate metals processes. It provides a representation of the spectrum of applications from simulation of atomic-level effects to manufacturing optimization. The article tabulates the software name, function or process applications, vendor or developer, and website information.

This article discusses the two major applications of hot isostatic pressing (HIP), such as healing of inherent internal defects in castings and welds, and consolidation of powder materials. It describes the design principles of the HIP tooling, as well as the problems associated with mathematical modeling of HIP. The article presents an example for the modeling process of the HIP. It reviews the numerical modeling and tooling design of a casing component demonstration.

Brittle materials, such as ceramics, intermetallics, and graphites, are increasingly being used in the fabrication of lightweight components. This article focuses on the design methodologies and characterization of certain material properties. It describes the fundamental concepts and models associated with performing time-independent and time-dependent reliability analyses for brittle materials exhibiting scatter in ultimate strength. The article discusses the two-parameter and three-parameter Weibull distribution for representing the underlying probability density function for tensile strength. It reviews life prediction reliability models used for predicting the life of a component with complex geometry and loading. The article outlines reliability algorithms and presents several applications to illustrate the utilization of these reliability algorithms in structural applications.

The six types of statistical distributions are normal distribution, log normal distribution, Weibull distribution, exponential distribution, binomial distribution, and Poisson distribution. This article discusses the applicability of each distribution, providing information on the probability density function, cumulative distribution function, population mean and variance, and parameter and percentile estimation.