This article focuses on the basic turbulent flow, and the thermal, mass-transfer, and hydrodynamic phenomena for use in modeling physical processes during induction melting. It provides a discussion on transport phenomena equations that includes the approximation of convective terms in the transport equation and computational schemes for the fluid dynamics equation. The aspects of computational algorithms for specific magnetohydrodynamic problems with mutual influence of the magnetic field and melt flow due to the changing shape of the free surface are also considered. The article illustrates the application of the basic equations and approaches formulated for electromagnetic field and melt turbulent flow for the numerical study of an induction crucible furnace.

Optimization plays a key role in the design of any structure or system, and electromagnetic devices are no exception. This article provides a description of the formulation of a design problem, and provides a review of the Paretian optimality. It focuses on nondominating sorting algorithms and multiobjective evolutionary strategy algorithms associated with evolutionary computing. The article provides information on field-based optimization problems. It also discusses the design of the pancake inductor that implies the solution of coupled electromagnetic and thermal fields, along with the use of optimal design procedures, to identify the best possible device or process.

This article discusses tools that are used for the systematic optimization of engineering designs. It focuses on the practical application of optimization technology in a computer-aided engineering environment. The article presents numerical optimization algorithms and provides some background on how these algorithms make decisions when searching for the optimal design. It also provides information on structural optimization, topology optimization, materials processing optimization, multidisciplinary optimization, and global optimization.

Induction heating computations deal with a multiphysics problem containing analysis of several coupled physical fields such as electromagnetic, temperature, mechanical, and metallurgical. In order to solve coupled electromagnetic-temperature field problems, it is necessary to develop suitable algorithms and numerical procedures, which make it possible to deal with these nonlinear coupled problems. This article focuses on the most common approaches to coupled electromagnetic and heat transfer problems, namely, weak-, quasi-, and hard-coupled formulations.

Homogenization heat treatment can be useful for improving the performance and life of an alloy while in service or for improving the processability during fabrication and hot working. This article describes the identification of incipient melt point, slowest-diffusing elements, and microstructural scale for homogenization of metal alloys. It also discusses the CALPHAD software to optimize the homogenization heat treatment and the Scheil module of the commercial thermodynamic modeling software.

This article describes the historical background, uncertainties in structural parameters, classifications, and application areas of probabilistic analysis. It provides a discussion on the basic definition of random variables, some common distribution functions used in engineering, selection of a probability distribution, the failure model definition, and a definition of the probability of failure. The article also explains the solution techniques for special cases and general solution techniques, such as first-second-order reliability methods, the advanced mean value method, the response surface method, and Monte Carlo sampling. A brief introduction to importance sampling, time-variant reliability, system reliability, and risk analysis and target reliabilities is also provided. The article examines the various application problems for which probabilistic analysis is an essential element. Examples of the use of probabilistic analysis are presented. The article concludes with an overview of some of the commercially available software programs for performing probabilistic analysis.

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.

This article focuses on approximate closed-form analytical methods, such as slab and upper bound methods, used for forward and inverse design of metal forming problems. Selected examples of application of these methods to metal forming processes are also discussed.

This article describes the effects of furnace atmospheric elements, including air, water vapor, molecular nitrogen, carbon dioxide, and carbon monoxide, on steels. It provides useful information on six groups of commercially important prepared atmospheres classified by the American Gas Association on the basis of the method of preparation or on the original constituents employed. These groups are designated and defined as follows: Class 100, exothermic base; Class 200, prepared nitrogen base; Class 300, endothermic base; Class 400, charcoal base; Class 500, exothermic-endothermic base; and Class 600, ammonia base. These are subclassified and numerically designated to indicate variations in the method by which they are prepared. The article also contains a table that lists significant furnace atmospheres and typical applications.

The process of optimization involves choosing the best solution from a pool of potential candidate solutions. This article provides a description of some classes of problems and the optimization methods that solve them. These problems include the deterministic single-objective problem, the deterministic multiobjective problem, and the nondeterministic, stochastic optimization problem. The article presents several complementary approaches to solve a wide variety of single-objective and multiobjective mechanical engineering applications. Multiobjective optimization study and stochastic optimization studies are also discussed.

Neural-network (NN) modeling is most suitable for simulations of correlations that are hard to describe or cannot be accurately predicted by physical models. This article describes the principles and procedures of NN modeling. It discusses the use of NN modeling in general organization of software and graphical user interfaces. The article also provides information on the ways to improve and upgrade the NN models.

Thermoelastic stress analysis (TSA) an increasingly popular infrared (IR)-based technique for measuring stress on the surface of a part subjected to time-varying loads. This article begins by providing a theoretical and historical background of thermoelastic stress analysis. It then describes infrared detectors, such as quantum detectors and thermal/nonquantum detectors, for thermoelastic stress analysis. The article discusses the theoretical aspects for producing thermoelastic stress analysis data and the applications amenable to thermoelastic stress analysis. It concludes with information on the qualitative applications of thermoelastic stress analysis.

Several methods are developed for the numerical solution of partial differential equations, namely, meshed-solution methods such as the finite-element method (FEM), finite-difference method, and boundary-element method; and numerical algorithms consisting of so-called meshed-solution methods. This article introduces the methods of so-called meshed solutions, with an emphasis on the FEM. It presents some basic differential equations that are used to model the responses of structures, components, processes, or systems with emphasis on continuum mechanics. The article provides an outline on the mathematical principles of solving differential equations. It also reviews linear structural problems to illustrate the concept of the FEMs.

Continuous fiber composite materials offer dramatic opportunities for producing lightweight laminates with tremendous performance capabilities. This article describes the kinematics of fabric deformation and explains the algorithms used in draping simulation. It discusses the basic components, such as laminate and ply, of continuous fiber composite. The article provides information on the core sample and ply analysis. It details producibility, flat-pattern evaluations, and laminate surface offset. The article discusses various interfaces, such as the structural analysis interface, the resin transfer molding interface, the fiber placement and tape-laying interface, and the laser projection interface.

The misorientation of a boundary of a growing grain is defined not only by its crystallography but also by the crystallography of the grain into which it is growing. This article focuses on the Monte Carlo Potts model that is typically used to model grain growth, Zener-Smith pinning, abnormal grain growth, and recrystallization. It introduces the basics of the model, providing details of the dynamics, simulation variables, boundary energy, boundary mobility, pinning systems, and stored energy. The article explains how to incorporate experimental parameters and how to validate the model by comparing the observed behavior quantitatively with theory. The industrial applications of the model are also discussed. The article also provides a wide selection of the algorithms for implementing the Potts model, such as boundary-site models, n -fold way models, and parallel models, which are needed to simulate large-scale industrial applications.

This article examines how cellular automaton (CA) can be applied to the simulation of static and dynamic recrystallization. It describes the steps involved in the CA simulation of recrystallization. These include defining the CA framework, generating the initial microstructure, distributing nuclei of recrystallized grains, growing the recrystallized grains, and updating the dislocation density. The article concludes with information on the developments in CA simulations.

Ultrasound is an ideal modality for nondestructive evaluation (NDE) because it enables the interior of objects to be assessed without the safety and access issues associated with radiography. This article summarizes the history of array usage in NDE and its relationship to medical applications. It discusses the mathematics behind classical beamforming, full matrix capture, and total focusing methods of imaging. The article shows how ultrasonic array data can be simulated by direct numerical methods (most commonly using finite-element methods), analytical methods, or hybrid methods. It also considers various methods of comparing the performance of arrays and imaging algorithms. The article provides a comparison of various advanced and nonlinear imaging algorithm and looks at some practical industrial applications of arrays. It concludes with some future perspectives for arrays in NDE.

Three-dimensional microscopy can be used to reveal the shape, distribution, and connectivity of three-dimensional (3D) features that lie buried within an opaque material. This article discusses several experimental techniques that can be used to generate 3D images. These include serial sectioning, focused ion beam tomography, atom probe tomography, and X-ray microtomography. Nine case studies are presented that represent the work of the various research groups currently working on 3D microscopy using serial sectioning and illustrate the variants of the basic experimental techniques. The article also discusses the techniques for reconstruction and visualization of 3D microstructures with advanced computer software and hardware.

Simulation programs are becoming more effective tools in reducing the need for physical testing and the avoidance of costly downstream problems by solving the problems upfront in the early development stage. This article provides a brief review of the history and applied analysis of simple forming operations. It focuses on metal stamping simulation based on the finite-element methods or model (FEM) with emphasis on software tools using the three-dimensional FEM technology. The article discusses two aspects of particular importance in finite-element analysis of sheet forming and springback analysis: the type of solution algorithm/governing equation and the type of element. The article provides information on various models for material yield criteria.

A phase diagram is a graphical representation of the phase equilibria of materials in terms of temperature, composition, and pressure. This article provides an overview on the background of phase diagram calculation software. It presents an algorithm to calculate binary stable phase equilibria. The article summarizes a rapid method to obtain a thermodynamic description of a multicomponent system. It also provides information on thermodynamically calculated phase diagrams.