Search Results for boundary-element modeling

Corrosion modeling is an essential benchmarking element for the selection and life prediction associated with the introduction of new materials or processes. These models are most naturally expressed in terms of differential equations or in other nonexplicit forms of mathematics. This article discusses the principles and applications of various models developed for understanding the corrosion mechanism. These models include mechanistic models, including Pourbaix model, thermophysical module, electrochemical module, and ion association model; risk-based models; and knowledge models. The risk-based model and knowledge models are illustrated with examples for better understanding. The article also describes boundary-element modeling and pitting corrosion fatigue models.

Designing of induction heating, or, generally electro technological installations, requires mathematical modeling for solving problems related to various physical phenomena, including electromagnetic (EM), thermal, mechanical, fluidic, and metallurgical fields. This article focuses on the solution of Maxwell's equations (MEs) and provides some basic information regarding the heat transfer and fluid equations, because these physical phenomena usually are strongly coupled to magnetic and electric fields. The solutions are usually obtained by using specific numerical methods such as finite-element method, finite difference method, boundary-element method or volume-integral method, and direct-solution method. The article also discusses the typical structure of commercial codes (preprocessor, solver, and postprocessor) to solve field problems mainly in finite-element method.

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.

This article illustrates the simulation procedure of casting process. It describes important elements and points of the simulations. These include the setting of clear simulation objectives, selection of proper simulation code, hints in modeling of shape and phenomena, initial and boundary conditions, physical properties, enmeshing, and evaluation of simulation results. The article also provides some insights into the application of models to real world problem for foundry process engineers.

The constitutive relations for metalworking include elements of behavior at ambient temperature as well as high-temperature response. This article presents equations for strain hardening and strain-rate-sensitive flow, with alternate sections on empirically determined properties, followed by the models of constitutive behavior. It provides a discussion on creep mechanisms involving dislocation and diffusional flow, such as the Nabarro-Herring creep and the Coble creep. The equations for the several creep rates are also presented. Research on the mechanism of the superplastic flow in fine-grain metals has encompassed many ideas, such as the diffusional creep, dislocation creep with diffusional accommodation at grain boundaries, and concepts of grain-mantle deformation. The article concludes with information on the kinetics of superplastic deformation processes, including low stress behavior, concurrent grain growth, and high stress behavior.

This article summarizes many approaches that are used to simulate relaxation of bulk residual stresses in components. It presents analytical examples to highlight the complexity of residual stress and strain distributions observed in simple geometries, with ideal material behavior and trivial loading and boundary conditions. The article discusses approximate and advanced solution techniques that can be employed in practice for simulation of residual stress relief: finite-difference method and finite-element method. It also describes advanced techniques applicable to transient creep, advanced constitutive models, and complicated stress and temperature loading histories.

Finite element analysis is a computer-based numerical method for solving engineering problems in bodies of user-defined geometry. This article introduces the important issues of finite elements (especially accuracy and efficiency) in a nonacademic manner. It describes the Rayleigh-Ritz procedure for solving structural problems based on the principle of virtual work. The article discusses continuum elements, such as hexahedra, pentahedra, tetrahedra, quadrilaterals, and triangles, commonly used in three- or two-dimensional domains. It considers structural elements such as beam element, plate element, shell element, and elbow element. The article presents three examples to illustrate the types of problems that can be addressed and the decisions that must be made when using finite element analysis.

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.

The systematic study of microstructural evolution during deformation under hot working conditions is important in controlling processing variables to achieve dimensional accuracy. This article explains the microstructural features that need to be modeled and provides an outline of the principles and achievements of each of the various microstructural models, including black-box modeling, gray-box modeling, white-box modeling, and hybrid modeling.

This article focuses on the various assumptions involved in the numerical modeling of welds, including the geometry of the welded structure and the weld joint, thermal stress, strain, residual stress, and the microstructure in the heat-affected and fusion zones.

This article is a comprehensive collection of formulas and numerical solutions, addressing many heat-transfer scenarios encountered in welds. It provides detailed explanations and dimensioned drawings in order to discuss the geometry of weld models, transfer of energy and heat in welds, microstructure evaluation, thermal stress analysis, and fluid flow in the weld pool.

Temperature is a typical parameter characterizing the heating level of any particle belonging to a heated body. The basic problem of heat transfer computation is associated with appropriate determination of heat transfer coefficients. This article provides a discussion on the basic equations, initial and boundary conditions, and multiple reflection phenomena of mathematical modeling. These boundary conditions include the Dirichlet, Neumann, and Henkel conditions.

This article reviews network models and their applications for the simulation of various physical phenomena related to grain-boundary migration. It discusses the steps involved in the implementation of two and three-dimensional network models, namely, acquisition and discretization of the microstructure, formulation of the equation of motion, and implementation of the topological transformations. The article presents examples that illustrate the simulation of physical phenomena to demonstrate the predictive power and flexibility of network models.

Computational fluid dynamics (CFD) is one of the tools available for understanding and predicting the performance of thermal-fluids systems. This article qualitatively describes the basic principles of CFD. The numerical methods, such as geometry description and discretization, used to solve the CFD equations are discussed. The article also demonstrates the application of CFD to a few casting problems.

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.

Manufacturing processes typically involve the reshaping of materials from one form to another under a set of processing conditions. This article discusses the two classification schemes of modeling for manufacturing processes, namely, on-line or off-line models and empirical, mechanistic, or deterministic models along with their important considerations. It describes the various aspects of modeling of deformation processes, casting operations, and fusion welding processes, with examples.

This article presents various equations that are essential for the modeling of both single-phase and multiphase profiles. It includes the fundamental laws of diffusion, along with its equations and solutions. The article provides information on the series of applications that illustrate how various diffusional processes can be modeled.