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Mathematical Modeling of Inelastic Deformation by J.F. Besseling,E. Van Der Giessen Pdf
Mathematical Modeling of Inelastic Deformation details the mathematical modeling of the inelastic behavior of engineering materials. The authors use a thermodynamic approach to the subject and focus on crystalline materials, but not to the exclusion of macro-moleular solids. Within a unified theory for small and large deformations, they develop simple models, such as the elastic-perfectly plastic model, as well as complex models dealing with anisotropic hardening. The book includes finite element implementation of the theory and illustrates the implementation with examples from heat production and conduction processes.
There have been many excellent books written on the subject of plastic deformation in solids, but rarely can one find a textbook on this subject. “Plasticity Modeling & Computation” is a textbook written specifically for students who want to learn the theoretical, mathematical, and computational aspects of inelastic deformation in solids. It adopts a simple narrative style that is not mathematically overbearing, and has been written to emulate a professor giving a lecture on this subject inside a classroom. Each section is written to provide a balance between the relevant equations and the explanations behind them. Where relevant, sections end with one or more exercises designed to reinforce the understanding of the “lecture.” Color figures enhance the presentation and make the book very pleasant to read. For professors planning to use this textbook for their classes, the contents are sufficient for Parts A and B that can be taught in sequence over a period of two semesters or quarters.
Mesomechanical Constitutive Modeling by Vratislav Kafka Pdf
"This carefully written book, based to a large degree on original and new research, is an essential source of information for anyone dealing with property modeling aspects in modern materials science. It can be warmly recommended for graduate students and researchers in the respective fields." Ceramics - Silikaty, 2001
Inelasticity of Materials by Arun R Srinivasa,Sivakumar M Srinivasan Pdf
With the advent of a host of new materials ranging from shape memory alloys to biomaterials to multiphase alloys, acquiring the capacity to model inelastic behavior and to choose the right model in a commercial analysis software has become a pressing need for practicing engineers. Even with the traditional materials, there is a continued emphasis on optimizing and extending their full range of capability in the applications. This textbook builds upon the existing knowledge of elasticity and thermodynamics, and allows the reader to gain confidence in extending one's skills in understanding and analyzing problems in inelasticity. By reading this textbook and working through the assigned exercises, the reader will gain a level of comfort and competence in developing and using inelasticity models. Thus, the book serves as a valuable book for practicing engineers and senior-level undergraduate/graduate-level students in the mechanical, civil, aeronautical, metallurgical and other disciplines. The book is written in three parts. Part 1 is primarily focused on lumped parameter models and simple structural elements such as trusses and beams. This is suitable for an advanced undergraduate class with just a strength of materials background. Part II is focused on small deformation multi-dimensional inelasticity and is suitable for a beginning graduate class. Sufficient material is included on how to numerically implement an inelastic model and solve either using a simple stress function type of approach or using commercial software. Case studies are included as examples. There is also an extensive discussion of thermodynamics in the context of small deformations. Part III focuses on more advanced situations such as finite deformation inelasticity, thermodynamical ideas and crystal plasticity. More advanced case studies are included in this part. • This textbook takes a new, task- or scenario-based approach to teaching and learning inelasticity. The book is written in an active learning style that appeals to engineers and students who wish to design or analyze structures and components that are subject to inelasticity. • The book incorporates thermodynamical considerations into the modeling right from an early stage. Extensive discussions are provided throughout the book on the thermodynamical underpinnings of the models. • This textbook is the first to make extensive use of MATLAB to implement many inelasticity models. It includes the use of concepts such as Airy stress functions to solve plane problems for inelastic materials. The MATLAB codes are listed in the appendix for one to modify with their own models and requirements. • Step-by-step procedures for formulations and calculations are provided for the reader to readily adapt to the inelastic problems that he or she attempts to solve. • A large number of problems, exercises and projects for one to teach or learn from are included. These can be assigned as homework, in-class exercises or projects. • The book is written in a modular fashion, which provides adequate flexibility for adaptation in classes that cater to different audiences such as senior-level students, graduate students, research scholars, and practicing engineers.
A Variational Approach to Fracture and Other Inelastic Phenomena by Gianpietro Del Piero Pdf
This book exposes a number of mathematical models for fracture of growing difficulty. All models are treated in a unified way, based on incremental energy minimization. They differ from each other by the assumptions made on the inelastic part of the total energy, here called the "cohesive energy". Each model describes a specific aspect of material response, and particular care is devoted to underline the correspondence of each model to the experiments. The content of the book is a re-elaboration of the lectures delivered at the First Sperlonga Summer School on Mechanics and Engineering Sciences in September 2011. In the year and a half elapsed after the course, the material has been revised and enriched with new and partially unpublished results. Significant additions have been introduced in the occasion of the course "The variational approach to fracture and other inelastic phenomena", delivered at SISSA, Trieste, in March 2013. The Notes reflect a research line carried on by the writer over the years, addressed to a comprehensive description of the many aspects of the phenomenon of fracture, and to its relations with other phenomena, such as the formation of microstructure and the changes in the material’s strength induced by plasticity and damage. Reprinted from the Journal of Elasticity, volume 112, issue 1, 2013.
Mathematical Foundations of Elasticity by Jerrold E. Marsden,Thomas J. R. Hughes Pdf
Graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It presents a classical subject in a modern setting, with examples of newer mathematical contributions. 1983 edition.
Inelastic Deformation of Metals by Donald C. Stouffer,L. Thomas Dame Pdf
Using a totally new approach, this groundbreaking book establishesthe logical connections between metallurgy, materials modeling, andnumerical applications. In recognition of the fact that classicalmethods are inadequate when time effects are present, or whencertain types of multiaxial loads are applied, the new, physicallybased state variable method has evolved to meet these needs.Inelastic Deformation of Metals is the first comprehensivepresentation of this new technology in book form. It developsphysically based, numerically efficient, and accurate methods forpredicting the inelastic response of metals under a variety ofloading and environmental conditions. More specifically, Inelastic Deformation of Metals: * Demonstrates how to use the metallurgical information to developmaterial models for structural simulations and low cyclic fatiguepredictions. It presents the key features of classical and statevariable modeling, describes the different types of models andtheir attributes, and provides methods for developing models forspecial situations. This book's innovative approach covers such newtopics as multiaxial loading, thermomechanical loading, and singlecrystal superalloys. * Provides comparisons between data and theory to help the readermake meaningful judgments about the value and accuracy of aparticular model and to instill an understanding of how metalsrespond in real service environments. * Analyzes the numerical methods associated with nonlinearconstitutive modeling, including time independent, time dependentnumerical procedures, time integration schemes, inversiontechniques, and sub-incrementing. Inelastic Deformation of Metals is designed to give theprofessional engineer and advanced student new and expandedknowledge of metals and modeling that will lead to more accuratejudgments and more efficient designs. In contrast to existing plasticity books, which discuss few if anycorrelations between data and models, this breakthrough volumeshows engineers and advanced students how materials and modelsactually do behave in real service environments. As greater demandsare placed on technology, the need for more meaningful judgmentsand more efficient designs increases dramatically. Incorporatingthe state variable approach, Inelastic Deformation of Metals: * Provides an overview of a wide variety of metal responsecharacteristics for rate dependent and rate independent loadingconditions * Shows the correlations between the mechanical response propertiesand the deformation mechanisms, and describes how to use thisinformation in constitutive modeling * Presents different modeling options and discusses the usefulnessand limitations of each modeling approach, with material parametersfor each model * Offers numerous examples of material response and correlationwith model predictions for many alloys * Shows how to implement nonlinear material models in stand-aloneconstitutive model codes and finite element codes An innovative, comprehensive, and essential book, InelasticDeformation of Metals will help practicing engineers and advancedstudents in mechanical, aerospace, civil, and metallurgicalengineering increase their professional skills in the moderntechnological environment.
Mathematical Models in Boundary Layer Theory by V.N. Samokhin Pdf
Since Prandtl first suggested it in 1904, boundary layer theory has become a fundamental aspect of fluid dynamics. Although a vast literature exists for theoretical and experimental aspects of the theory, for the most part, mathematical studies can be found only in separate, scattered articles. Mathematical Models in Boundary Layer Theory offers the first systematic exposition of the mathematical methods and main results of the theory. Beginning with the basics, the authors detail the techniques and results that reveal the nature of the equations that govern the flow within boundary layers and ultimately describe the laws underlying the motion of fluids with small viscosity. They investigate the questions of existence and uniqueness of solutions, the stability of solutions with respect to perturbations, and the qualitative behavior of solutions and their asymptotics. Of particular importance for applications, they present methods for an approximate solution of the Prandtl system and a subsequent evaluation of the rate of convergence of the approximations to the exact solution. Written by the world's foremost experts on the subject, Mathematical Models in Boundary Layer Theory provides the opportunity to explore its mathematical studies and their importance to the nonlinear theory of viscous and electrically conducting flows, the theory of heat and mass transfer, and the dynamics of reactive and muliphase media. With the theory's importance to a wide variety of applications, applied mathematicians-especially those in fluid dynamics-along with engineers of aeronautical and ship design will undoubtedly welcome this authoritative, state-of-the-art treatise.
The Linearized Theory of Elasticity by William S. Slaughter Pdf
This book is derived from notes used in teaching a first-year graduate-level course in elasticity in the Department of Mechanical Engineering at the University of Pittsburgh. This is a modern treatment of the linearized theory of elasticity, which is presented as a specialization of the general theory of continuum mechanics. It includes a comprehensive introduction to tensor analysis, a rigorous development of the governing field equations with an emphasis on recognizing the assumptions and approximations in herent in the linearized theory, specification of boundary conditions, and a survey of solution methods for important classes of problems. Two- and three-dimensional problems, torsion of noncircular cylinders, variational methods, and complex variable methods are covered. This book is intended as the text for a first-year graduate course in me chanical or civil engineering. Sufficient depth is provided such that the text can be used without a prerequisite course in continuum mechanics, and the material is presented in such a way as to prepare students for subsequent courses in nonlinear elasticity, inelasticity, and fracture mechanics. Alter natively, for a course that is preceded by a course in continuum mechanics, there is enough additional content for a full semester of linearized elasticity.
Mathematical Elasticity by Philippe G. Ciarlet Pdf
The first book of a three-volume set, Three-Dimensional Elasticity covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. It includes the known existence theorems, either via the implicit function theorem or via the minimization of the energy (John Ball’s theory). An extended preface and extensive bibliography have been added to highlight the progress that has been made since the volume’s original publication. While each one of the three volumes is self-contained, together the Mathematical Elasticity set provides the only modern treatise on elasticity; introduces contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells; and contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.
Inelastic Behavior of Materials and Structures Under Monotonic and Cyclic Loading by Holm Altenbach,Michael Brünig Pdf
This book presents studies on the inelastic behavior of materials and structures under monotonic and cyclic loads. It focuses on the description of new effects like purely thermal cycles or cases of non-trivial damages. The various models are based on different approaches and methods and scaling aspects are taken into account. In addition to purely phenomenological models, the book also presents mechanisms-based approaches. It includes contributions written by leading authors from a host of different countries.