nonlinear continuum mechanics and large inelastic deformations 174 solid mechanics and its applications

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Nonlinear Continuum Mechanics And Large Inelastic Deformations

Author : Yuriy I. Dimitrienko
ISBN : 9400700342
Genre : Technology & Engineering
File Size : 53. 62 MB
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The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics – kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead to different results. The analysis is accompanied by experimental data and detailed numerical results for rubber, the ground, alloys, etc. The book will be an invaluable text for graduate students and researchers in solid mechanics, mechanical engineering, applied mathematics, physics and crystallography, as also for scientists developing advanced materials.

The State Of Deformation In Earthlike Self Gravitating Objects

Author : Wolfgang H. Müller
ISBN : 9783319325804
Genre : Technology & Engineering
File Size : 41. 70 MB
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This book presents an in-depth continuum mechanics analysis of the deformation due to self-gravitation in terrestrial objects, such as the inner planets, rocky moons and asteroids. Following a brief history of the problem, modern continuum mechanics tools are presented in order to derive the underlying field equations, both for solid and fluid material models. Various numerical solution techniques are discussed, such as Runge-Kutta integration, series expansion, finite differences, and (adaptive) FE analysis. Analytical solutions for selected special cases, which are worked out in detail, are also included. All of these methods are then applied to the problem, quantitative results are compared, and the pros and cons of the analytical solutions and of all the numerical methods are discussed. The book culminates in a multi-layer model for planet Earth according to the PREM Model (Preliminary Earth Model) and in a viscoelastic analysis of the deformation problem, all from the viewpoint of rational continuum theory and numerical analysis.

Thermomechanics Of Composite Structures Under High Temperatures

Author : Yu. I. Dimitrienko
ISBN : 9789401774949
Genre : Technology & Engineering
File Size : 59. 71 MB
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This pioneering book presents new models for the thermomechanical behavior of composite materials and structures taking into account internal physico-chemical transformations such as thermodecomposition, sublimation and melting at high temperatures (up to 3000 K). It is of great importance for the design of new thermostable materials and for the investigation of reliability and fire safety of composite structures. It also supports the investigation of interaction of composites with laser irradiation and the design of heat-shield systems. Structural methods are presented for calculating the effective mechanical and thermal properties of matrices, fibres and unidirectional, reinforced by dispersed particles and textile composites, in terms of properties of their constituent phases. Useful calculation methods are developed for characteristics such as the rate of thermomechanical erosion of composites under high-speed flow and the heat deformation of composites with account of chemical shrinkage. The author expansively compares modeling results with experimental data, and readers will find unique experimental results on mechanical and thermal properties of composites under temperatures up to 3000 K. Chapters show how the behavior of composite shells under high temperatures is simulated by the finite-element method and so cylindrical and axisymmetric composite shells and composite plates are investigated under local high-temperature heating. The book will be of interest to researchers and to engineers designing composite structures, and invaluable to materials scientists developing advanced performance thermostable materials.

Virtual Work And Shape Change In Solid Mechanics

Author : Michel Frémond
ISBN : 9783319406824
Genre : Technology & Engineering
File Size : 73. 10 MB
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This book provides novel insights into two fundamental subjects in solid mechanics: virtual work and shape change. The author explains how the principle of virtual work represents a tool for analysis of the mechanical effects of the evolution of the shape of a system, how it can be applied to observations and experiments, and how it may be adapted to produce predictive theories of numerous phenomena. The book is divided into three parts. The first relates the principle of virtual work to what we observe with our eyes, the second demonstrates its flexibility on the basis of many examples, and the third applies the principle to predict the motion of solids with large deformations. Examples of both usual and unusual shape changes are presented, and equations of motion, some of which are entirely new, are derived for smooth and non-smooth motions associated with, for instance, systems of disks, systems of balls, classical and non-classical small deformation theories, systems involving volume and surface damage, systems with interactions at a distance (e.g., solids reinforced by fibers), systems involving porosity, collisions, and fracturing of solids.

Introduction To Practical Peridynamics

Author : Walter Herbert Gerstle
ISBN : 9789814699563
Genre : Technology & Engineering
File Size : 26. 10 MB
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Parting with the classical continuum concepts of stress and strain in the computational simulation of solids, this book proposes a peridynamic model that applies the model directly to particle lattices. The model is directly solvable on a computer. Introduction to Practical Peridynamics is both a graduate-level textbook and a treatise. The text provides the necessary foundations to understand and apply the state-based peridynamic lattice model, as well as a guide for the practical use of the model — for solving realistic structural engineering problems (particularly in reinforced concrete structures) in elasticity, plasticity, damage, fracture, and large deformations. Contents in this book include introductory chapters presenting the historical background of the subject; classical elasticity; computational solid modeling; continuum mechanics; fracture mechanics; particle dynamics simulations on parallel computers; as well as example simulations (with model applications). Request Inspection Copy

Computational Methods In Nonlinear Structural And Solid Mechanics

Author : Ahmed K. Noor
ISBN : 9781483145648
Genre : Technology & Engineering
File Size : 39. 65 MB
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Computational Methods in Nonlinear Structural and Solid Mechanics covers the proceedings of the Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics. The book covers the development of efficient discretization approaches; advanced numerical methods; improved programming techniques; and applications of these developments to nonlinear analysis of structures and solids. The chapters of the text are organized into 10 parts according to the issue they tackle. The first part deals with nonlinear mathematical theories and formulation aspects, while the second part covers computational strategies for nonlinear programs. Part 3 deals with time integration and numerical solution of nonlinear algebraic equations, while Part 4 discusses material characterization and nonlinear fracture mechanics, and Part 5 tackles nonlinear interaction problems. The sixth part discusses seismic response and nonlinear analysis of concrete structure, and the seventh part tackles nonlinear problems for nuclear reactors. Part 8 covers crash dynamics and impact problems, while Part 9 deals with nonlinear problems of fibrous composites and advanced nonlinear applications. The last part discusses computerized symbolic manipulation and nonlinear analysis software systems. The book will be of great interest to numerical analysts, computer scientists, structural engineers, and other professionals concerned with nonlinear structural and solid mechanics.

Encyclopedia Of Computational Mechanics

Author : Erwin Stein
ISBN : 0470846992
Genre : Mechanics, Applied
File Size : 51. 63 MB
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Computational Contact And Impact Mechanics

Author : Tod A. Laursen
ISBN : 3540429069
Genre : Science
File Size : 32. 50 MB
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Many physical systems require the description of mechanical interaction across interfaces if they are to be successfully analyzed. Examples in the engineered world range from the design of prosthetics in biomedical engi neering (e. g. , hip replacements); to characterization of the response and durability of head/disk interfaces in computer magnetic storage devices; to development of pneumatic tires with better handling characteristics and increased longevity in automotive engineering; to description of the adhe sion and/or relative slip between concrete and reinforcing steel in structural engineering. Such mechanical interactions, often called contact/impact in teractions, usually necessitate at minimum the determination of areas over which compressive pressures must act to prevent interpenetration of the mechanical entities involved. Depending on the application, frictional be havior, transient interaction of interfaces with their surroundings (e. g. , in termittent stick/slip), thermo-mechanical coupling, interaction with an in tervening lubricant and/or fluid layer, and damage of the interface (i. e. , wear) may also be featured. When taken together (or even separately!), these features have the effect of making the equations of mechanical evolu tion not only highly nonlinear, but highly nonsmooth as well. While many modern engineering simulation packages possess impressive capabilities in the general area of nonlinear mechanics, it can be contended that methodologies typically utilized for contact interactions are relatively immature in comparison to other components of a nonlinear finite element package, such as large deformation kinematics, inelastic material modeling, nonlinear equation solving, or linear solver technology.

Applied Mechanics Reviews

Author :
ISBN : OSU:32435051265205
Genre : Mechanics, Applied
File Size : 28. 68 MB
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Principles Of Continuum Mechanics

Author : Mysore N. L. Narasimhan
ISBN : STANFORD:36105002231384
Genre : Mathematics
File Size : 57. 73 MB
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Continuum mechanics is the mathematical study of material behavior as well as the principles governing this behavior where the basic constituents of the material are regarded as continua rather than as molecules, atoms, or grains. From this perspective one sees that the basic constituents are assumed to possess a continuous distribution of matter and the material as a whole is composed of such elements. Principles of Continuum Mechanics deals with the behavior of materials and their qualitative and quantitative treatment by means of a continuum approach in which materials are regarded as possessing a continuous distribution of matter. The book is ideally suited for use by first- or second-year graduate students. The book is also written for the benefit of researchers in engineering mechanics, applied mathematics, atmospheric science, oceanography, and for those in the biomedical sciences. This book is devoted to the classical continuum theory of solids and fluids as well as to certain topics of modern continuum mechanics of viscoelasticity and microcontinua together with their applications to problems of practical interest. Complete mathematical derivations of most of the fundamental equations and inequalities in continuum mechanics are included, thereby freeing the reader from having to go to other sources to find these derivations. The book contains an extensive bibliography which will be most useful for students and researchers wishing to pursue problems engendered by the text. And a Solutions Manual is available upon request to the Publisher. All in all, Principles of Continuum Mechanics should reach a wide audience of scientists, engineers, and mathematicians. Itseasy-to-understand style and the simple elegance of the work it presents make it a valuable addition to the literature in the field.

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