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 : 75. 17 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 Mueller
ISBN : 9783319325804
Genre : Technology & Engineering
File Size : 82. 41 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 : 68. 21 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.

Nonlinear Mechanics Of Crystals

Author : John D. Clayton
ISBN : 9400703503
Genre : Technology & Engineering
File Size : 51. 1 MB
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This book describes behavior of crystalline solids primarily via methods of modern continuum mechanics. Emphasis is given to geometrically nonlinear descriptions, i.e., finite deformations. Primary topics include anisotropic crystal elasticity, plasticity, and methods for representing effects of defects in the solid on the material's mechanical response. Defects include crystal dislocations, point defects, twins, voids or pores, and micro-cracks. Thermoelastic, dielectric, and piezoelectric behaviors are addressed. Traditional and higher-order gradient theories of mechanical behavior of crystalline solids are discussed. Differential-geometric representations of kinematics of finite deformations and lattice defect distributions are presented. Multi-scale modeling concepts are described in the context of elastic and plastic material behavior. Representative substances towards which modeling techniques may be applied are single- and poly- crystalline metals and alloys, ceramics, and minerals. This book is intended for use by scientists and engineers involved in advanced constitutive modeling of nonlinear mechanical behavior of solid crystalline materials. Knowledge of fundamentals of continuum mechanics and tensor calculus is a prerequisite for accessing much of the text. This book could be used as supplemental material for graduate courses on continuum mechanics, elasticity, plasticity, micromechanics, or dislocation mechanics, for students in various disciplines of engineering, materials science, applied mathematics, and condensed matter physics.

Introduction To Practical Peridynamics

Author : Walter Herbert Gerstle
ISBN : 9789814699563
Genre : Technology & Engineering
File Size : 49. 6 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

Tensor Analysis And Nonlinear Tensor Functions

Author : Yuriy I. Dimitrienko
ISBN : 9789401732215
Genre : Mathematics
File Size : 78. 62 MB
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Tensor Analysis and Nonlinear Tensor Functions embraces the basic fields of tensor calculus: tensor algebra, tensor analysis, tensor description of curves and surfaces, tensor integral calculus, the basis of tensor calculus in Riemannian spaces and affinely connected spaces, - which are used in mechanics and electrodynamics of continua, crystallophysics, quantum chemistry etc. The book suggests a new approach to definition of a tensor in space R3, which allows us to show a geometric representation of a tensor and operations on tensors. Based on this approach, the author gives a mathematically rigorous definition of a tensor as an individual object in arbitrary linear, Riemannian and other spaces for the first time. It is the first book to present a systematized theory of tensor invariants, a theory of nonlinear anisotropic tensor functions and a theory of indifferent tensors describing the physical properties of continua. The book will be useful for students and postgraduates of mathematical, mechanical engineering and physical departments of universities and also for investigators and academic scientists working in continuum mechanics, solid physics, general relativity, crystallophysics, quantum chemistry of solids and material science.

Introduction To The Mechanics Of A Continuous Medium

Author : Lawrence E. Malvern
ISBN : OCLC:2309235
Genre : Continuum mechanics
File Size : 41. 98 MB
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Computational Inelasticity

Author : J.C. Simo
ISBN : 9780387227634
Genre : Computers
File Size : 81. 44 MB
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A description of the theoretical foundations of inelasticity, its numerical formulation and implementation, constituting a representative sample of state-of-the-art methodology currently used in inelastic calculations. Among the numerous topics covered are small deformation plasticity and viscoplasticity, convex optimisation theory, integration algorithms for the constitutive equation of plasticity and viscoplasticity, the variational setting of boundary value problems and discretization by finite element methods. Also addressed are the generalisation of the theory to non-smooth yield surface, mathematical numerical analysis issues of general return mapping algorithms, the generalisation to finite-strain inelasticity theory, objective integration algorithms for rate constitutive equations, the theory of hyperelastic-based plasticity models and small and large deformation viscoelasticity. Of great interest to researchers and graduate students in various branches of engineering, especially civil, aeronautical and mechanical, and applied mathematics.

An Introduction To Continuum Mechanics

Author : J. N. Reddy
ISBN : 9781107025431
Genre : Mathematics
File Size : 35. 9 MB
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This best-selling textbook presents the concepts of continuum mechanics, and the second edition includes additional explanations, examples and exercises.

Multiaxial Fatigue And Deformation Testing Techniques

Author : Sreeramesh Kalluri
ISBN : 0803120451
Genre : Technology & Engineering
File Size : 62. 13 MB
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Fourteen papers from the May 1995 symposium focus on the advances that new materials testing equipment and digital computers have made possible. Representative topics: testing facilities for multiaxial loading of tubular specimens, biaxial deformation experiments over multiple string regimes, charac

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