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Computational Methods for Plasticity: Theory and Applications is a self-contained, comprehensive text that will appeal to postgraduate students and research engineers alike wanting either an introduction to the subject or to develop their knowledge of more advanced concepts and applications. Split into 3 parts: basic concepts, small strains, and large strains, it begins with elementary theory and progresses to advanced, complex theory and computer implementation. It describes the theory of the associated numerical methods for the simulation of a wide range of plastic engineering materials, from the simplest strain plasticity theory to more complex damage mechanics. Allows the reader to learn all aspects of computational plasticity and its implementation from one volume. Suitable for use at an introductory as well as an advanced level. Accompanied by a purpose-developed software that illustrates many of the techniques discussed in the text, downloadable from an accompanying companion website. Includes many numerical examples that illustrate the application of the described methodologies. Introductory material on related disciplines and procedures such as tensor analysis, continuum mechanics and computational finite element methods is included, as is a computer program of approximately 11,000 lines of FORTAN code and many numerical examples that will assist the reader in learning to apply the described methodologies.
Sommaire
Part One Basic concepts
1 Introduction
1.1 Aims and scope
1.2 Layout
1.3 General scheme of notation
2 ELEMENTS OF TENSOR ANALYSIS
2.1 Vectors
2.2 Second order tensors
2.3 Higher order tensors
2.4 Isotropic tensors
2.5 Differentiation
2.6 Linearisation of nonlinear problems
3 THERMODYNAMICS
3.1 Kinematics of deformation
3.2 Infinitesimal deformations
3.3 Forces. Stress Measures
3.4 Fundamental laws of thermodynamics
3.5 Constitutive theory
3.6 Weak equilibrium. The principle of virtual work
3.7 The quasi static initial boundary value problem
4 The finite element method in quasi static nonlinear solid mechanics
4.1 Displacement based finite elements
4.2 Path dependent materials. The incremental finite element procedure
4.3 Large strain formulation
4.4 Unstable equilibrium. The arc length method
5 Overview of the program structure
5.1 Introduction
5.2 The main program
5.3 Data input and initialisation
5.4 The load incrementation loop. Overview
5.5 Material and element modularity
5.6 Elements. Implementation and management
5.7 Material models: implementation and management
Part Two Small strains
6 The mathematical theory of plasticity
6.1 Phenomenological aspects
6.2 One dimensional constitutive model
6.3 General elastoplastic constitutive model
6.4 Classical yield criteria
6.5 Plastic flow rules
6.6 Hardening laws
7 Finite elements in small strain plasticity problems
7.1 Preliminary implementation aspects
7.2 General numerical integration algorithm for elastoplastic constitutive equations
7.3 Application: integration algorithm for the isotropically hardening von Mises model
7.4 The consistent tangent modulus
7.5 Numerical examples with the von Mises model
7.6 Further application: the von Mises model with nonlinear mixed hardening
8 Computations with other basic plasticity models
8.1 The Tresca model
8.2 The Mohr Coulomb model
8.3 The Drucker Prager model
8.4 Examples
9 Plane stress plasticity
9.1 The basic plane stress plasticity problem
9.2 Plane stress constraint at the Gauss point level
9.3 Plane stress constraint at the structural level
9.4 Plane stress projected plasticity models
9.5 Numerical examples
9.6 Other stress constrained states
10 Advanced plasticity models
10.1 A modified Cam Clay model for soils
10.2 A capped Drucker Prager model for geomaterials
10.3 Anisotropic plasticity: the Hill, Hoffman and Barlat Lian models
11 Viscoplasticity
11.1 Viscoplasticity: phenomenological aspects
11.2 One dimensional viscoplasticity model
11.3 A von Mises based multidimensional model
11.4 General viscoplastic constitutive model
11.5 General numerical framework
11.6 Application: computational implementation of a von Mises based model
11.7 Examples
12 Damage mechanics
12.1 Physical aspects of internal damage in solids
12.2...
Thèmes :
* Mathematiques & physique / Mecanique / Ouvrages généraux
* Genie & construction mecanique / Ouvrages généraux
* Informatique / Langages et programmation / Autres langages (perl, fortran, pasca l, delphi, corba, prolog, lisp...) |
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