Elastoplastic Modeling 1st Edition by Jean Salencon ISBN 978-1786306234 1786306239
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ISBN 10: 1786306239
ISBN 13: 978-1786306234
Author: Jean Salencon
Elastoplastic behavior has long been part of the constitutive models incorporated in most computer codes, used in the design of civil and mechanical engineering structures. Elastoplastic Modeling offers a compact presentation of the fundamentals of classical elastoplastic modeling, the basis for many engineering applications currently implemented. This book provides a general background to enhance understanding of the modeling assumptions that govern the rationales of these applications. With this understanding comes the ability to assess their validation range and propose possible improvements. An instructive approach replaces excessive mathematical developments with a semi-phenomenological method, where mathematical modeling is driven by – and derived from – experimental observations. A logical track is followed, starting from material behavior modeling and leading to the analysis of the anelastic response of systems, subjected to quasi-static loading processes.
Table of contents:
Chapter 1. Elastic Domains: Yield Conditions
1.1. Introductory Remarks
1.2. An Overview of the Model
The Infinitesimal Transformation Framework
Time Variable
1.3. One-Dimensional Approach
Uniaxial Tension Test
Uniaxial Tension-Compression Test
The Bauschinger Effect
Other One-Dimensional Experiments
1.4. Multidimensional Approach
A Multidimensional Experiment
Initial Elastic Domain
Work-Hardening
Perfectly Plastic Material
Bui’s Experimental Results
1.5. Yield Conditions
Initial Yield Condition and Yield Function
Loading Function and Work-Hardening
Simple Work-Hardening Models
1.6. Yield Criteria and Loading Functions
Convexity
Isotropy
The Tresca Yield Criterion
The von Mises Yield Criterion
Other Yield Criteria for Metals
Yield Criteria for Anisotropic Materials
Yield Criteria for Granular Materials
1.7. Final Comments
Chapter 2. The Plastic Flow Rule
2.1. One-Dimensional Approach
Work-Hardening Material
Perfectly Plastic Material
2.2. Multidimensional Approach for a Work-Hardening Material
Loading and Unloading Processes
General Properties of the Plastic Flow Rule
Plastic Potential: Associated Plasticity
Principle of Maximum Plastic Work
Validation of the Principle of Maximum Plastic Work
Piecewise Continuously Differentiable Loading Functions
2.3. Multidimensional Approach for a Perfectly Plastic Material
Loading and Unloading Processes
Application of the Principle of Maximum Plastic Work
Drucker’s Postulate
2.4. Plastic Dissipation
Per Unit Volume
Support Function of the Elastic Domain
Plastic Velocity Jumps
2.5. Generalized Standard Materials
2.6. Mises’, Tresca’s and Coulomb’s Perfectly Plastic Standard Materials
Mises’
Tresca’s
Coulomb’s
Edge and Vertex Regimes
Chapter 3. Elastoplastic Modeling in Generalized Variables
3.1. About Generalized Variables
3.2. Elastic Domains
Initial Elastic Domain
Work-Hardening and Perfect Plasticity
3.3. The Anelastic Flow Rule
Anelasticity or Plasticity?
Principle of Maximum Work
Work-Hardening Anelastic Flow Rule
Perfectly Plastic Anelastic Flow Rule
Anelastic Dissipation
3.4. Generalized Continua
Curvilinear Generalized Continuum
Planar Generalized Continuum
Chapter 4. Quasi-static Elastoplastic Processes
4.1. Quasi-static Loading Processes
Within the SPH Framework
Admissible Fields
Parametric Problems
4.2. Elastoplastic Loading Processes
Problematics
Existence and Uniqueness Theorems
Uniqueness for Stress and Strain Rates
4.3. System with Elastic and Perfectly Plastic Material
Initial Elastic Domain
Solution Existence
Limit Loads
Linear and Anelastic Responses
Geometry Changes
4.4. System with Work-Hardening Elastoplastic Material
Initial Domain
Residual Rates
Maximum Work Theorem
Summary
Chapter 5. Quasi-static Elastoplastic Processes: Minimum Principles
5.1. Elastic and Perfectly Plastic Material
Minimum Principle for Stress Rate Field
Minimum Principle for Velocity Field
Alternative Forms
5.2. Elastic and Work-Hardening Material
Revisiting the Constitutive Equation
Minimum Principles
Historical Comments
5.3. Minimum Principles for Stress and Strain Fields
Colonnetti’s Theorem
Alternative Expressions
Chapter 6. Limit Loads: Limit Analysis
6.1. Limit Loads and Yield Design (1)
6.2. Static Approach – First Plastic Collapse Theorem
Safe Loads
Lower Bound Theorem
6.3. Kinematic Approach – Second Plastic Collapse Theorem
Admissible Velocity Fields
Necessary Conditions
Upper Bound Theorem
6.4. Combining Approaches
Limit Load Determination
Association Theorem
Duality
6.5. Limit Analysis and Rigid Perfectly Plastic Material
Rigid Plastic Model
Connection to Limit Loads
6.6. Limit Loads and Yield Design (2)
Fundamentals
Material Resistance
Safe Loads and Lower Bound
Maximum Work Rate and Upper Bound
Matching Theories
6.7. Two-Dimensional Limit Analysis
Plane Strain Problems
Static and Kinematic Solutions
Incomplete and Complete Solutions
Plane Stress and Axisymmetric Problems
6.8. Implementation
Analytical, Numerical, and Hybrid Solutions
Example Problem
Final Comments
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