Muutke küpsiste eelistusi

Inelasticity Of Materials: An Engineering Approach And A Practical Guide [Kõva köide]

(Indian Inst Of Technology Madras, India), (Texas A&m Univ, Usa)
Teised raamatud teemal:
Teised raamatud teemal:
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.
Foreword vii
About the book... ix
Acknowledgments xvii
Introduction to Inelasticity
Simple Structural Elements
1(2)
Introduction to Inelasticity
3(24)
What is inelasticity?
5(1)
Why should one study inelasticity?
5(1)
A sample scenario
6(2)
Observation, experimentation and modeling of material response
8(1)
Experimental observations and model development
9(4)
Plastic deformations and the friction block analogy
13(6)
Creep and time dependent behavior
19(7)
Summary and Conclusions
26(1)
Thermodynamics of Inelastic Materials: A lumped parameter approach
27(62)
Notion of a lumped parameter model
31(5)
The role of lumped parameter models
31(1)
Elements of lumped parameter systems: Extending the results of
Chapter 1
32(1)
Equations of motion
33(3)
General considerations of springs and dashpots
36(11)
Linear and nonlinear springs
36(3)
Viscous dashpots
39(1)
Frictional dashpots
40(3)
Springs and dashpots in 2 dimensions
43(4)
Energy formulation of the equations of motion
47(1)
Mechanical power theorem
48(17)
Frequently asked questions and clarifications
52(13)
Thermal considerations: The Helmholtz and Gibbs potentials
65(20)
Extension of the power theorem
69(7)
Finding the Helmholtz and Gibbs potentials for a system
76(2)
Determination of the equations of motion and the temperature of the system
78(7)
Solving the thermo-mechanical evolution equations for an inertialess system
85(1)
Lumped parameter models: Gibbs potential approach
86(2)
Projects and exercises
88(1)
Inelastic Response of Truss Elements
89(36)
An example problem
91(2)
Inelastic bars under axial loading
93(17)
Make a preliminary list of the variables of interest
93(1)
Make simplifying assumptions about the response
93(2)
Modeling of the response of the truss
95(15)
Prescribed displacements
110(2)
The Bauschinger effect
112(4)
Modeling the Bauschinger effect
114(2)
An example cyclic loading problem
116(3)
Stress cycling
116(1)
Strain cycling
117(2)
General loading conditions
119(3)
Summary
122(3)
Elastoplastic Beams: An Introduction to a Boundary Value Problem
125(26)
An example task
127(1)
Modeling of a thermoelastoplastic beam
127(3)
The elastoplastic beam
130(19)
Make a preliminary list of variables of interest
130(1)
Make simplifying assumptions on the response
131(1)
Modeling the response of the beam
132(7)
Formulate the solution strategy
139(1)
No axial confinement
140(4)
Beam with axial confinement
144(1)
Statically indeterminate problems / general beam problems
145(4)
Summary
149(1)
Projects
149(2)
Simple Problems
151(28)
Rehabilitation of a crane girder
153(5)
Passive Damping of a frame structure using superelastic shape memory alloys (SMA) bracings
158(21)
Modeling the material response
160(4)
Modeling the SMA braced frame
164(6)
Dynamic analysis of the SMA braced system
170(1)
Simulation studies
171(6)
INELASTICITY OF CONTINUA
Small Deformations
177(2)
Introduction to Small Deformation Plasticity
179(34)
An example task
181(1)
The J2 rigid-plasticity model
182(8)
3-D kinematics
182(1)
3-D equations of motion
183(1)
Constitutive laws: The J2 rigid plasticity equations
183(4)
Standard form for rigid plastic (Kuhn-Tucker form)
187(1)
Example problems
188(2)
The J2 elasto-plasticity model
190(11)
The value of Ø and the ``tangent modulus''
194(6)
Non-dimensionalization
200(1)
Hardening and the plastic are length
201(5)
Definition of hardening, softening and perfectly plastic behavior
201(5)
Finding the response of the material
206(3)
Finding the tangent modulus
207(2)
Summary
209(2)
Projects
211(1)
Homework
211(2)
The Boundary Value Problem for J2 Elastoplasticity
213(24)
The governing equations
215(3)
3-D case
215(2)
Compatibility equations
217(1)
Plane problems
218(8)
Plane strain
218(3)
Plane stress
221(5)
The stress function and the equations of compatibility
226(1)
Boundary conditions for the stress function
227(4)
Numerical solution
231(2)
Modifying the MATLAB PDE toolbox to solve elastoplasticity problems
232(1)
Concluding remarks and summary
233(1)
Projects
233(4)
Examples of Other Yield Surfaces: Associative and Non-associative Plasticity
237(28)
The general, small strain elastoplastic model
239(3)
General characteristics of yield surfaces
239(3)
Examples of general yield surfaces
242(7)
Pressure dependent yielding and the strength-differential or S-D effect
242(1)
Three-invariant or isotropic yield functions
242(5)
Anisotropic yield functions
247(2)
Examples of plastic potentials and non-associative flow rules
249(3)
Changes in the size, location and shape of yield surfaces and methods to quantify them
252(10)
Isotropic hardening
256(1)
The Bauschinger effect, the back stress α and certain predictable characteristics of cyclic loading
257(1)
Quadratic yield surface plasticity with kinematic hardening
258(3)
Homogeneous motions and governing differential equations
261(1)
Summary
262(1)
Projects
263(1)
Exercises
264(1)
Thermodynamics of Elasto-plastic Materials: The Central Role of Dissipation
265(54)
Generalization of J2 plasticity: the rationale
267(3)
Foundations of the thermodynamics of continua
270(6)
Governing balance laws for small deformation
270(2)
The macroscopic state variables
272(4)
The entropy and the equation of state
276(5)
Equations of state
277(2)
Heating and working
279(2)
Equivalent forms of the equation of state: Legendre transformations
281(5)
The Helmholtz potential
282(3)
Further transformations: The Gibbs potential
285(1)
The ``heat'' or entropy equation and dissipative processes
286(8)
Results in terms of the Helmholtz potential
288(2)
Generalization of the state variables and obtaining small-strain, continuum versions of spring-dashpot models
290(4)
Constitutive Laws for εp and the satisfaction of the second law
294(3)
Viscoelastic and viscoplastic models
295(1)
Rate independent models without yield criteria
296(1)
The maximum rate of dissipation criterion
297(8)
Graphical understanding of the MRDH
304(1)
Rate-independent plasticity: How to get the yield function and the flow rule by using MRDH
305(4)
The yield function
306(3)
The Bauschinger effect and history dependence
309(7)
A simple model for the Bauschinger effect
312(4)
Summary
316(2)
Homework
318(1)
Numerical Solutions of Boundary Value Problems
319(36)
Background
321(1)
The modeling exercise
322(4)
The mesh-free method
326(13)
Moving least squares approximation
327(7)
Weak form of the balance law
334(3)
Generating and solving the nonlinear algebraic equations
337(2)
Integration of the plastic flow equations
339(7)
Non-dimensionalization and its importance
339(3)
The convex cutting plane algorithm
342(3)
Homogeneous deformation examples
345(1)
Numerical examples of boundary value problems
346(9)
Rod with varying cross-section
346(1)
Plate with a hole subjected to tension
347(6)
INELASTICITY OF CONTINUA
Finite Deformations
353(2)
Summary of Continuum Thermodynamics
355(44)
Overview of kinematics for finite deformation
357(16)
Temporal and spatial gradients of the motion
359(1)
Local motion: Deformation of line, area and volume elements
360(4)
Sequential versus simultaneous action
364(2)
Stretch and rotation
366(7)
Strain measures
373(4)
Dynamics and thermodynamics of motion
377(1)
Dynamics and thermodynamics of motion
377(12)
Thermodynamics or how to avoid creating perpetual motion machines
380(3)
Constitutive equations for thermoelasticity
383(3)
Isotropic elastic materials: Large strain
386(3)
Invariant and objective tensors
389(10)
When is a tensor objective?
393(3)
Other rotating frames
396(1)
Why do we not need to worry about objective rates?
396(3)
Finite Deformation Plasticity
399(56)
Introduction to finite deformation inelasticity
401(4)
The objective of a finite inelasticity constitutive model
403(2)
Classification of different macroscopic inelasticity models
405(2)
Recapitulation of small deformation inelasticity results
407(1)
How to develop a minimalist model for isotropic inelastic materials subject to finite deformation
408(9)
The modeling procedure
410(7)
Dissipative behavior of inelastic materials
417(15)
Isotropic hardening in finite plasticity
430(2)
Loading/unloading criteria and the value of Ø The advantages of strain space yield functions
432(7)
Results in terms of eigenvalues
437(2)
Numerical implementation of the plastic flow equations using the Convex Cutting Plane Algorithm
439(3)
Summary
442(1)
Moving natural states, aka multiplicative decompositions
442(6)
Geometrical significance of Dp
448(1)
The model can be extended to viscoplasticity and other dissipative responses
449(4)
Homework projects and exercises
453(2)
Inelasticity of Single Crystals
455(40)
Why is the study of the plasticity of single crystals important?
457(2)
Crystals and lattice vectors
459(3)
A word regarding our approach
459(1)
Introduction to crystal lattices
460(2)
Lattice deformation and crystallographic slip
462(4)
Deformation and slip of single crystals
466(4)
The Helmholtz potential and equation of state for a crystal
470(2)
Thermomechanical equation of state
472(1)
The dissipation function and constitutive equations for slip
472(11)
Independence of slip systems and other equations for the rate of slip
475(1)
Explicit expressions for the resolved shear stress in terms of the lattice vectors
476(1)
The evolution equation for ai
477(6)
Hardening
483(9)
Phenomenological model of hardening: Single slip
485(1)
Hardening with multiple slip
486(6)
Concluding remarks
492(1)
Exercises and projects
493(2)
Advanced Cases Studies
495(20)
Shot Peening - A Process for Creating Wear Resistant Surfaces
497(4)
Background and problem statement
497(1)
Simplifications and assumptions on modeling the system
498(2)
Sample results of the analysis
500(1)
Equal Channel Angular Extrusion - A Materials Processing Route
501(8)
Background and problem statement
501(2)
Need analysis and specification of the system
503(2)
Embodiment of the model
505(3)
Concluding remarks
508(1)
Modeling of an Aging Face - An Application in Biomechanics
509(6)
Background and problem statement
509(1)
Need analysis and specification of the system
510(1)
Embodiment of the model
511(2)
Concluding remarks
513(2)
Bibliography 515(16)
Index 531