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El. knyga: Continuum Mechanics and Theory of Materials

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  • Formatas: PDF+DRM
  • Serija: Advanced Texts in Physics
  • Išleidimo metai: 14-Mar-2013
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Kalba: eng
  • ISBN-13: 9783662047750
  • Formatas: PDF+DRM
  • Serija: Advanced Texts in Physics
  • Išleidimo metai: 14-Mar-2013
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Kalba: eng
  • ISBN-13: 9783662047750

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The new edition includes additional analytical methods in the classical theory of viscoelasticity. This leads to a new theory of finite linear viscoelasticity of incompressible isotropic materials. Anisotropic viscoplasticity is completely reformulated and extended to a general constitutive theory that covers crystal plasticity as a special case.



This treatise attempts to portray the ideas and general principles of the theory of materials within the framework of phenomenological continuum mechanics. It is a well-written mathematical introduction to classical continuum mechanics and deals with concepts such as elasticity, plasticity, viscoelasticity and viscoplasticity in nonlinear materials. The aim of a general theory of material behaviour is to provide a classified range of possibilities from which a user can select the constitutive model that applies best. The book will be invaluable to graduate students of materials science in engineering and in physics.

Recenzijos

"The author, a well-known expert in the field, contributed important suggestions on endochronic models, finite viscoelasticity, plasticity, polymer mechanics, and many other topics. He certainly has a broad overview over current problems and issues in material theory. At the same time, Haupt is a talented and experienced teacher, giving clear and comprehensive introductions into such complex theories as plasticity and viscoplasticity, both still far from being well-established textbook knowledge. The outcome is a careful introduction into material theory, and a detailed presentation of numerous different suggestions of some novelty. The book is therefore recommendable not only for students with some background in tensor calculus and continuum mechanics, but also for advanced researchers and engineers in the field, who will surely find fruitful stimulations when reading this rich source of material theory." (Zentralblatt Mathematik, 2000)



"In striving toward the encyclopedic, Haupt employs a full arsenal of geometric tools, from curvilinear coordinates to several different strain tensors for both the spatial and material formulations. The emphasis throughout is on the mechanics of solids." (SIAM Review, 44/1, 2002)

Daugiau informacijos

2nd edition
Introduction 1(6)
Kinematics
7(68)
Material Bodies
7(12)
Material and Spatial Representation
19(4)
Deformation Gradient
23(9)
Strain Tensors
32(6)
Convective Coordinates
38(4)
Velocity Gradient
42(4)
Strain Rate Tensors
46(4)
Strain Rates in Convective Coordinates
50(3)
Geometric Linearisation
53(4)
Incompatible Configurations
57(18)
Euclidean Space
58(5)
Non-Euclidean Spaces
63(1)
Conditions of Compatibility
64(11)
Balance Relations of Mechanics
75(44)
Preliminary Remarks
75(3)
Mass
78(6)
Balance of Mass: Global Form
78(1)
Balance of Mass: Local Form
79(5)
Linear Momentum and Rotational Momentum
84(20)
Balance of Linear Momentum and Rotational Momentum: Global Formulation
84(6)
Stress Tensors
90(5)
Stress Tensors in Convective Coordinates
95(1)
Local Formulation of the Balance of Linear Momentum and Rotational Momentum
95(6)
Initial and Boundary Conditions
101(3)
Conclusions from the Balance Equations of Mechanics
104(15)
Balance of Mechanical Energy
105(4)
The Principle of d'Alembert
109(5)
Principle of Virtual Work
114(1)
Incremental Form of the Principle of d'Alembert
115(4)
Balance Relations of Thermodynamics
119(36)
Preliminary Remarks
119(1)
Energy
120(5)
Temperature and Entropy
125(5)
Initial and Boundary Conditions
130(2)
Balance Relations for Open Systems
132(21)
Transport Theorem
132(3)
Balance of Linear Momentum for Systems with Time-Dependent Mass
135(2)
Balance Relations: Conservation Laws
137(3)
Discontinuity Surfaces and Jump Conditions
140(4)
Multi-Component Systems (Mixtures)
144(9)
Summary: Basic Relations of Thermomechanics
153(2)
Objectivity
155(22)
Frames of Reference
155(1)
Affine Spaces
156(3)
Change of Frame: Passive Interpretation
159(3)
Change of Frame: Active Interpretation
162(2)
Objective Quantities
164(7)
Observer-Invariant Relations
171(6)
Classical Theories of Continuum Mechanics
177(74)
Introduction
177(1)
Elastic Fluid
178(4)
Linear-Viscous Fluid
182(3)
Linear-Elastic Solid
185(3)
Linear-Viscoelastic Solid
188(39)
Perfectly Plastic Solid
227(4)
Plasticity with Hardening
231(12)
Viscoplasticity with Elastic Range
243(6)
Remarks on the Classical Theories
249(2)
Experimental Observation and Mathematical Modelling
251(24)
General Aspects
251(4)
Information from Experiments
255(14)
Material Properties of Steel XCrNi 18.9
255(8)
Material Properties of Carbon-Black-Filled Elastomers
263(6)
Four Categories of Material Behaviour
269(2)
Four Theories of Material Behaviour
271(2)
Contribution of the Classical Theories
273(2)
General Theory of Mechanical Material Behaviour
275(42)
General Principles
275(4)
Constitutive Equations
279(14)
Simple Materials
279(4)
Reduced Forms of the General Constitutive Equation
283(5)
Simple Examples of Material Objectivity
288(1)
Frame-Indifference and Observer-Invariance
289(4)
Properties of Material Symmetry
293(12)
The Concept of the Symmetry Group
293(5)
Classification of Simple Materials into Fluids and Solids
298(7)
Kinematic Conditions of Internal Constraint
305(6)
General Theory
305(3)
Special Conditions of Internal Constraint
308(3)
Formulation of Material Models
311(6)
General Aspects
311(1)
Representation by Means of Functionals
312(1)
Representation by Means of Internal Variables
313(2)
Comparison
315(2)
Dual Variables
317(28)
Tensor-Valued Evolution Equations
317(12)
Introduction
317(2)
Objective Time Derivatives of Objective Tensors
319(3)
Example: Maxwell Fluid
322(3)
Example: Rigid-Plastic Solid with Hardening
325(4)
The Concept of Dual Variables
329(16)
Motivation
329(2)
Strain and Stress Tensors (Summary)
331(3)
Dual Variables and Derivatives
334(11)
Elasticity
345(52)
Elasticity and Hyperelasticity
345(7)
Isotropic Elastic Bodies
352(24)
General Constitutive Equation for Elastic Fluids and Solids
352(6)
Isotropic Hyperelastic Bodies
358(5)
Incompressible Isotropic Elastic Materials
363(2)
Constitutive Equations of Isotropic Elasticity (Examples)
365(11)
Anisotropic Hyperelastic Solids
376(21)
Approximation of the General Constitutive Equation
376(3)
General Representation of the Strain Energy Function
379(9)
Physical Linearisation
388(9)
Viscoelasticity
397(38)
Representation by Means of Functionals
397(22)
Rate-Dependent Functionals with Fading Memory Properties
398(12)
Continuity Properties and Approximations
410(9)
Representation by Means of Internal Variables
419(16)
General Concept
419(7)
Internal Variables of the Strain Type
426(7)
A General Model of Finite Viscoelasticity
433(2)
Plasticity
435(40)
Rate-Independent Functionals
435(9)
Representation by Means of Internal Variables
444(6)
Elastoplasticity
450(25)
Preliminary Remarks
450(4)
Stress-Free Intermediate Configuration
454(5)
Isotropic Elasticity
459(1)
Yield Function and Evolution Equations
460(3)
Consistency Condition
463(12)
Viscoplasticity
475(34)
Preliminary Remarks
475(2)
Viscoplasticity with Elastic Domain
477(7)
A General Constitutive Model
477(3)
Application of the Intermediate Configuration
480(4)
Plasticity as a Limit Case of Viscoplasticity
484(15)
The Differential Equation of the Yield Function
484(5)
Relaxation Property
489(2)
Slow Deformation Processes
491(6)
Elastoplasticity and Arclength Representation
497(2)
A Concept for General Viscoplasticity
499(10)
Motivation
499(1)
Equilibrium Stress and Overstress
500(1)
An Example of General Viscoplasticity
501(6)
Conclusions Regarding the Modelling of Mechanical Material Behaviour
507(2)
Constitutive Models in Thermomechanics
509(110)
Thermomechanical Consistency
509(5)
Thermoelasticity
514(16)
General Theory
514(6)
Thermoelastic Fluid
520(7)
Linear-Thermoelastic Solids
527(3)
Thermoviscoelasticity
530(24)
General Concept
530(7)
Thermoelasticity as a Limit Case of Thermoviscoelasticity
537(4)
Internal Variables of Strain Type
541(4)
Incorporation of Anisotropic Elasticity Properties
545(1)
Incompressible Materials: An Extension of the Mooney-Rivlin Model to Thermoviscoelasticity
545(9)
Thermoviscoplasticity with Elastic Domain
554(23)
Uniaxial Viscoplasticity
554(6)
General Concept
560(4)
Application of the Intermediate Configuration
564(4)
Thermoplasticity as a Limit Case of Thermoviscoplasticity
568(9)
General Thermoviscoplasticity
577(9)
Small Deformations
578(3)
Finite Deformations
581(4)
Conclusion
585(1)
Anisotropic Material Properties
586(5)
Motivation
586(1)
Axes of Elastic Anisotropy
587(4)
Anisotropic Viscoplasticity
591(28)
General Considerations
591(2)
Free Energy Function
593(3)
Evolution Equations
596(7)
Lattice Spin
603(3)
Summary: A Constitutive Model of Anisotropic Viscoplasticity
606(2)
Numerical Simulations
608(10)
Closing Remark
618(1)
References 619(16)
Index 635