Ebook: Principles of Hyperplasticity: An Approach to Plasticity Theory Based on Thermodynamic Principles
- Tags: Continuum Mechanics and Mechanics of Materials, Geotechnical Engineering, Engineering Thermodynamics Transport Phenomena, Thermodynamics, Civil Engineering, Numerical and Computational Methods in Engineering
- Year: 2007
- Publisher: Springer-Verlag London
- Edition: 1
- Language: English
- pdf
Principles of Hyperplasticity is concerned with the theoretical modelling of the behaviour of solids which undergo nonlinear and irreversible deformation. The approach to plasticity theory developed here is firmly rooted in thermodynamics, so that the models developed are guaranteed to obey the First and Second Laws. Major emphasis is placed on the use of potentials, and the derivation of constitutive models for irreversible behaviour entirely from two scalar potentials is shown. It is to accentuate this feature that the authors use the term "hyperplasticity", by analogy with the use of "hyperelasticity" in elasticity theory.
The use of potentials has several advantages. First it allows models to be very simply defined, classified and, if necessary, developed. Secondly, by employing Legendre Transformations, it permits dependent and independent variables to be interchanged, making possible different forms of the same model for different applications. Emphasis is also placed on the derivation of incremental response, which is necessary for numerical analysis.
In the later parts of the book the theory is extended to include treatment of rate-dependent materials. A new and powerful concept, in which a single plastic strain is replaced by a plastic strain function, allowing smooth transitions between elastic and plastic behaviour is also introduced.
Illustrated with many examples of models derived within this framework, and including material particularly relevant to the field of geomechanics, this monograph will benefit academic researchers in mechanics, civil engineering and geomechanics and practising geotechnical engineers; it will also interest numerical analysts in engineering mechanics.
Principles of Hyperplasticity is concerned with the theoretical modelling of the behaviour of solids which undergo nonlinear and irreversible deformation. The approach to plasticity theory developed here is firmly rooted in thermodynamics, so that the models developed are guaranteed to obey the First and Second Laws. Major emphasis is placed on the use of potentials, and the derivation of constitutive models for irreversible behaviour entirely from two scalar potentials is shown. It is to accentuate this feature that the authors use the term "hyperplasticity", by analogy with the use of "hyperelasticity" in elasticity theory.
The use of potentials has several advantages. First it allows models to be very simply defined, classified and, if necessary, developed. Secondly, by employing Legendre Transformations, it permits dependent and independent variables to be interchanged, making possible different forms of the same model for different applications. Emphasis is also placed on the derivation of incremental response, which is necessary for numerical analysis.
In the later parts of the book the theory is extended to include treatment of rate-dependent materials. A new and powerful concept, in which a single plastic strain is replaced by a plastic strain function, allowing smooth transitions between elastic and plastic behaviour is also introduced.
Illustrated with many examples of models derived within this framework, and including material particularly relevant to the field of geomechanics, this monograph will benefit academic researchers in mechanics, civil engineering and geomechanics and practising geotechnical engineers; it will also interest numerical analysts in engineering mechanics.
Principles of Hyperplasticity is concerned with the theoretical modelling of the behaviour of solids which undergo nonlinear and irreversible deformation. The approach to plasticity theory developed here is firmly rooted in thermodynamics, so that the models developed are guaranteed to obey the First and Second Laws. Major emphasis is placed on the use of potentials, and the derivation of constitutive models for irreversible behaviour entirely from two scalar potentials is shown. It is to accentuate this feature that the authors use the term "hyperplasticity", by analogy with the use of "hyperelasticity" in elasticity theory.
The use of potentials has several advantages. First it allows models to be very simply defined, classified and, if necessary, developed. Secondly, by employing Legendre Transformations, it permits dependent and independent variables to be interchanged, making possible different forms of the same model for different applications. Emphasis is also placed on the derivation of incremental response, which is necessary for numerical analysis.
In the later parts of the book the theory is extended to include treatment of rate-dependent materials. A new and powerful concept, in which a single plastic strain is replaced by a plastic strain function, allowing smooth transitions between elastic and plastic behaviour is also introduced.
Illustrated with many examples of models derived within this framework, and including material particularly relevant to the field of geomechanics, this monograph will benefit academic researchers in mechanics, civil engineering and geomechanics and practising geotechnical engineers; it will also interest numerical analysts in engineering mechanics.
Content:
Front Matter....Pages i-xxiii
Introduction....Pages 1-11
Classical Elasticity and Plasticity....Pages 13-33
Thermodynamics....Pages 35-51
The Hyperplastic Formalism....Pages 53-75
Elastic and Plastic Models in Hyperplasticity....Pages 77-103
Advanced Plasticity Theories....Pages 105-118
Multisurface Hyperplasticity....Pages 119-131
Continuous Hyperplasticity....Pages 133-158
Applications in Geomechanics: Elasticity and Small Strains....Pages 159-186
Applications in Geomechanics: Plasticity and Friction....Pages 187-210
Rate Effects....Pages 211-239
Behaviour of Porous Continua....Pages 241-262
Convex Analysis and Hyperplasticity....Pages 263-271
Further Topics in Hyperplasticity....Pages 273-300
Concluding Remarks....Pages 301-304
Back Matter....Pages 305-351
Principles of Hyperplasticity is concerned with the theoretical modelling of the behaviour of solids which undergo nonlinear and irreversible deformation. The approach to plasticity theory developed here is firmly rooted in thermodynamics, so that the models developed are guaranteed to obey the First and Second Laws. Major emphasis is placed on the use of potentials, and the derivation of constitutive models for irreversible behaviour entirely from two scalar potentials is shown. It is to accentuate this feature that the authors use the term "hyperplasticity", by analogy with the use of "hyperelasticity" in elasticity theory.
The use of potentials has several advantages. First it allows models to be very simply defined, classified and, if necessary, developed. Secondly, by employing Legendre Transformations, it permits dependent and independent variables to be interchanged, making possible different forms of the same model for different applications. Emphasis is also placed on the derivation of incremental response, which is necessary for numerical analysis.
In the later parts of the book the theory is extended to include treatment of rate-dependent materials. A new and powerful concept, in which a single plastic strain is replaced by a plastic strain function, allowing smooth transitions between elastic and plastic behaviour is also introduced.
Illustrated with many examples of models derived within this framework, and including material particularly relevant to the field of geomechanics, this monograph will benefit academic researchers in mechanics, civil engineering and geomechanics and practising geotechnical engineers; it will also interest numerical analysts in engineering mechanics.
Content:
Front Matter....Pages i-xxiii
Introduction....Pages 1-11
Classical Elasticity and Plasticity....Pages 13-33
Thermodynamics....Pages 35-51
The Hyperplastic Formalism....Pages 53-75
Elastic and Plastic Models in Hyperplasticity....Pages 77-103
Advanced Plasticity Theories....Pages 105-118
Multisurface Hyperplasticity....Pages 119-131
Continuous Hyperplasticity....Pages 133-158
Applications in Geomechanics: Elasticity and Small Strains....Pages 159-186
Applications in Geomechanics: Plasticity and Friction....Pages 187-210
Rate Effects....Pages 211-239
Behaviour of Porous Continua....Pages 241-262
Convex Analysis and Hyperplasticity....Pages 263-271
Further Topics in Hyperplasticity....Pages 273-300
Concluding Remarks....Pages 301-304
Back Matter....Pages 305-351
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