Ioan R Ionescu, Mircea Sofonea

Functional and Numerical Methods in Viscoplasticity

• Gebundenes Buch

Produktbeschreibung

This book studies problems of viscoplasticity using various and different mathematical methods. The mathematical results obtained are carefully interpreted from a mechanical point of view. The theory is developed to deal with numerical results from practical problems in industry and technology.

Produktdetails

• Verlag: McGraw Hill LLC
• Seitenzahl: 284
• Erscheinungstermin: 8. Juli 1993
• Englisch
• Abmessung: 241mm x 160mm x 22mm
• Gewicht: 608g
• ISBN-13: 9780198535904
• ISBN-10: 0198535902
• Artikelnr.: 24489850

Inhaltsangabe

* Chapter 1. Preliminaries on Mechanics of Continuous Media
* 1: Kinematics of continuous media
* 1.1: Material and spatial description
* 1.2: Deformation and strain tensors
* 1.3: The rate of deformation tensor
* 2: Balance laws and stress tensors
* 2.1: The balance law of mass
* 2.2: The balance law of momentum
* 2.3: The Cauchy stress tensor
* 2.4: The Piola-Kirchhoff stress tensors and the linearized theory
* 3: Some experiments and models for solids
* 3.1: Standard tests and elastic laws
* 3.2: Loading and unloading tests. Plastic laws
* 3.3: Long-range tests and viscoplastic laws
* Bibliographical notes
* Chapter 2. Functional Spaces in Viscoplasticity
* 1: Functional spaces of scalar-valued functions
* 1.1: Test functions, distributions, and L* spaces
* 1.2: Sobolev spaces of integer order
* 2: Functional spaces attached to some linear differential operators
of first order
* 2.1: Linear differential operators of first order
* 2.2: Functional spaces associated with the deformation operator
* 2.3: A Hilbert space associated with the divergence operator
* 3: Functional spaces of vector-valued functions defined on real
intervals
* 3.1: Weak and strong measurability and L* spaces
* 3.2: Absolutely continuous vectorial functions and A** spaces
* 3.3: Vectorial distributions and W** spaces
* Bibliographical notes
* Chapter 3. Quasistatic Processes for Rate-Type Viscoplastic Materials
* 1: Discussion of a quasistatic elastic-viscoplastic problem
* 1.1: Rate-type constitutive equations
* 1.2: Statement of the problems
* 1.3: An existence and uniqueness result
* 1.4: The dependence of the solution upon the input data
* 2: Behaviour of the solution in the viscoelastic case
* 2.1: Asymptotic stability
* 2.2: Periodic solutions
* 2.3: An approach to elasticity
* 2.4: Long-term behaviour of the solution
* 3: An approach to perfect plasticity
* 3.1: A convergence result
* 3.2: Quasistatic processes in perfect plasticity
* 3.3: Some 'pathological' examples
* 4A numerical approach
* 4.1: Error estimates over a finite time interval
* 4.2: Error estimation over an infinite time interval in the
viscoelastic case
* 4.3: Numerical examples
* 5: Quasistatic processes for rate-type viscoplastic materials with
internal state variables
* 5.1: Rate-type constituve equations with internal state variables
* 5.2: Problem statement
* 5.3: Existence, uniqueness, and continuous dependence of the
solutions
* 5.4: A numerical approach
* 6: An application to a mining engineering problem
* 6.1: Constitutive assumptions and material constants
* 6.2: Boundary conditiions and initial data
* 6.3: Numerical results
* 6.4: Failure
* Bibliographical notes
* Chapter 4. Dynamic Processes for Rate-Type Elastic-Viscoplastic
Materials
* 1: Discussion of a dynamic elastic-viscoplastic problem
* 1.1: Problem statement
* 1.2: An existence and uniqueness result
* 1.3: The dependence of the solution upon the input data
* 1.4: Weak solutions
* 2: The behaviour of the solution in the viscoelastic case
* 2.1: The energy function
* 2.2: An energy bound for isolated bodies
* 2.3: An approach to linear elasticity
* 3: An approach to perfect plasticity
* 3.1: A convergence result
* 3.2: Dynamic processes in perfect plasticity
* 4: Dynamic processes for rate-type elastic-viscoplastic materials
with internal state variables
* 4.1: Problem statement and constitutive assumptions
* 4.2: Existence, uniqueness and continuous dependence of the solution
* 4.3: A local existence result
* 5: Other functional methods in the study of dynamic problems
* 5.1: Monotony methods
* 5.2: A fixed point method
* 6: Perturbations of homogeneous simple shear and strain localization
* 6.1: Problem statement
* 6.2: Existence and uniqueness of smooth solutions
* 6.3: Perturbations of the homogeneous solutions
* 6.4: Numerical results
* Bibliographical notes
* Chapter 5. The Flow of the Bingham Fluid with Friction
* 1: Boundary value problems for the Bingham fluid with friction
* 1.1: The constitutive equations of the Bingham fluid
* 1.2: Statement of the problems and friction laws
* 1.3: An existence and uniqueness result in the local friction law
case
* 1.4: An existence result in the non-local friction law case
* 2: The blocking property of the solution
* 2.1: Problem statements and blocking property
* 2.2: The blocking property for abstract variational inequalities
* 2.3: The blocking property in the case without friction
* 2.4: The blocking property in the case with friction
* 3: A numerical approach
* 3.1: The penalized problem
* 3.2: The discrete and regularized problem
* 3.3: A Newton iterative method
* 3.4: An application to the wire drawing problem
* Bibliographical notes
* Appendix
* 1: Elements of linear analysis
* 1.1: Normed linear spaces and linear operators
* 1.2: Duality and weak topologies
* 1.3: Hilbert spaces
* 2: Elements of non-linear analysis
* 2.1: Convex functions
* 2.2: Elliptic variational inequalities
* 2.3: Maximal monotone operators in Hilbert spaces
* 3: Evolution equations in Banach spaces
* 3.1: Ordinary differential equations in Banach spaces
* 3.2: Linear evolution equations
* 3.3: Lipschitz perturbation of linear evolution equations
* 3.4: Non-linear evolution equations in Hilbert spaces
* 4: Some numerical methods and complements
* 4.1: Numerical methods for elliptic problems
* 4.2: Euler's methods for ordinary differential equations in Hilbert
spaces
* 4.3: A numerical method for non-linear evolution equation
* 4.4: Some technical results
* Bibliographical notes
* References