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Produktbild: Functional and Numerical Methods in Viscoplasticity

Functional and Numerical Methods in Viscoplasticity

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

08.07.1993

Abbildungen

line figures

Verlag

Oxford Academic

Seitenzahl

284

Maße (L/B/H)

24,1/16/2,2 cm

Gewicht

608 g

Sprache

Englisch

ISBN

978-0-19-853590-4

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

08.07.1993

Abbildungen

line figures

Verlag

Oxford Academic

Seitenzahl

284

Maße (L/B/H)

24,1/16/2,2 cm

Gewicht

608 g

Sprache

Englisch

ISBN

978-0-19-853590-4

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: Functional and Numerical Methods in Viscoplasticity


    • 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