A course on plasticity theory / David J. Steigmann.

Format:

Book

Author/Creator:

Steigmann, David J., author.

Series:

Oxford Series on Materials Modelling

Oxford Series on Materials Modelling ; v.7

Language:

English

Subjects (All):

Plasticity.

Plasticity--Mathematical models.

Physical Description:

1 online resource (209 pages)

Place of Publication:

Oxford, UK : Oxford University Press, [2023]

Summary:

This book seeks to strengthen the foundations of continuum plasticity theory, emphasizing a unifying perspective grounded in the fundamental notion of material symmetry.

Contents:

Cover

Titlepage

Copyright

Dedication

Preface

Contents

1 Preliminaries

1.1 Phenomenology

1.2 Elements of continuum mechanics

2 Brief resumé of nonlinear elasticity theory

2.1 Stress and strain energy

2.2 Conservative problems and potential energy

2.3 The Legendre-Hadamard inequality

2.4 Material symmetry

3 A primer on tensor analysis in three-dimensional space

3.1 Coordinates, bases, vectors, and metrics

3.2 Second-order tensors

3.3 Derivatives and connections

3.4 The Levi-Civita connection

3.5 The curl, Stokes' theorem, and curvature

3.6 Torsion and the Weitzenböck connection

4 Deformation and stress in convected coordinates

4.1 Deformation gradient and strain

4.2 Strain compatibility

4.3 Stress, equations of motion

5 Elastic and plastic deformations

5.1 Elastic-plastic deformation, dislocation density

5.2 Differential-geometric considerations

5.3 Incompatibility of the elastic strain

6 Energy, stress, dissipation, and plastic evolution

6.1 Materially uniform elastic bodies

6.2 Surface dislocations and stress relaxation

6.3 Dissipation due to plastic evolution

6.4 Superposed rigid-body motions

6.5 Yielding and plastic flow

6.6 Crystallinity versus isotropy

6.7 Discontinuous fields

7 Isotropy

7.1 The flow rule

7.2 Von Mises' yield function

7.3 The classical theory for isotropic rigid-plastic materials

7.4 Bingham's model of viscoplasticity

7.4.1 Example: Steady channel flow

7.5 Plane strain of rigid-perfectly plastic materials: Slip-line theory

7.5.1 Stress, equilibrium

7.5.2 Velocity field

7.5.3 Cartesian form of the equations

7.5.4 Further theory for plane strain

7.5.5 Axisymmetric state exterior to a traction-free circular hole

7.6 Anti-plane shear

8 Small-deformation theory.

8.1 The displacement field

8.2 Approximations for small displacement gradients

8.3 The frame-invariant Prandtl-Reuss theory

9 Strain hardening, rate sensitivity, and gradient plasticity

9.1 "Isotropic" hardening

9.2 Rate sensitivity: Viscoplasticity

9.3 Scale effects

9.3.1 Crystalline symmetry

9.3.2 Isotropy

9.4 Scale-dependent yielding

9.5 Gradient plasticity

9.5.1 Energetic response functions

9.5.2 Stress power, balance laws, and dissipation

9.5.3 Example

Solutions to selected problems

Index.

Notes:

Description based on print version record.

Other Format:

Print version: Steigmann, David J. A Course on Plasticity Theory

ISBN:

0-19-198005-6

0-19-288415-8