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Elastodynamics. Sinusoidal progressive waves

Lallit Anand and Sanjay Govindjee

in Continuum Mechanics of Solids

Published in print:
2020
Published Online:
September 2020
ISBN:
9780198864721
eISBN:
9780191896767
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198864721.003.0013
Subject:
Physics, Condensed Matter Physics / Materials

This chapter briefly considers linear elasticity under circumstances in which inertial effects are accounted for, and states the initial-boundary-value-problem of linear elastodynamics. Sinusoidal ... More


Small deformation rate-independent plasticity based on a postulate of maximum dissipation

Lallit Anand and Sanjay Govindjee

in Continuum Mechanics of Solids

Published in print:
2020
Published Online:
September 2020
ISBN:
9780198864721
eISBN:
9780191896767
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198864721.003.0023
Subject:
Physics, Condensed Matter Physics / Materials

This chapter introduces the concept of maximum dissipation. The elastic set is introduced, and the plastic dissipation is maximized over the elastic set using classical methods from linear ... More


Limits to elastic response. Yielding and failure

Lallit Anand and Sanjay Govindjee

in Continuum Mechanics of Solids

Published in print:
2020
Published Online:
September 2020
ISBN:
9780198864721
eISBN:
9780191896767
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198864721.003.0019
Subject:
Physics, Condensed Matter Physics / Materials

This chapter presents conditions for determining the limits of elastic behaviour for isotropic materials. The stress invariants of equivalent pressure, equivalent shear stress, and equivalent tensile ... More


The Modern Object I

Thomas Nail

in Theory of the Object

Published in print:
2021
Published Online:
May 2022
ISBN:
9781474487924
eISBN:
9781399509749
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9781474487924.003.0014
Subject:
Philosophy, General

Modern objects followed a predominantly elastic pattern of motion. This chapter and the next show how this shared pattern of movement emerged historically among several modern sciences: the ... More


The Modern Object II

Thomas Nail

in Theory of the Object

Published in print:
2021
Published Online:
May 2022
ISBN:
9781474487924
eISBN:
9781399509749
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9781474487924.003.0015
Subject:
Philosophy, General

This chapter continues the discussion from the last by looking closely at two more significant sciences that shaped the modern object’s elastic structure: digital logic and transcendental ... More


Tensors and physical properties

Robert E. Newnham

in Properties of Materials: Anisotropy, Symmetry, Structure

Published in print:
2004
Published Online:
November 2020
ISBN:
9780198520757
eISBN:
9780191916601
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198520757.003.0007
Subject:
Earth Sciences and Geography, Geochemistry

In this chapter we introduce the tensor description of physical properties along with Neumann’s Principle relating symmetry to physical properties. As pointed out in the introduction, many ... More


Pyroelectricity

Robert E. Newnham

in Properties of Materials: Anisotropy, Symmetry, Structure

Published in print:
2004
Published Online:
November 2020
ISBN:
9780198520757
eISBN:
9780191916601
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198520757.003.0010
Subject:
Earth Sciences and Geography, Geochemistry

As the name implies, pyroelectricity is a first rank tensor property relating a change polarization P to a change in temperature δT. The defining relation can also be written in terms of the ... More


Elasticity

Robert E. Newnham

in Properties of Materials: Anisotropy, Symmetry, Structure

Published in print:
2004
Published Online:
November 2020
ISBN:
9780198520757
eISBN:
9780191916601
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198520757.003.0015
Subject:
Earth Sciences and Geography, Geochemistry

All solids change shape under mechanical force. Under small stresses, the strain x is related to stress X by Hooke’s Law (x) = (s)(X), or the converse relationship (X) = (c)(x). The elastic ... More


Nonlinear phenomena

Robert E. Newnham

in Properties of Materials: Anisotropy, Symmetry, Structure

Published in print:
2004
Published Online:
November 2020
ISBN:
9780198520757
eISBN:
9780191916601
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198520757.003.0017
Subject:
Earth Sciences and Geography, Geochemistry

The physical properties discussed thus far are linear relationships between two measured quantities. This is only an approximation to the truth, and often not a very good approximation, especially ... More


Acoustic waves II

Robert E. Newnham

in Properties of Materials: Anisotropy, Symmetry, Structure

Published in print:
2004
Published Online:
November 2020
ISBN:
9780198520757
eISBN:
9780191916601
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198520757.003.0026
Subject:
Earth Sciences and Geography, Geochemistry

Acoustic impedance, acoustic losses, acoustic waves in piezoelectric solids, and surface waves are discussed in this chapter, along with a number of nonlinear acoustic phenomena. The reflection and ... More


Crystal optics

Robert E. Newnham

in Properties of Materials: Anisotropy, Symmetry, Structure

Published in print:
2004
Published Online:
November 2020
ISBN:
9780198520757
eISBN:
9780191916601
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198520757.003.0027
Subject:
Earth Sciences and Geography, Geochemistry

Calcite (CaCO3) is a beautiful transparent mineral that readily cleaves into rhombohedra. Images viewed through a thin slice of a cleaved calcite crystal are split into two images, an effect known ... More


Photoelasticity and acousto-optics

Robert E. Newnham

in Properties of Materials: Anisotropy, Symmetry, Structure

Published in print:
2004
Published Online:
November 2020
ISBN:
9780198520757
eISBN:
9780191916601
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198520757.003.0029
Subject:
Earth Sciences and Geography, Geochemistry

The change in refractive indices with mechanical stress, the photoelastic effect, is used in analyzing stress patterns in engineering components of complicated shape. It is also important in ... More


Metamaterials

Adrian P Sutton

in Concepts of Materials Science

Published in print:
2021
Published Online:
September 2021
ISBN:
9780192846839
eISBN:
9780191938764
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192846839.003.0010
Subject:
Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

Metamaterials are composites that have extended the concept of a material. They derive their properties from strong coupling between carefully designed and positioned structural units within them and ... More


Elastic Surfaces

Troy Shinbrot

in Biomedical Fluid Dynamics: Flow and Form

Published in print:
2019
Published Online:
June 2019
ISBN:
9780198812586
eISBN:
9780191850721
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198812586.003.0002
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

In this chapter, the effects of elasticity are overviewed, the Young–Laplace equation is introduced, and the importance of nondimensionalization is emphasized. Topics covered include the ... More


Flow through Elastic Tubes

Troy Shinbrot

in Biomedical Fluid Dynamics: Flow and Form

Published in print:
2019
Published Online:
June 2019
ISBN:
9780198812586
eISBN:
9780191850721
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198812586.003.0003
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Fluids equations from Chapter 1 and elasticity equations from Chapter 2 are combined to establish how flow through elastic tubes (as in the vasculature) must occur. Unstable versus stable flows are ... More


Intermolecular Effects: I. The Constrained-Junction Model

Burak Erman and James E. Mark

in Structures and Properties of Rubberlike Networks

Published in print:
1997
Published Online:
November 2020
ISBN:
9780195082371
eISBN:
9780197560433
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195082371.003.0005
Subject:
Chemistry, Materials Chemistry

The classical theories of rubber elasticity presented in chapter 2 are based on a hypothetical chain which may pass freely through its neighbors as well as through itself. In a real chain, however, ... More


Swelling of Networks

Burak Erman and James E. Mark

in Structures and Properties of Rubberlike Networks

Published in print:
1997
Published Online:
November 2020
ISBN:
9780195082371
eISBN:
9780197560433
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195082371.003.0008
Subject:
Chemistry, Materials Chemistry

In the preceding chapter, the stress-strain behavior of networks was described for the case where the swollen network was assumed to be a thermodynamically closed system (such that solvent ... More


Line Dislocation Dynamics

Vasily Bulatov and Wei Cai

in Computer Simulations of Dislocations

Published in print:
2006
Published Online:
November 2020
ISBN:
9780198526148
eISBN:
9780191916618
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198526148.003.0015
Subject:
Computer Science, Software Engineering

In the preceding chapters we have discussed several computational approaches focused on the structure and motion of single dislocations. Here we turn our attention to collective motion of many ... More


Phase Field Method

Vasily Bulatov and Wei Cai

in Computer Simulations of Dislocations

Published in print:
2006
Published Online:
November 2020
ISBN:
9780198526148
eISBN:
9780191916618
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198526148.003.0016
Subject:
Computer Science, Software Engineering

The phase field method (PFM) can be used as an approach to dislocation dynamics simulations alternative to the line DD method discussed in Chapter 10. The degrees of freedom in PFM are continuous ... More


Fundamentals of Composite Elastic Properties

Dale Chimenti, Stanislav Rokhlin, and Peter Nagy

in Physical Ultrasonics of Composites

Published in print:
2011
Published Online:
November 2020
ISBN:
9780195079609
eISBN:
9780197560389
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195079609.003.0005
Subject:
Chemistry, Industrial Chemistry

In this chapter, we review the mechanical behavior of composites considered from a macroscopic perspective, i.e., the microscopic heterogeneity of the material is ignored in this treatment. Our ... More


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