Thermoelastic-plastic flow equations in general coordinates

Blaschke, Daniel N.; Preston, Dean L.

doi:10.1016/j.jpcs.2018.03.026

Title: Thermoelastic-plastic flow equations in general coordinates

Abstract

The equations governing the thermoelastic-plastic flow of isotropic solids in the Prandtl- Reuss and small anisotropy approximations in Cartesian coordinates are generalized to arbitrary coordinate systems. In applications the choice of coordinates is dictated by the symmetry of the solid flow. Here, the generally invariant equations are evaluated in spherical, cylindrical (including uniaxial), and both prolate and oblate spheroidal coordinates.

Authors:

Blaschke, Daniel N. ^[1]; Preston, Dean L. ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: Wed Mar 28 00:00:00 EDT 2018

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1431061

Alternate Identifier(s):: OSTI ID: 1548524

Report Number(s):: LA-UR-16-24560
Journal ID: ISSN 0022-3697; TRN: US1802436

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Physics and Chemistry of Solids

Additional Journal Information:: Journal Volume: 119; Journal ID: ISSN 0022-3697

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats


                    Blaschke, Daniel N., and Preston, Dean L. Thermoelastic-plastic flow equations in general coordinates.  United States: N. p., 2018. 
Web.  doi:10.1016/j.jpcs.2018.03.026.

Copy to clipboard


                    Blaschke, Daniel N., & Preston, Dean L. Thermoelastic-plastic flow equations in general coordinates.  United States.  https://doi.org/10.1016/j.jpcs.2018.03.026

Copy to clipboard


                    Blaschke, Daniel N., and Preston, Dean L. Wed .  
"Thermoelastic-plastic flow equations in general coordinates".  United States.  https://doi.org/10.1016/j.jpcs.2018.03.026.  https://www.osti.gov/servlets/purl/1431061.

Copy to clipboard


                    
@article{osti_1431061,

  title        = {Thermoelastic-plastic flow equations in general coordinates},

  author       = {Blaschke, Daniel N. and Preston, Dean L.},

  abstractNote = {The equations governing the thermoelastic-plastic flow of isotropic solids in the Prandtl- Reuss and small anisotropy approximations in Cartesian coordinates are generalized to arbitrary coordinate systems. In applications the choice of coordinates is dictated by the symmetry of the solid flow. Here, the generally invariant equations are evaluated in spherical, cylindrical (including uniaxial), and both prolate and oblate spheroidal coordinates.},

  doi          = {10.1016/j.jpcs.2018.03.026},

  journal      = {Journal of Physics and Chemistry of Solids},

  number       = ,

  volume       = 119,

  place        = {United States},

  year         = {Wed Mar 28 00:00:00 EDT 2018},

  month        = {Wed Mar 28 00:00:00 EDT 2018}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1016/j.jpcs.2018.03.026

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 3 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

The energy–momentum tensor(s) in classical gauge theories
journal, November 2016

Blaschke, Daniel N.; Gieres, François; Reboud, Méril
Nuclear Physics B, Vol. 912
DOI: 10.1016/j.nuclphysb.2016.07.001

An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields
journal, January 2007

Monchiet, Vincent; Charkaluk, Eric; Kondo, Djimedo
Comptes Rendus Mécanique, Vol. 335, Issue 1
DOI: 10.1016/j.crme.2006.12.002

Zur Theorie plastischer Deformationen und der hierdurch im Material hervorgerufenen Nachspannungen
journal, January 1924

Hencky, Heinrich
ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 4, Issue 4
DOI: 10.1002/zamm.19240040405

A dislocation-based multi-rate single crystal plasticity model
journal, May 2013

Hansen, B. L.; Beyerlein, I. J.; Bronkhorst, C. A.
International Journal of Plasticity, Vol. 44
DOI: 10.1016/j.ijplas.2012.12.006

Constitutive Equations for Rate-Dependent Plasticity
journal, August 1985

Swearengen, J. C.; Lowe, T. C.; Lipkin, J.
Annual Review of Materials Science, Vol. 15, Issue 1
DOI: 10.1146/annurev.ms.15.080185.001341

Second order effects in the theory of plasticity
journal, March 1969

Freudenthal, A. M.; Gou, P. F.
Acta Mechanica, Vol. 8, Issue 1-2
DOI: 10.1007/BF01178532

On second-order strain accumulation in aluminum in reversed cyclic torsion at elevated temperatures
journal, March 1967

Ronay, Maria
International Journal of Solids and Structures, Vol. 3, Issue 2
DOI: 10.1016/0020-7683(67)90066-2

Berücksichtigung der elastischen Formänderung in der Plastizitätstheorie
journal, January 1930

Reuss, A.
ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 10, Issue 3
DOI: 10.1002/zamm.19300100308

Shock compression of solids
journal, October 1979

Davison, Lee; Graham, R. A.
Physics Reports, Vol. 55, Issue 4
DOI: 10.1016/0370-1573(79)90026-7

Review of experimental techniques for high rate deformation and shock studies
journal, August 2004

Field, J. E.; Walley, S. M.; Proud, W. G.
International Journal of Impact Engineering, Vol. 30, Issue 7
DOI: 10.1016/j.ijimpeng.2004.03.005

Revisiting shock waves in metals
journal, February 1997

Chitanvis, S. M.
Shock Waves, Vol. 7, Issue 1
DOI: 10.1007/s001930050062

Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media
journal, January 1977

Gurson, A. L.
Journal of Engineering Materials and Technology, Vol. 99, Issue 1
DOI: 10.1115/1.3443401

Approximate models for ductile metals containing non-spherical voids—Case of axisymmetric prolate ellipsoidal cavities
journal, November 1993

Gologanu, Mihai; Leblond, Jean-Baptiste; Devaux, Josette
Journal of the Mechanics and Physics of Solids, Vol. 41, Issue 11
DOI: 10.1016/0022-5096(93)90029-F

An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields
journal, January 2007

Monchiet, Vincent; Charkaluk, Eric; Kondo, Djimedo
Comptes Rendus Mécanique, Vol. 335, Issue 1
DOI: 10.1016/j.crme.2006.12.002

A multi-surface plasticity model for ductile fracture simulations
journal, June 2017

Keralavarma, Shyam M.
Journal of the Mechanics and Physics of Solids, Vol. 103
DOI: 10.1016/j.jmps.2017.03.005

The energy–momentum tensor(s) in classical gauge theories
journal, November 2016

Blaschke, Daniel N.; Gieres, François; Reboud, Méril
Nuclear Physics B, Vol. 912
DOI: 10.1016/j.nuclphysb.2016.07.001

Finite Deformations of an Elastic Solid
journal, April 1937

Murnaghan, F. D.
American Journal of Mathematics, Vol. 59, Issue 2
DOI: 10.2307/2371405

The Heat Developed during Plastic Extension of Metals
journal, March 1925

Farren, W. S.; Taylor, G. I.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 107, Issue 743
DOI: 10.1098/rspa.1925.0034

The stored energy of cold work
journal, January 1958

Titchener, A. L.; Bever, M. B.
Progress in Metal Physics, Vol. 7
DOI: 10.1016/0502-8205(58)90006-6

Irreversible thermodynamics of flow in solids
journal, August 1980

Wallace, Duane C.
Physical Review B, Vol. 22, Issue 4
DOI: 10.1103/PhysRevB.22.1477

Similar Records in DOE PAGES and OSTI.GOV collections:

Internal variable theory of plasticity based on dislocation mechanics

Technical Report Werne, R W

Using the internal variable theory of material behavior, a theory of plasticity for polycrystalline solids has been developed. Assuming that the motion of a dislocation flux is the primary cause of plastic flow, the average mobile and immobile dislocation density tensors and the dislocation velocity vector are chosen as the internal variables. By decomposing the deformation gradient into its elastic and plastic components, the dislocation density tensor is expressed in terms of the plastic deformation gradient. Similarly, the rate of plastic deformation tensor is expressed as a function of the mobile dislocation density tensor and the dislocation velocity vector. Formore »« less
Iterative methods applied to matrix equations found in calculating spheroidal functions

Journal Article Brown, D J ; Stringfield, R M - Journal of Computational Physics

The authors looked at iterative methods for solving matrix equations, particularly those matrices with small entries. Iterative methods aid computational stability by relying on the topological structure of Banach or Hilbert spaces rather than depending on a calculation's numerical precision. When applicable, they are also quicker than Gaussian elimination. As an example, the authors used these methods to tabulate the expansion of periodic spheroidal functions in associated Legendre functions, given arbitrary values of the parameters appearing in its defining differential equation. These functions appear in solutions to 3-D Helmholtz equations in oblate and prolate spheroidal coordinates as well as amore » 1-D Schroedinger equation.« less
https://doi.org/10.1006/jcph.2000.6448
Thermally induced vibrations in a generalized thermoelastic solid with a cavity

Journal Article Erbay, H A ; Erbay, S ; Dost, S - Journal of Thermal Stresses; (United States)

The present work deals with thermally induced vibrations in an infinite solid with a cavity. The medium is assumed to be linear, isotropic, temperature-rate-dependent thermoelastic. The problem is solved for the cases of cylindrical and spherical cavities. The surface of the cavity is assumed to be subjected to a temperature varying harmonically with time, and free of stress. For the cases considered, the coupled field equations admit exact solutions in terms of Hankel and the spherical Hankel functions, respectively. Numerical results are compared with those of classical thermoelasticity. The contribution of the second sound parameters in these problems becomes moremore »« less
https://doi.org/10.1080/01495739108927059
Cuboidal Liquid Crystal Phases Under Multiaxial Geometrical Frustration.

Journal Article Palacio-Betancur, Viviana ; Armas-Perez, Julio C. ; Villada-Gil, Stiven ; ... - Soft Matter

Cuboidal liquid crystal phases - the so-called blue phases - consist of a network of topological defects arranged into a cubic symmetry. They exhibit striking optical properties, including Bragg reflection in the visible range and fast response times. Confining surfaces can interfere with the packing of such a network, leading to structures that have not been explored before. In this work, a Landau-de Gennes free energy formalism for the tensor alignment field Q is used to investigate the behavior of chiral liquid crystals under non-isotropic confinement. The underlying free energy functional is solved by relying on a Monte Carlo methodmore »« less
https://doi.org/10.1039/c9sm02021g
Cuboidal liquid crystal phases under multiaxial geometrical frustration

Journal Article Palacio-Betancur, Viviana ; Armas-Pérez, Julio C. ; Villada-Gil, Stiven ; ... - Soft Matter

Cuboidal liquid crystal phases – the so-called blue phases – consist of a network of topological defects arranged into a cubic symmetry. They exhibit striking optical properties, including Bragg reflection in the visible range and fast response times. Confining surfaces can interfere with the packing of such a network, leading to structures that have not been explored before. In this work, a Landau–de Gennes free energy formalism for the tensor alignment field Q is used to investigate the behavior of chiral liquid crystals under non-isotropic confinement. The underlying free energy functional is solved by relying on a Monte Carlo methodmore »« less
Cited by 9
https://doi.org/10.1039/C9SM02021G

Full Text Available

Similar Records

Title: Thermoelastic-plastic flow equations in general coordinates

Abstract

Citation Formats

The energy–momentum tensor(s) in classical gauge theories journal, November 2016

An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields journal, January 2007

Zur Theorie plastischer Deformationen und der hierdurch im Material hervorgerufenen Nachspannungen journal, January 1924

A dislocation-based multi-rate single crystal plasticity model journal, May 2013

Constitutive Equations for Rate-Dependent Plasticity journal, August 1985

Second order effects in the theory of plasticity journal, March 1969

On second-order strain accumulation in aluminum in reversed cyclic torsion at elevated temperatures journal, March 1967

Berücksichtigung der elastischen Formänderung in der Plastizitätstheorie journal, January 1930

Shock compression of solids journal, October 1979

Review of experimental techniques for high rate deformation and shock studies journal, August 2004

Revisiting shock waves in metals journal, February 1997

Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media journal, January 1977

Approximate models for ductile metals containing non-spherical voids—Case of axisymmetric prolate ellipsoidal cavities journal, November 1993

An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields journal, January 2007

A multi-surface plasticity model for ductile fracture simulations journal, June 2017

The energy–momentum tensor(s) in classical gauge theories journal, November 2016

Finite Deformations of an Elastic Solid journal, April 1937

The Heat Developed during Plastic Extension of Metals journal, March 1925

The stored energy of cold work journal, January 1958

Irreversible thermodynamics of flow in solids journal, August 1980

The energy–momentum tensor(s) in classical gauge theories
journal, November 2016

An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields
journal, January 2007

Zur Theorie plastischer Deformationen und der hierdurch im Material hervorgerufenen Nachspannungen
journal, January 1924

A dislocation-based multi-rate single crystal plasticity model
journal, May 2013

Constitutive Equations for Rate-Dependent Plasticity
journal, August 1985

Second order effects in the theory of plasticity
journal, March 1969

On second-order strain accumulation in aluminum in reversed cyclic torsion at elevated temperatures
journal, March 1967

Berücksichtigung der elastischen Formänderung in der Plastizitätstheorie
journal, January 1930

Shock compression of solids
journal, October 1979

Review of experimental techniques for high rate deformation and shock studies
journal, August 2004

Revisiting shock waves in metals
journal, February 1997

Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media
journal, January 1977

Approximate models for ductile metals containing non-spherical voids—Case of axisymmetric prolate ellipsoidal cavities
journal, November 1993

An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields
journal, January 2007

A multi-surface plasticity model for ductile fracture simulations
journal, June 2017

The energy–momentum tensor(s) in classical gauge theories
journal, November 2016

Finite Deformations of an Elastic Solid
journal, April 1937

The Heat Developed during Plastic Extension of Metals
journal, March 1925

The stored energy of cold work
journal, January 1958

Irreversible thermodynamics of flow in solids
journal, August 1980