On the relationship between the Eulerian and Lagrangian descriptions of finite rigid plasticity

Abstract The motivation for the present paper is to clarify certain unresolved issues pertaining to the relation between the Lagrangian (or referential) and Eulerian (or spatial) strain-space formulations of finite plasticity. For conceptual simplicity, attention is confined to rigid-plastic materia...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Casey, J. [verfasserIn] Naghdi, P. M.

Format:	Artikel
Sprache:	Englisch

Erschienen:	1988

Schlagwörter:	Neural Network Complex System Nonlinear Dynamics Constitutive Equation Electromagnetism

Anmerkung:	© Springer-Verlag GmbH & Co 1988

Übergeordnetes Werk:	Enthalten in: Archive for rational mechanics and analysis - Springer-Verlag, 1957, 102(1988), 4 vom: Dez., Seite 351-375
Übergeordnetes Werk:	volume:102 ; year:1988 ; number:4 ; month:12 ; pages:351-375

Links:	Volltext

DOI / URN:	10.1007/BF00251535

Katalog-ID:	OLC2056405504

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520			\|a Abstract The motivation for the present paper is to clarify certain unresolved issues pertaining to the relation between the Lagrangian (or referential) and Eulerian (or spatial) strain-space formulations of finite plasticity. For conceptual simplicity, attention is confined to rigid-plastic materials. It is shown first that for constitutive equations in which the hardening parameter is a scalar, the Lagrangian and Eulerian descriptions are equivalent; and that, additionally, the choice of objective stress rate is immaterial. In the light of these developments, the role of objective rates is further explored in connection with more general (“anisotropic”) hardening laws which contain a shift tensor. A form of the constitutive equation for the rate of the shift tensor is motivated in which the choice of objective rate is arbitrary. It is then demonstrated that the structure of the constitutive equations of the theory — in both the Eulerian and Lagrangian descriptions — is form-invariant under arbitrary transformations of objective rate. The approach taken here contrasts with that adopted in a number of recent papers in which preference is given to one particular objective rate or another.
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allfields	10.1007/BF00251535 doi (DE-627)OLC2056405504 (DE-He213)BF00251535-p DE-627 ger DE-627 rakwb eng 530 510 VZ Casey, J. verfasserin aut On the relationship between the Eulerian and Lagrangian descriptions of finite rigid plasticity 1988 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH & Co 1988 Abstract The motivation for the present paper is to clarify certain unresolved issues pertaining to the relation between the Lagrangian (or referential) and Eulerian (or spatial) strain-space formulations of finite plasticity. For conceptual simplicity, attention is confined to rigid-plastic materials. It is shown first that for constitutive equations in which the hardening parameter is a scalar, the Lagrangian and Eulerian descriptions are equivalent; and that, additionally, the choice of objective stress rate is immaterial. In the light of these developments, the role of objective rates is further explored in connection with more general (“anisotropic”) hardening laws which contain a shift tensor. A form of the constitutive equation for the rate of the shift tensor is motivated in which the choice of objective rate is arbitrary. It is then demonstrated that the structure of the constitutive equations of the theory — in both the Eulerian and Lagrangian descriptions — is form-invariant under arbitrary transformations of objective rate. The approach taken here contrasts with that adopted in a number of recent papers in which preference is given to one particular objective rate or another. Neural Network Complex System Nonlinear Dynamics Constitutive Equation Electromagnetism Naghdi, P. M. aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 102(1988), 4 vom: Dez., Seite 351-375 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:102 year:1988 number:4 month:12 pages:351-375 https://doi.org/10.1007/BF00251535 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_59 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2333 GBV_ILN_2409 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 102 1988 4 12 351-375
spelling	10.1007/BF00251535 doi (DE-627)OLC2056405504 (DE-He213)BF00251535-p DE-627 ger DE-627 rakwb eng 530 510 VZ Casey, J. verfasserin aut On the relationship between the Eulerian and Lagrangian descriptions of finite rigid plasticity 1988 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH & Co 1988 Abstract The motivation for the present paper is to clarify certain unresolved issues pertaining to the relation between the Lagrangian (or referential) and Eulerian (or spatial) strain-space formulations of finite plasticity. For conceptual simplicity, attention is confined to rigid-plastic materials. It is shown first that for constitutive equations in which the hardening parameter is a scalar, the Lagrangian and Eulerian descriptions are equivalent; and that, additionally, the choice of objective stress rate is immaterial. In the light of these developments, the role of objective rates is further explored in connection with more general (“anisotropic”) hardening laws which contain a shift tensor. A form of the constitutive equation for the rate of the shift tensor is motivated in which the choice of objective rate is arbitrary. It is then demonstrated that the structure of the constitutive equations of the theory — in both the Eulerian and Lagrangian descriptions — is form-invariant under arbitrary transformations of objective rate. The approach taken here contrasts with that adopted in a number of recent papers in which preference is given to one particular objective rate or another. Neural Network Complex System Nonlinear Dynamics Constitutive Equation Electromagnetism Naghdi, P. M. aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 102(1988), 4 vom: Dez., Seite 351-375 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:102 year:1988 number:4 month:12 pages:351-375 https://doi.org/10.1007/BF00251535 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_59 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2333 GBV_ILN_2409 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 102 1988 4 12 351-375
allfields_unstemmed	10.1007/BF00251535 doi (DE-627)OLC2056405504 (DE-He213)BF00251535-p DE-627 ger DE-627 rakwb eng 530 510 VZ Casey, J. verfasserin aut On the relationship between the Eulerian and Lagrangian descriptions of finite rigid plasticity 1988 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH & Co 1988 Abstract The motivation for the present paper is to clarify certain unresolved issues pertaining to the relation between the Lagrangian (or referential) and Eulerian (or spatial) strain-space formulations of finite plasticity. For conceptual simplicity, attention is confined to rigid-plastic materials. It is shown first that for constitutive equations in which the hardening parameter is a scalar, the Lagrangian and Eulerian descriptions are equivalent; and that, additionally, the choice of objective stress rate is immaterial. In the light of these developments, the role of objective rates is further explored in connection with more general (“anisotropic”) hardening laws which contain a shift tensor. A form of the constitutive equation for the rate of the shift tensor is motivated in which the choice of objective rate is arbitrary. It is then demonstrated that the structure of the constitutive equations of the theory — in both the Eulerian and Lagrangian descriptions — is form-invariant under arbitrary transformations of objective rate. The approach taken here contrasts with that adopted in a number of recent papers in which preference is given to one particular objective rate or another. Neural Network Complex System Nonlinear Dynamics Constitutive Equation Electromagnetism Naghdi, P. M. aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 102(1988), 4 vom: Dez., Seite 351-375 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:102 year:1988 number:4 month:12 pages:351-375 https://doi.org/10.1007/BF00251535 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_59 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2333 GBV_ILN_2409 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 102 1988 4 12 351-375
allfieldsGer	10.1007/BF00251535 doi (DE-627)OLC2056405504 (DE-He213)BF00251535-p DE-627 ger DE-627 rakwb eng 530 510 VZ Casey, J. verfasserin aut On the relationship between the Eulerian and Lagrangian descriptions of finite rigid plasticity 1988 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH & Co 1988 Abstract The motivation for the present paper is to clarify certain unresolved issues pertaining to the relation between the Lagrangian (or referential) and Eulerian (or spatial) strain-space formulations of finite plasticity. For conceptual simplicity, attention is confined to rigid-plastic materials. It is shown first that for constitutive equations in which the hardening parameter is a scalar, the Lagrangian and Eulerian descriptions are equivalent; and that, additionally, the choice of objective stress rate is immaterial. In the light of these developments, the role of objective rates is further explored in connection with more general (“anisotropic”) hardening laws which contain a shift tensor. A form of the constitutive equation for the rate of the shift tensor is motivated in which the choice of objective rate is arbitrary. It is then demonstrated that the structure of the constitutive equations of the theory — in both the Eulerian and Lagrangian descriptions — is form-invariant under arbitrary transformations of objective rate. The approach taken here contrasts with that adopted in a number of recent papers in which preference is given to one particular objective rate or another. Neural Network Complex System Nonlinear Dynamics Constitutive Equation Electromagnetism Naghdi, P. M. aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 102(1988), 4 vom: Dez., Seite 351-375 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:102 year:1988 number:4 month:12 pages:351-375 https://doi.org/10.1007/BF00251535 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_59 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2333 GBV_ILN_2409 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 102 1988 4 12 351-375
allfieldsSound	10.1007/BF00251535 doi (DE-627)OLC2056405504 (DE-He213)BF00251535-p DE-627 ger DE-627 rakwb eng 530 510 VZ Casey, J. verfasserin aut On the relationship between the Eulerian and Lagrangian descriptions of finite rigid plasticity 1988 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH & Co 1988 Abstract The motivation for the present paper is to clarify certain unresolved issues pertaining to the relation between the Lagrangian (or referential) and Eulerian (or spatial) strain-space formulations of finite plasticity. For conceptual simplicity, attention is confined to rigid-plastic materials. It is shown first that for constitutive equations in which the hardening parameter is a scalar, the Lagrangian and Eulerian descriptions are equivalent; and that, additionally, the choice of objective stress rate is immaterial. In the light of these developments, the role of objective rates is further explored in connection with more general (“anisotropic”) hardening laws which contain a shift tensor. A form of the constitutive equation for the rate of the shift tensor is motivated in which the choice of objective rate is arbitrary. It is then demonstrated that the structure of the constitutive equations of the theory — in both the Eulerian and Lagrangian descriptions — is form-invariant under arbitrary transformations of objective rate. The approach taken here contrasts with that adopted in a number of recent papers in which preference is given to one particular objective rate or another. Neural Network Complex System Nonlinear Dynamics Constitutive Equation Electromagnetism Naghdi, P. M. aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 102(1988), 4 vom: Dez., Seite 351-375 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:102 year:1988 number:4 month:12 pages:351-375 https://doi.org/10.1007/BF00251535 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_59 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2333 GBV_ILN_2409 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 102 1988 4 12 351-375
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source	Enthalten in Archive for rational mechanics and analysis 102(1988), 4 vom: Dez., Seite 351-375 volume:102 year:1988 number:4 month:12 pages:351-375
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author	Casey, J.
spellingShingle	Casey, J. ddc 530 misc Neural Network misc Complex System misc Nonlinear Dynamics misc Constitutive Equation misc Electromagnetism On the relationship between the Eulerian and Lagrangian descriptions of finite rigid plasticity
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title	On the relationship between the Eulerian and Lagrangian descriptions of finite rigid plasticity
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title_full	On the relationship between the Eulerian and Lagrangian descriptions of finite rigid plasticity
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title_sort	on the relationship between the eulerian and lagrangian descriptions of finite rigid plasticity
title_auth	On the relationship between the Eulerian and Lagrangian descriptions of finite rigid plasticity
abstract	Abstract The motivation for the present paper is to clarify certain unresolved issues pertaining to the relation between the Lagrangian (or referential) and Eulerian (or spatial) strain-space formulations of finite plasticity. For conceptual simplicity, attention is confined to rigid-plastic materials. It is shown first that for constitutive equations in which the hardening parameter is a scalar, the Lagrangian and Eulerian descriptions are equivalent; and that, additionally, the choice of objective stress rate is immaterial. In the light of these developments, the role of objective rates is further explored in connection with more general (“anisotropic”) hardening laws which contain a shift tensor. A form of the constitutive equation for the rate of the shift tensor is motivated in which the choice of objective rate is arbitrary. It is then demonstrated that the structure of the constitutive equations of the theory — in both the Eulerian and Lagrangian descriptions — is form-invariant under arbitrary transformations of objective rate. The approach taken here contrasts with that adopted in a number of recent papers in which preference is given to one particular objective rate or another. © Springer-Verlag GmbH & Co 1988
abstractGer	Abstract The motivation for the present paper is to clarify certain unresolved issues pertaining to the relation between the Lagrangian (or referential) and Eulerian (or spatial) strain-space formulations of finite plasticity. For conceptual simplicity, attention is confined to rigid-plastic materials. It is shown first that for constitutive equations in which the hardening parameter is a scalar, the Lagrangian and Eulerian descriptions are equivalent; and that, additionally, the choice of objective stress rate is immaterial. In the light of these developments, the role of objective rates is further explored in connection with more general (“anisotropic”) hardening laws which contain a shift tensor. A form of the constitutive equation for the rate of the shift tensor is motivated in which the choice of objective rate is arbitrary. It is then demonstrated that the structure of the constitutive equations of the theory — in both the Eulerian and Lagrangian descriptions — is form-invariant under arbitrary transformations of objective rate. The approach taken here contrasts with that adopted in a number of recent papers in which preference is given to one particular objective rate or another. © Springer-Verlag GmbH & Co 1988
abstract_unstemmed	Abstract The motivation for the present paper is to clarify certain unresolved issues pertaining to the relation between the Lagrangian (or referential) and Eulerian (or spatial) strain-space formulations of finite plasticity. For conceptual simplicity, attention is confined to rigid-plastic materials. It is shown first that for constitutive equations in which the hardening parameter is a scalar, the Lagrangian and Eulerian descriptions are equivalent; and that, additionally, the choice of objective stress rate is immaterial. In the light of these developments, the role of objective rates is further explored in connection with more general (“anisotropic”) hardening laws which contain a shift tensor. A form of the constitutive equation for the rate of the shift tensor is motivated in which the choice of objective rate is arbitrary. It is then demonstrated that the structure of the constitutive equations of the theory — in both the Eulerian and Lagrangian descriptions — is form-invariant under arbitrary transformations of objective rate. The approach taken here contrasts with that adopted in a number of recent papers in which preference is given to one particular objective rate or another. © Springer-Verlag GmbH & Co 1988
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title_short	On the relationship between the Eulerian and Lagrangian descriptions of finite rigid plasticity
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