A Godunov method for localization in elastoplastic granular flow
The equations governing the elastic-plastic deformation of granular materials are typically hyperbolic, or contain small-magnitude damping or rate effects. A finite element algorithm is the standard method for the numerical integration of these systems. In particular, finite elements allow great fle...
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E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1993 |
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| Umfang: |
6 Ill. 16 |
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| Reproduktion: |
Wiley InterScience Backfile Collection 1832-2000 |
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in: International Journal for Numerical and Analytical Methods in Geomechanics - New York, NY [u.a.] : Wiley, 17(1993) vom: Juni, Seite 385-400 |
| Übergeordnetes Werk: |
volume:17 ; year:1993 ; month:06 ; pages:385-400 ; extent:16 |
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| 520 | |a The equations governing the elastic-plastic deformation of granular materials are typically hyperbolic, or contain small-magnitude damping or rate effects. A finite element algorithm is the standard method for the numerical integration of these systems. In particular, finite elements allow great flexibility in the design of grid geometry. However, modern finite difference methods for hyperbolic systems have been successful in aerodynamics computations, resolving wave structures more sharply than finite element schemes. In this paper we develop a finite difference scheme for granular flow problems. We report on a second-order Godunov-type scheme for the integration of hyperbolic equations for the elastoplastic deformation of a simple model of granular flow. The Godunov method includes a characteristic tracing step in the integration, providing minimal wave dispersion, and a slope limiting step, preventing unphysical oscillations.The granular flow model we consider is hyperbolic, but hyperbolicity is lost at a large value of accumulated plastic strain. This loss of hyperbolicity is a tell-tale signal for the formation of a shear band within the sample. Typically, when systems lose hyperbolicity a regularization mechanism is added to the model equations in order to maintain the well posedness of the system. These regularizations include viscosity, viscoplasticity, higher-order gradient effects or stress coupling. Here we appeal to a very different kind of regularization. When the system loses hyperbolicity and a shear band forms, we treat the band as an internal boundary, and impose jump conditions at this boundary. Away from the band, the system remains hyperbolic and the integration step proceeds as usual. | ||
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(DE-627)NLEJ163239940 DE-627 ger DE-627 rakwb eng A Godunov method for localization in elastoplastic granular flow 1993 6 Ill. 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The equations governing the elastic-plastic deformation of granular materials are typically hyperbolic, or contain small-magnitude damping or rate effects. A finite element algorithm is the standard method for the numerical integration of these systems. In particular, finite elements allow great flexibility in the design of grid geometry. However, modern finite difference methods for hyperbolic systems have been successful in aerodynamics computations, resolving wave structures more sharply than finite element schemes. In this paper we develop a finite difference scheme for granular flow problems. We report on a second-order Godunov-type scheme for the integration of hyperbolic equations for the elastoplastic deformation of a simple model of granular flow. The Godunov method includes a characteristic tracing step in the integration, providing minimal wave dispersion, and a slope limiting step, preventing unphysical oscillations.The granular flow model we consider is hyperbolic, but hyperbolicity is lost at a large value of accumulated plastic strain. This loss of hyperbolicity is a tell-tale signal for the formation of a shear band within the sample. Typically, when systems lose hyperbolicity a regularization mechanism is added to the model equations in order to maintain the well posedness of the system. These regularizations include viscosity, viscoplasticity, higher-order gradient effects or stress coupling. Here we appeal to a very different kind of regularization. When the system loses hyperbolicity and a shear band forms, we treat the band as an internal boundary, and impose jump conditions at this boundary. Away from the band, the system remains hyperbolic and the integration step proceeds as usual. Wiley InterScience Backfile Collection 1832-2000 Pitman, E. Bruce oth in International Journal for Numerical and Analytical Methods in Geomechanics New York, NY [u.a.] : Wiley 17(1993) vom: Juni, Seite 385-400 (DE-627)NLEJ159071232 0363-9061 nnns volume:17 year:1993 month:06 pages:385-400 extent:16 http://dx.doi.org/10.1002/nag.1610170603 text/html Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-WIS GBV_NL_ARTICLE AR 17 1993 6 385-400 16 |
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(DE-627)NLEJ163239940 DE-627 ger DE-627 rakwb eng A Godunov method for localization in elastoplastic granular flow 1993 6 Ill. 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The equations governing the elastic-plastic deformation of granular materials are typically hyperbolic, or contain small-magnitude damping or rate effects. A finite element algorithm is the standard method for the numerical integration of these systems. In particular, finite elements allow great flexibility in the design of grid geometry. However, modern finite difference methods for hyperbolic systems have been successful in aerodynamics computations, resolving wave structures more sharply than finite element schemes. In this paper we develop a finite difference scheme for granular flow problems. We report on a second-order Godunov-type scheme for the integration of hyperbolic equations for the elastoplastic deformation of a simple model of granular flow. The Godunov method includes a characteristic tracing step in the integration, providing minimal wave dispersion, and a slope limiting step, preventing unphysical oscillations.The granular flow model we consider is hyperbolic, but hyperbolicity is lost at a large value of accumulated plastic strain. This loss of hyperbolicity is a tell-tale signal for the formation of a shear band within the sample. Typically, when systems lose hyperbolicity a regularization mechanism is added to the model equations in order to maintain the well posedness of the system. These regularizations include viscosity, viscoplasticity, higher-order gradient effects or stress coupling. Here we appeal to a very different kind of regularization. When the system loses hyperbolicity and a shear band forms, we treat the band as an internal boundary, and impose jump conditions at this boundary. Away from the band, the system remains hyperbolic and the integration step proceeds as usual. Wiley InterScience Backfile Collection 1832-2000 Pitman, E. Bruce oth in International Journal for Numerical and Analytical Methods in Geomechanics New York, NY [u.a.] : Wiley 17(1993) vom: Juni, Seite 385-400 (DE-627)NLEJ159071232 0363-9061 nnns volume:17 year:1993 month:06 pages:385-400 extent:16 http://dx.doi.org/10.1002/nag.1610170603 text/html Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-WIS GBV_NL_ARTICLE AR 17 1993 6 385-400 16 |
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(DE-627)NLEJ163239940 DE-627 ger DE-627 rakwb eng A Godunov method for localization in elastoplastic granular flow 1993 6 Ill. 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The equations governing the elastic-plastic deformation of granular materials are typically hyperbolic, or contain small-magnitude damping or rate effects. A finite element algorithm is the standard method for the numerical integration of these systems. In particular, finite elements allow great flexibility in the design of grid geometry. However, modern finite difference methods for hyperbolic systems have been successful in aerodynamics computations, resolving wave structures more sharply than finite element schemes. In this paper we develop a finite difference scheme for granular flow problems. We report on a second-order Godunov-type scheme for the integration of hyperbolic equations for the elastoplastic deformation of a simple model of granular flow. The Godunov method includes a characteristic tracing step in the integration, providing minimal wave dispersion, and a slope limiting step, preventing unphysical oscillations.The granular flow model we consider is hyperbolic, but hyperbolicity is lost at a large value of accumulated plastic strain. This loss of hyperbolicity is a tell-tale signal for the formation of a shear band within the sample. Typically, when systems lose hyperbolicity a regularization mechanism is added to the model equations in order to maintain the well posedness of the system. These regularizations include viscosity, viscoplasticity, higher-order gradient effects or stress coupling. Here we appeal to a very different kind of regularization. When the system loses hyperbolicity and a shear band forms, we treat the band as an internal boundary, and impose jump conditions at this boundary. Away from the band, the system remains hyperbolic and the integration step proceeds as usual. Wiley InterScience Backfile Collection 1832-2000 Pitman, E. Bruce oth in International Journal for Numerical and Analytical Methods in Geomechanics New York, NY [u.a.] : Wiley 17(1993) vom: Juni, Seite 385-400 (DE-627)NLEJ159071232 0363-9061 nnns volume:17 year:1993 month:06 pages:385-400 extent:16 http://dx.doi.org/10.1002/nag.1610170603 text/html Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-WIS GBV_NL_ARTICLE AR 17 1993 6 385-400 16 |
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(DE-627)NLEJ163239940 DE-627 ger DE-627 rakwb eng A Godunov method for localization in elastoplastic granular flow 1993 6 Ill. 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The equations governing the elastic-plastic deformation of granular materials are typically hyperbolic, or contain small-magnitude damping or rate effects. A finite element algorithm is the standard method for the numerical integration of these systems. In particular, finite elements allow great flexibility in the design of grid geometry. However, modern finite difference methods for hyperbolic systems have been successful in aerodynamics computations, resolving wave structures more sharply than finite element schemes. In this paper we develop a finite difference scheme for granular flow problems. We report on a second-order Godunov-type scheme for the integration of hyperbolic equations for the elastoplastic deformation of a simple model of granular flow. The Godunov method includes a characteristic tracing step in the integration, providing minimal wave dispersion, and a slope limiting step, preventing unphysical oscillations.The granular flow model we consider is hyperbolic, but hyperbolicity is lost at a large value of accumulated plastic strain. This loss of hyperbolicity is a tell-tale signal for the formation of a shear band within the sample. Typically, when systems lose hyperbolicity a regularization mechanism is added to the model equations in order to maintain the well posedness of the system. These regularizations include viscosity, viscoplasticity, higher-order gradient effects or stress coupling. Here we appeal to a very different kind of regularization. When the system loses hyperbolicity and a shear band forms, we treat the band as an internal boundary, and impose jump conditions at this boundary. Away from the band, the system remains hyperbolic and the integration step proceeds as usual. Wiley InterScience Backfile Collection 1832-2000 Pitman, E. Bruce oth in International Journal for Numerical and Analytical Methods in Geomechanics New York, NY [u.a.] : Wiley 17(1993) vom: Juni, Seite 385-400 (DE-627)NLEJ159071232 0363-9061 nnns volume:17 year:1993 month:06 pages:385-400 extent:16 http://dx.doi.org/10.1002/nag.1610170603 text/html Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-WIS GBV_NL_ARTICLE AR 17 1993 6 385-400 16 |
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(DE-627)NLEJ163239940 DE-627 ger DE-627 rakwb eng A Godunov method for localization in elastoplastic granular flow 1993 6 Ill. 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The equations governing the elastic-plastic deformation of granular materials are typically hyperbolic, or contain small-magnitude damping or rate effects. A finite element algorithm is the standard method for the numerical integration of these systems. In particular, finite elements allow great flexibility in the design of grid geometry. However, modern finite difference methods for hyperbolic systems have been successful in aerodynamics computations, resolving wave structures more sharply than finite element schemes. In this paper we develop a finite difference scheme for granular flow problems. We report on a second-order Godunov-type scheme for the integration of hyperbolic equations for the elastoplastic deformation of a simple model of granular flow. The Godunov method includes a characteristic tracing step in the integration, providing minimal wave dispersion, and a slope limiting step, preventing unphysical oscillations.The granular flow model we consider is hyperbolic, but hyperbolicity is lost at a large value of accumulated plastic strain. This loss of hyperbolicity is a tell-tale signal for the formation of a shear band within the sample. Typically, when systems lose hyperbolicity a regularization mechanism is added to the model equations in order to maintain the well posedness of the system. These regularizations include viscosity, viscoplasticity, higher-order gradient effects or stress coupling. Here we appeal to a very different kind of regularization. When the system loses hyperbolicity and a shear band forms, we treat the band as an internal boundary, and impose jump conditions at this boundary. Away from the band, the system remains hyperbolic and the integration step proceeds as usual. Wiley InterScience Backfile Collection 1832-2000 Pitman, E. Bruce oth in International Journal for Numerical and Analytical Methods in Geomechanics New York, NY [u.a.] : Wiley 17(1993) vom: Juni, Seite 385-400 (DE-627)NLEJ159071232 0363-9061 nnns volume:17 year:1993 month:06 pages:385-400 extent:16 http://dx.doi.org/10.1002/nag.1610170603 text/html Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-WIS GBV_NL_ARTICLE AR 17 1993 6 385-400 16 |
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A Godunov method for localization in elastoplastic granular flow |
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The equations governing the elastic-plastic deformation of granular materials are typically hyperbolic, or contain small-magnitude damping or rate effects. A finite element algorithm is the standard method for the numerical integration of these systems. In particular, finite elements allow great flexibility in the design of grid geometry. However, modern finite difference methods for hyperbolic systems have been successful in aerodynamics computations, resolving wave structures more sharply than finite element schemes. In this paper we develop a finite difference scheme for granular flow problems. We report on a second-order Godunov-type scheme for the integration of hyperbolic equations for the elastoplastic deformation of a simple model of granular flow. The Godunov method includes a characteristic tracing step in the integration, providing minimal wave dispersion, and a slope limiting step, preventing unphysical oscillations.The granular flow model we consider is hyperbolic, but hyperbolicity is lost at a large value of accumulated plastic strain. This loss of hyperbolicity is a tell-tale signal for the formation of a shear band within the sample. Typically, when systems lose hyperbolicity a regularization mechanism is added to the model equations in order to maintain the well posedness of the system. These regularizations include viscosity, viscoplasticity, higher-order gradient effects or stress coupling. Here we appeal to a very different kind of regularization. When the system loses hyperbolicity and a shear band forms, we treat the band as an internal boundary, and impose jump conditions at this boundary. Away from the band, the system remains hyperbolic and the integration step proceeds as usual. |
| abstractGer |
The equations governing the elastic-plastic deformation of granular materials are typically hyperbolic, or contain small-magnitude damping or rate effects. A finite element algorithm is the standard method for the numerical integration of these systems. In particular, finite elements allow great flexibility in the design of grid geometry. However, modern finite difference methods for hyperbolic systems have been successful in aerodynamics computations, resolving wave structures more sharply than finite element schemes. In this paper we develop a finite difference scheme for granular flow problems. We report on a second-order Godunov-type scheme for the integration of hyperbolic equations for the elastoplastic deformation of a simple model of granular flow. The Godunov method includes a characteristic tracing step in the integration, providing minimal wave dispersion, and a slope limiting step, preventing unphysical oscillations.The granular flow model we consider is hyperbolic, but hyperbolicity is lost at a large value of accumulated plastic strain. This loss of hyperbolicity is a tell-tale signal for the formation of a shear band within the sample. Typically, when systems lose hyperbolicity a regularization mechanism is added to the model equations in order to maintain the well posedness of the system. These regularizations include viscosity, viscoplasticity, higher-order gradient effects or stress coupling. Here we appeal to a very different kind of regularization. When the system loses hyperbolicity and a shear band forms, we treat the band as an internal boundary, and impose jump conditions at this boundary. Away from the band, the system remains hyperbolic and the integration step proceeds as usual. |
| abstract_unstemmed |
The equations governing the elastic-plastic deformation of granular materials are typically hyperbolic, or contain small-magnitude damping or rate effects. A finite element algorithm is the standard method for the numerical integration of these systems. In particular, finite elements allow great flexibility in the design of grid geometry. However, modern finite difference methods for hyperbolic systems have been successful in aerodynamics computations, resolving wave structures more sharply than finite element schemes. In this paper we develop a finite difference scheme for granular flow problems. We report on a second-order Godunov-type scheme for the integration of hyperbolic equations for the elastoplastic deformation of a simple model of granular flow. The Godunov method includes a characteristic tracing step in the integration, providing minimal wave dispersion, and a slope limiting step, preventing unphysical oscillations.The granular flow model we consider is hyperbolic, but hyperbolicity is lost at a large value of accumulated plastic strain. This loss of hyperbolicity is a tell-tale signal for the formation of a shear band within the sample. Typically, when systems lose hyperbolicity a regularization mechanism is added to the model equations in order to maintain the well posedness of the system. These regularizations include viscosity, viscoplasticity, higher-order gradient effects or stress coupling. Here we appeal to a very different kind of regularization. When the system loses hyperbolicity and a shear band forms, we treat the band as an internal boundary, and impose jump conditions at this boundary. Away from the band, the system remains hyperbolic and the integration step proceeds as usual. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">NLEJ163239940</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20210707111514.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">070201s1993 xx |||||o 00| ||eng c</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ163239940</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A Godunov method for localization in elastoplastic granular flow</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">1993</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="b">6 Ill.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">16</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The equations governing the elastic-plastic deformation of granular materials are typically hyperbolic, or contain small-magnitude damping or rate effects. A finite element algorithm is the standard method for the numerical integration of these systems. In particular, finite elements allow great flexibility in the design of grid geometry. However, modern finite difference methods for hyperbolic systems have been successful in aerodynamics computations, resolving wave structures more sharply than finite element schemes. In this paper we develop a finite difference scheme for granular flow problems. We report on a second-order Godunov-type scheme for the integration of hyperbolic equations for the elastoplastic deformation of a simple model of granular flow. The Godunov method includes a characteristic tracing step in the integration, providing minimal wave dispersion, and a slope limiting step, preventing unphysical oscillations.The granular flow model we consider is hyperbolic, but hyperbolicity is lost at a large value of accumulated plastic strain. This loss of hyperbolicity is a tell-tale signal for the formation of a shear band within the sample. Typically, when systems lose hyperbolicity a regularization mechanism is added to the model equations in order to maintain the well posedness of the system. These regularizations include viscosity, viscoplasticity, higher-order gradient effects or stress coupling. Here we appeal to a very different kind of regularization. When the system loses hyperbolicity and a shear band forms, we treat the band as an internal boundary, and impose jump conditions at this boundary. Away from the band, the system remains hyperbolic and the integration step proceeds as usual.</subfield></datafield><datafield tag="533" ind1=" " ind2=" "><subfield code="f">Wiley InterScience Backfile Collection 1832-2000</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Pitman, E. Bruce</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">in</subfield><subfield code="t">International Journal for Numerical and Analytical Methods in Geomechanics</subfield><subfield code="d">New York, NY [u.a.] : Wiley</subfield><subfield code="g">17(1993) vom: Juni, Seite 385-400</subfield><subfield code="w">(DE-627)NLEJ159071232</subfield><subfield code="x">0363-9061</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:17</subfield><subfield code="g">year:1993</subfield><subfield code="g">month:06</subfield><subfield code="g">pages:385-400</subfield><subfield code="g">extent:16</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://dx.doi.org/10.1002/nag.1610170603</subfield><subfield code="q">text/html</subfield><subfield code="z">Deutschlandweit zugänglich</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-WIS</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">17</subfield><subfield code="j">1993</subfield><subfield code="c">6</subfield><subfield code="h">385-400</subfield><subfield code="g">16</subfield></datafield></record></collection>
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