A New Mathematical Foundation for Contact Interactions in Continuum Physics
Abstract The investigation of contact interactions, such as traction and heat flux, that are exerted by contiguous bodies across the common boundary is a fundamental issue in continuum physics. However, the traditional theory of stress established by Cauchy and extended by Noll and his successors is...
Ausführliche Beschreibung
Autor*in: |
Schuricht, Friedemann [verfasserIn] |
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Format: |
Artikel |
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Sprache: |
Englisch |
Erschienen: |
2006 |
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Schlagwörter: |
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Anmerkung: |
© Springer-Verlag 2006 |
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Übergeordnetes Werk: |
Enthalten in: Archive for rational mechanics and analysis - Springer Berlin Heidelberg, 1957, 184(2006), 3 vom: 19. Sept., Seite 495-551 |
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Übergeordnetes Werk: |
volume:184 ; year:2006 ; number:3 ; day:19 ; month:09 ; pages:495-551 |
Links: |
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DOI / URN: |
10.1007/s00205-006-0032-6 |
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Katalog-ID: |
OLC2056416085 |
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10.1007/s00205-006-0032-6 doi (DE-627)OLC2056416085 (DE-He213)s00205-006-0032-6-p DE-627 ger DE-627 rakwb eng 530 510 VZ Schuricht, Friedemann verfasserin aut A New Mathematical Foundation for Contact Interactions in Continuum Physics 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2006 Abstract The investigation of contact interactions, such as traction and heat flux, that are exerted by contiguous bodies across the common boundary is a fundamental issue in continuum physics. However, the traditional theory of stress established by Cauchy and extended by Noll and his successors is insufficient for handling the lack of regularity in continuum physics due to shocks, corner singularities, and fracture. This paper provides a new mathematical foundation for the treatment of contact interactions. Based on mild physically motivated postulates, which differ essentially from those used before, the existence of a corresponding interaction tensor is established. While in earlier treatments contact interactions are basically defined on surfaces, here contact interactions are rigorously considered as maps on pairs of subbodies. This allows the action exerted on a subbody to be defined not only, as usual, for sets with a sufficiently regular boundary, but also for Borel sets (which include all open and all closed sets). In addition to the classical representation of such interactions by means of integrals on smooth surfaces, a general representation using the distributional divergence of the tensor is derived. In the case where concentrations occur, this new approach allows a description of contact phenomena more precise than before. Contact Interaction Measure Zero Radon Measure Representation Formula Partial Restriction Enthalten in Archive for rational mechanics and analysis Springer Berlin Heidelberg, 1957 184(2006), 3 vom: 19. Sept., Seite 495-551 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:184 year:2006 number:3 day:19 month:09 pages:495-551 https://doi.org/10.1007/s00205-006-0032-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4323 GBV_ILN_4700 AR 184 2006 3 19 09 495-551 |
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10.1007/s00205-006-0032-6 doi (DE-627)OLC2056416085 (DE-He213)s00205-006-0032-6-p DE-627 ger DE-627 rakwb eng 530 510 VZ Schuricht, Friedemann verfasserin aut A New Mathematical Foundation for Contact Interactions in Continuum Physics 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2006 Abstract The investigation of contact interactions, such as traction and heat flux, that are exerted by contiguous bodies across the common boundary is a fundamental issue in continuum physics. However, the traditional theory of stress established by Cauchy and extended by Noll and his successors is insufficient for handling the lack of regularity in continuum physics due to shocks, corner singularities, and fracture. This paper provides a new mathematical foundation for the treatment of contact interactions. Based on mild physically motivated postulates, which differ essentially from those used before, the existence of a corresponding interaction tensor is established. While in earlier treatments contact interactions are basically defined on surfaces, here contact interactions are rigorously considered as maps on pairs of subbodies. This allows the action exerted on a subbody to be defined not only, as usual, for sets with a sufficiently regular boundary, but also for Borel sets (which include all open and all closed sets). In addition to the classical representation of such interactions by means of integrals on smooth surfaces, a general representation using the distributional divergence of the tensor is derived. In the case where concentrations occur, this new approach allows a description of contact phenomena more precise than before. Contact Interaction Measure Zero Radon Measure Representation Formula Partial Restriction Enthalten in Archive for rational mechanics and analysis Springer Berlin Heidelberg, 1957 184(2006), 3 vom: 19. Sept., Seite 495-551 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:184 year:2006 number:3 day:19 month:09 pages:495-551 https://doi.org/10.1007/s00205-006-0032-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4323 GBV_ILN_4700 AR 184 2006 3 19 09 495-551 |
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10.1007/s00205-006-0032-6 doi (DE-627)OLC2056416085 (DE-He213)s00205-006-0032-6-p DE-627 ger DE-627 rakwb eng 530 510 VZ Schuricht, Friedemann verfasserin aut A New Mathematical Foundation for Contact Interactions in Continuum Physics 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2006 Abstract The investigation of contact interactions, such as traction and heat flux, that are exerted by contiguous bodies across the common boundary is a fundamental issue in continuum physics. However, the traditional theory of stress established by Cauchy and extended by Noll and his successors is insufficient for handling the lack of regularity in continuum physics due to shocks, corner singularities, and fracture. This paper provides a new mathematical foundation for the treatment of contact interactions. Based on mild physically motivated postulates, which differ essentially from those used before, the existence of a corresponding interaction tensor is established. While in earlier treatments contact interactions are basically defined on surfaces, here contact interactions are rigorously considered as maps on pairs of subbodies. This allows the action exerted on a subbody to be defined not only, as usual, for sets with a sufficiently regular boundary, but also for Borel sets (which include all open and all closed sets). In addition to the classical representation of such interactions by means of integrals on smooth surfaces, a general representation using the distributional divergence of the tensor is derived. In the case where concentrations occur, this new approach allows a description of contact phenomena more precise than before. Contact Interaction Measure Zero Radon Measure Representation Formula Partial Restriction Enthalten in Archive for rational mechanics and analysis Springer Berlin Heidelberg, 1957 184(2006), 3 vom: 19. Sept., Seite 495-551 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:184 year:2006 number:3 day:19 month:09 pages:495-551 https://doi.org/10.1007/s00205-006-0032-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4323 GBV_ILN_4700 AR 184 2006 3 19 09 495-551 |
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10.1007/s00205-006-0032-6 doi (DE-627)OLC2056416085 (DE-He213)s00205-006-0032-6-p DE-627 ger DE-627 rakwb eng 530 510 VZ Schuricht, Friedemann verfasserin aut A New Mathematical Foundation for Contact Interactions in Continuum Physics 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2006 Abstract The investigation of contact interactions, such as traction and heat flux, that are exerted by contiguous bodies across the common boundary is a fundamental issue in continuum physics. However, the traditional theory of stress established by Cauchy and extended by Noll and his successors is insufficient for handling the lack of regularity in continuum physics due to shocks, corner singularities, and fracture. This paper provides a new mathematical foundation for the treatment of contact interactions. Based on mild physically motivated postulates, which differ essentially from those used before, the existence of a corresponding interaction tensor is established. While in earlier treatments contact interactions are basically defined on surfaces, here contact interactions are rigorously considered as maps on pairs of subbodies. This allows the action exerted on a subbody to be defined not only, as usual, for sets with a sufficiently regular boundary, but also for Borel sets (which include all open and all closed sets). In addition to the classical representation of such interactions by means of integrals on smooth surfaces, a general representation using the distributional divergence of the tensor is derived. In the case where concentrations occur, this new approach allows a description of contact phenomena more precise than before. Contact Interaction Measure Zero Radon Measure Representation Formula Partial Restriction Enthalten in Archive for rational mechanics and analysis Springer Berlin Heidelberg, 1957 184(2006), 3 vom: 19. Sept., Seite 495-551 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:184 year:2006 number:3 day:19 month:09 pages:495-551 https://doi.org/10.1007/s00205-006-0032-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4323 GBV_ILN_4700 AR 184 2006 3 19 09 495-551 |
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10.1007/s00205-006-0032-6 doi (DE-627)OLC2056416085 (DE-He213)s00205-006-0032-6-p DE-627 ger DE-627 rakwb eng 530 510 VZ Schuricht, Friedemann verfasserin aut A New Mathematical Foundation for Contact Interactions in Continuum Physics 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2006 Abstract The investigation of contact interactions, such as traction and heat flux, that are exerted by contiguous bodies across the common boundary is a fundamental issue in continuum physics. However, the traditional theory of stress established by Cauchy and extended by Noll and his successors is insufficient for handling the lack of regularity in continuum physics due to shocks, corner singularities, and fracture. This paper provides a new mathematical foundation for the treatment of contact interactions. Based on mild physically motivated postulates, which differ essentially from those used before, the existence of a corresponding interaction tensor is established. While in earlier treatments contact interactions are basically defined on surfaces, here contact interactions are rigorously considered as maps on pairs of subbodies. This allows the action exerted on a subbody to be defined not only, as usual, for sets with a sufficiently regular boundary, but also for Borel sets (which include all open and all closed sets). In addition to the classical representation of such interactions by means of integrals on smooth surfaces, a general representation using the distributional divergence of the tensor is derived. In the case where concentrations occur, this new approach allows a description of contact phenomena more precise than before. Contact Interaction Measure Zero Radon Measure Representation Formula Partial Restriction Enthalten in Archive for rational mechanics and analysis Springer Berlin Heidelberg, 1957 184(2006), 3 vom: 19. Sept., Seite 495-551 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:184 year:2006 number:3 day:19 month:09 pages:495-551 https://doi.org/10.1007/s00205-006-0032-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4323 GBV_ILN_4700 AR 184 2006 3 19 09 495-551 |
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A New Mathematical Foundation for Contact Interactions in Continuum Physics |
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Abstract The investigation of contact interactions, such as traction and heat flux, that are exerted by contiguous bodies across the common boundary is a fundamental issue in continuum physics. However, the traditional theory of stress established by Cauchy and extended by Noll and his successors is insufficient for handling the lack of regularity in continuum physics due to shocks, corner singularities, and fracture. This paper provides a new mathematical foundation for the treatment of contact interactions. Based on mild physically motivated postulates, which differ essentially from those used before, the existence of a corresponding interaction tensor is established. While in earlier treatments contact interactions are basically defined on surfaces, here contact interactions are rigorously considered as maps on pairs of subbodies. This allows the action exerted on a subbody to be defined not only, as usual, for sets with a sufficiently regular boundary, but also for Borel sets (which include all open and all closed sets). In addition to the classical representation of such interactions by means of integrals on smooth surfaces, a general representation using the distributional divergence of the tensor is derived. In the case where concentrations occur, this new approach allows a description of contact phenomena more precise than before. © Springer-Verlag 2006 |
abstractGer |
Abstract The investigation of contact interactions, such as traction and heat flux, that are exerted by contiguous bodies across the common boundary is a fundamental issue in continuum physics. However, the traditional theory of stress established by Cauchy and extended by Noll and his successors is insufficient for handling the lack of regularity in continuum physics due to shocks, corner singularities, and fracture. This paper provides a new mathematical foundation for the treatment of contact interactions. Based on mild physically motivated postulates, which differ essentially from those used before, the existence of a corresponding interaction tensor is established. While in earlier treatments contact interactions are basically defined on surfaces, here contact interactions are rigorously considered as maps on pairs of subbodies. This allows the action exerted on a subbody to be defined not only, as usual, for sets with a sufficiently regular boundary, but also for Borel sets (which include all open and all closed sets). In addition to the classical representation of such interactions by means of integrals on smooth surfaces, a general representation using the distributional divergence of the tensor is derived. In the case where concentrations occur, this new approach allows a description of contact phenomena more precise than before. © Springer-Verlag 2006 |
abstract_unstemmed |
Abstract The investigation of contact interactions, such as traction and heat flux, that are exerted by contiguous bodies across the common boundary is a fundamental issue in continuum physics. However, the traditional theory of stress established by Cauchy and extended by Noll and his successors is insufficient for handling the lack of regularity in continuum physics due to shocks, corner singularities, and fracture. This paper provides a new mathematical foundation for the treatment of contact interactions. Based on mild physically motivated postulates, which differ essentially from those used before, the existence of a corresponding interaction tensor is established. While in earlier treatments contact interactions are basically defined on surfaces, here contact interactions are rigorously considered as maps on pairs of subbodies. This allows the action exerted on a subbody to be defined not only, as usual, for sets with a sufficiently regular boundary, but also for Borel sets (which include all open and all closed sets). In addition to the classical representation of such interactions by means of integrals on smooth surfaces, a general representation using the distributional divergence of the tensor is derived. In the case where concentrations occur, this new approach allows a description of contact phenomena more precise than before. © Springer-Verlag 2006 |
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