Thermal and moisture expansion of material elements and macroscopic bodies with geometrical symmetries—wood logs and sawn goods as practical examples

Abstract Thermal and moisture expansion states available to material elements with particular symmetries, as well as macroscopic bodies with particular structural symmetries, are investigated in terms of Group Theory and Curie’s principle. It is found that in the case of one-dimensional material sym...
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Autor*in:	Kärenlampi, Petri P. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2011

Schlagwörter:	Group theory Geometric algebra Thermal expansion Hygroexpansion

Anmerkung:	© RILEM 2011

Übergeordnetes Werk:	Enthalten in: Materials and structures - Cachan : RILEM Publications SARL, 1968, 45(2011), 5 vom: 18. Okt., Seite 747-764
Übergeordnetes Werk:	volume:45 ; year:2011 ; number:5 ; day:18 ; month:10 ; pages:747-764

Links:	Volltext

DOI / URN:	10.1617/s11527-011-9795-9

Katalog-ID:	SPR020565526

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520			\|a Abstract Thermal and moisture expansion states available to material elements with particular symmetries, as well as macroscopic bodies with particular structural symmetries, are investigated in terms of Group Theory and Curie’s principle. It is found that in the case of one-dimensional material symmetry, Eigen shear strain of the material element must be zero within any plane perpendicular to the reflection plane. The same applies to the most simple two-dimensional rotation symmetry, within any plane including the rotation axis. The corresponding reflection-rotation symmetry requires all the Eigen shear strains to be zero. Greater 2-d rotation symmetries require, in addition, normal eigenstrains perpendicular to the rotation axis to be equal, which means transverse isotropy of the eigenstrain tensor. Such a strain state complies with three-dimensional rotation symmetries, as long as not more than one of the symmetries is of order greater than 2. In such case all the normal eigenstrains must be equal, corresponding to isotropy of the eigenstrain tensor. Unlike two-dimensional symmetries, any three-dimensional reflection–rotation symmetry does not place more restrictions on the eigenstrain state than the corresponding rotation symmetry. There is, however, a three-dimensional symmetry which places no restriction on the eigenstrain state. Possible non-uniform eigenstrain states of macroscopic bodies are discussed. Eigendeformations of wood logs are illustrated as examples. It is found that one abstract symmetry group may correspond to several geometrical symmetry groups, and the geometrical symmetry group of a body may depend on the choice of co-ordinate system. Log symmetries translate into sawn goods provided the sawing pattern complies with the log symmetries.
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allfields	10.1617/s11527-011-9795-9 doi (DE-627)SPR020565526 (SPR)s11527-011-9795-9-e DE-627 ger DE-627 rakwb eng Kärenlampi, Petri P. verfasserin aut Thermal and moisture expansion of material elements and macroscopic bodies with geometrical symmetries—wood logs and sawn goods as practical examples 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © RILEM 2011 Abstract Thermal and moisture expansion states available to material elements with particular symmetries, as well as macroscopic bodies with particular structural symmetries, are investigated in terms of Group Theory and Curie’s principle. It is found that in the case of one-dimensional material symmetry, Eigen shear strain of the material element must be zero within any plane perpendicular to the reflection plane. The same applies to the most simple two-dimensional rotation symmetry, within any plane including the rotation axis. The corresponding reflection-rotation symmetry requires all the Eigen shear strains to be zero. Greater 2-d rotation symmetries require, in addition, normal eigenstrains perpendicular to the rotation axis to be equal, which means transverse isotropy of the eigenstrain tensor. Such a strain state complies with three-dimensional rotation symmetries, as long as not more than one of the symmetries is of order greater than 2. In such case all the normal eigenstrains must be equal, corresponding to isotropy of the eigenstrain tensor. Unlike two-dimensional symmetries, any three-dimensional reflection–rotation symmetry does not place more restrictions on the eigenstrain state than the corresponding rotation symmetry. There is, however, a three-dimensional symmetry which places no restriction on the eigenstrain state. Possible non-uniform eigenstrain states of macroscopic bodies are discussed. Eigendeformations of wood logs are illustrated as examples. It is found that one abstract symmetry group may correspond to several geometrical symmetry groups, and the geometrical symmetry group of a body may depend on the choice of co-ordinate system. Log symmetries translate into sawn goods provided the sawing pattern complies with the log symmetries. Group theory (dpeaa)DE-He213 Geometric algebra (dpeaa)DE-He213 Thermal expansion (dpeaa)DE-He213 Hygroexpansion (dpeaa)DE-He213 Enthalten in Materials and structures Cachan : RILEM Publications SARL, 1968 45(2011), 5 vom: 18. Okt., Seite 747-764 (DE-627)356252612 (DE-600)2091922-0 1871-6873 nnns volume:45 year:2011 number:5 day:18 month:10 pages:747-764 https://dx.doi.org/10.1617/s11527-011-9795-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 45 2011 5 18 10 747-764
spelling	10.1617/s11527-011-9795-9 doi (DE-627)SPR020565526 (SPR)s11527-011-9795-9-e DE-627 ger DE-627 rakwb eng Kärenlampi, Petri P. verfasserin aut Thermal and moisture expansion of material elements and macroscopic bodies with geometrical symmetries—wood logs and sawn goods as practical examples 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © RILEM 2011 Abstract Thermal and moisture expansion states available to material elements with particular symmetries, as well as macroscopic bodies with particular structural symmetries, are investigated in terms of Group Theory and Curie’s principle. It is found that in the case of one-dimensional material symmetry, Eigen shear strain of the material element must be zero within any plane perpendicular to the reflection plane. The same applies to the most simple two-dimensional rotation symmetry, within any plane including the rotation axis. The corresponding reflection-rotation symmetry requires all the Eigen shear strains to be zero. Greater 2-d rotation symmetries require, in addition, normal eigenstrains perpendicular to the rotation axis to be equal, which means transverse isotropy of the eigenstrain tensor. Such a strain state complies with three-dimensional rotation symmetries, as long as not more than one of the symmetries is of order greater than 2. In such case all the normal eigenstrains must be equal, corresponding to isotropy of the eigenstrain tensor. Unlike two-dimensional symmetries, any three-dimensional reflection–rotation symmetry does not place more restrictions on the eigenstrain state than the corresponding rotation symmetry. There is, however, a three-dimensional symmetry which places no restriction on the eigenstrain state. Possible non-uniform eigenstrain states of macroscopic bodies are discussed. Eigendeformations of wood logs are illustrated as examples. It is found that one abstract symmetry group may correspond to several geometrical symmetry groups, and the geometrical symmetry group of a body may depend on the choice of co-ordinate system. Log symmetries translate into sawn goods provided the sawing pattern complies with the log symmetries. Group theory (dpeaa)DE-He213 Geometric algebra (dpeaa)DE-He213 Thermal expansion (dpeaa)DE-He213 Hygroexpansion (dpeaa)DE-He213 Enthalten in Materials and structures Cachan : RILEM Publications SARL, 1968 45(2011), 5 vom: 18. Okt., Seite 747-764 (DE-627)356252612 (DE-600)2091922-0 1871-6873 nnns volume:45 year:2011 number:5 day:18 month:10 pages:747-764 https://dx.doi.org/10.1617/s11527-011-9795-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 45 2011 5 18 10 747-764
allfields_unstemmed	10.1617/s11527-011-9795-9 doi (DE-627)SPR020565526 (SPR)s11527-011-9795-9-e DE-627 ger DE-627 rakwb eng Kärenlampi, Petri P. verfasserin aut Thermal and moisture expansion of material elements and macroscopic bodies with geometrical symmetries—wood logs and sawn goods as practical examples 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © RILEM 2011 Abstract Thermal and moisture expansion states available to material elements with particular symmetries, as well as macroscopic bodies with particular structural symmetries, are investigated in terms of Group Theory and Curie’s principle. It is found that in the case of one-dimensional material symmetry, Eigen shear strain of the material element must be zero within any plane perpendicular to the reflection plane. The same applies to the most simple two-dimensional rotation symmetry, within any plane including the rotation axis. The corresponding reflection-rotation symmetry requires all the Eigen shear strains to be zero. Greater 2-d rotation symmetries require, in addition, normal eigenstrains perpendicular to the rotation axis to be equal, which means transverse isotropy of the eigenstrain tensor. Such a strain state complies with three-dimensional rotation symmetries, as long as not more than one of the symmetries is of order greater than 2. In such case all the normal eigenstrains must be equal, corresponding to isotropy of the eigenstrain tensor. Unlike two-dimensional symmetries, any three-dimensional reflection–rotation symmetry does not place more restrictions on the eigenstrain state than the corresponding rotation symmetry. There is, however, a three-dimensional symmetry which places no restriction on the eigenstrain state. Possible non-uniform eigenstrain states of macroscopic bodies are discussed. Eigendeformations of wood logs are illustrated as examples. It is found that one abstract symmetry group may correspond to several geometrical symmetry groups, and the geometrical symmetry group of a body may depend on the choice of co-ordinate system. Log symmetries translate into sawn goods provided the sawing pattern complies with the log symmetries. Group theory (dpeaa)DE-He213 Geometric algebra (dpeaa)DE-He213 Thermal expansion (dpeaa)DE-He213 Hygroexpansion (dpeaa)DE-He213 Enthalten in Materials and structures Cachan : RILEM Publications SARL, 1968 45(2011), 5 vom: 18. Okt., Seite 747-764 (DE-627)356252612 (DE-600)2091922-0 1871-6873 nnns volume:45 year:2011 number:5 day:18 month:10 pages:747-764 https://dx.doi.org/10.1617/s11527-011-9795-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 45 2011 5 18 10 747-764
allfieldsGer	10.1617/s11527-011-9795-9 doi (DE-627)SPR020565526 (SPR)s11527-011-9795-9-e DE-627 ger DE-627 rakwb eng Kärenlampi, Petri P. verfasserin aut Thermal and moisture expansion of material elements and macroscopic bodies with geometrical symmetries—wood logs and sawn goods as practical examples 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © RILEM 2011 Abstract Thermal and moisture expansion states available to material elements with particular symmetries, as well as macroscopic bodies with particular structural symmetries, are investigated in terms of Group Theory and Curie’s principle. It is found that in the case of one-dimensional material symmetry, Eigen shear strain of the material element must be zero within any plane perpendicular to the reflection plane. The same applies to the most simple two-dimensional rotation symmetry, within any plane including the rotation axis. The corresponding reflection-rotation symmetry requires all the Eigen shear strains to be zero. Greater 2-d rotation symmetries require, in addition, normal eigenstrains perpendicular to the rotation axis to be equal, which means transverse isotropy of the eigenstrain tensor. Such a strain state complies with three-dimensional rotation symmetries, as long as not more than one of the symmetries is of order greater than 2. In such case all the normal eigenstrains must be equal, corresponding to isotropy of the eigenstrain tensor. Unlike two-dimensional symmetries, any three-dimensional reflection–rotation symmetry does not place more restrictions on the eigenstrain state than the corresponding rotation symmetry. There is, however, a three-dimensional symmetry which places no restriction on the eigenstrain state. Possible non-uniform eigenstrain states of macroscopic bodies are discussed. Eigendeformations of wood logs are illustrated as examples. It is found that one abstract symmetry group may correspond to several geometrical symmetry groups, and the geometrical symmetry group of a body may depend on the choice of co-ordinate system. Log symmetries translate into sawn goods provided the sawing pattern complies with the log symmetries. Group theory (dpeaa)DE-He213 Geometric algebra (dpeaa)DE-He213 Thermal expansion (dpeaa)DE-He213 Hygroexpansion (dpeaa)DE-He213 Enthalten in Materials and structures Cachan : RILEM Publications SARL, 1968 45(2011), 5 vom: 18. Okt., Seite 747-764 (DE-627)356252612 (DE-600)2091922-0 1871-6873 nnns volume:45 year:2011 number:5 day:18 month:10 pages:747-764 https://dx.doi.org/10.1617/s11527-011-9795-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 45 2011 5 18 10 747-764
allfieldsSound	10.1617/s11527-011-9795-9 doi (DE-627)SPR020565526 (SPR)s11527-011-9795-9-e DE-627 ger DE-627 rakwb eng Kärenlampi, Petri P. verfasserin aut Thermal and moisture expansion of material elements and macroscopic bodies with geometrical symmetries—wood logs and sawn goods as practical examples 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © RILEM 2011 Abstract Thermal and moisture expansion states available to material elements with particular symmetries, as well as macroscopic bodies with particular structural symmetries, are investigated in terms of Group Theory and Curie’s principle. It is found that in the case of one-dimensional material symmetry, Eigen shear strain of the material element must be zero within any plane perpendicular to the reflection plane. The same applies to the most simple two-dimensional rotation symmetry, within any plane including the rotation axis. The corresponding reflection-rotation symmetry requires all the Eigen shear strains to be zero. Greater 2-d rotation symmetries require, in addition, normal eigenstrains perpendicular to the rotation axis to be equal, which means transverse isotropy of the eigenstrain tensor. Such a strain state complies with three-dimensional rotation symmetries, as long as not more than one of the symmetries is of order greater than 2. In such case all the normal eigenstrains must be equal, corresponding to isotropy of the eigenstrain tensor. Unlike two-dimensional symmetries, any three-dimensional reflection–rotation symmetry does not place more restrictions on the eigenstrain state than the corresponding rotation symmetry. There is, however, a three-dimensional symmetry which places no restriction on the eigenstrain state. Possible non-uniform eigenstrain states of macroscopic bodies are discussed. Eigendeformations of wood logs are illustrated as examples. It is found that one abstract symmetry group may correspond to several geometrical symmetry groups, and the geometrical symmetry group of a body may depend on the choice of co-ordinate system. Log symmetries translate into sawn goods provided the sawing pattern complies with the log symmetries. Group theory (dpeaa)DE-He213 Geometric algebra (dpeaa)DE-He213 Thermal expansion (dpeaa)DE-He213 Hygroexpansion (dpeaa)DE-He213 Enthalten in Materials and structures Cachan : RILEM Publications SARL, 1968 45(2011), 5 vom: 18. Okt., Seite 747-764 (DE-627)356252612 (DE-600)2091922-0 1871-6873 nnns volume:45 year:2011 number:5 day:18 month:10 pages:747-764 https://dx.doi.org/10.1617/s11527-011-9795-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 45 2011 5 18 10 747-764
language	English
source	Enthalten in Materials and structures 45(2011), 5 vom: 18. Okt., Seite 747-764 volume:45 year:2011 number:5 day:18 month:10 pages:747-764
sourceStr	Enthalten in Materials and structures 45(2011), 5 vom: 18. Okt., Seite 747-764 volume:45 year:2011 number:5 day:18 month:10 pages:747-764
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Group theory Geometric algebra Thermal expansion Hygroexpansion
isfreeaccess_bool	false
container_title	Materials and structures
authorswithroles_txt_mv	Kärenlampi, Petri P. @@aut@@
publishDateDaySort_date	2011-10-18T00:00:00Z
hierarchy_top_id	356252612
id	SPR020565526
language_de	englisch
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author	Kärenlampi, Petri P.
spellingShingle	Kärenlampi, Petri P. misc Group theory misc Geometric algebra misc Thermal expansion misc Hygroexpansion Thermal and moisture expansion of material elements and macroscopic bodies with geometrical symmetries—wood logs and sawn goods as practical examples
authorStr	Kärenlampi, Petri P.
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topic_title	Thermal and moisture expansion of material elements and macroscopic bodies with geometrical symmetries—wood logs and sawn goods as practical examples Group theory (dpeaa)DE-He213 Geometric algebra (dpeaa)DE-He213 Thermal expansion (dpeaa)DE-He213 Hygroexpansion (dpeaa)DE-He213
topic	misc Group theory misc Geometric algebra misc Thermal expansion misc Hygroexpansion
topic_unstemmed	misc Group theory misc Geometric algebra misc Thermal expansion misc Hygroexpansion
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title	Thermal and moisture expansion of material elements and macroscopic bodies with geometrical symmetries—wood logs and sawn goods as practical examples
ctrlnum	(DE-627)SPR020565526 (SPR)s11527-011-9795-9-e
title_full	Thermal and moisture expansion of material elements and macroscopic bodies with geometrical symmetries—wood logs and sawn goods as practical examples
author_sort	Kärenlampi, Petri P.
journal	Materials and structures
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author_browse	Kärenlampi, Petri P.
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author-letter	Kärenlampi, Petri P.
doi_str_mv	10.1617/s11527-011-9795-9
title_sort	thermal and moisture expansion of material elements and macroscopic bodies with geometrical symmetries—wood logs and sawn goods as practical examples
title_auth	Thermal and moisture expansion of material elements and macroscopic bodies with geometrical symmetries—wood logs and sawn goods as practical examples
abstract	Abstract Thermal and moisture expansion states available to material elements with particular symmetries, as well as macroscopic bodies with particular structural symmetries, are investigated in terms of Group Theory and Curie’s principle. It is found that in the case of one-dimensional material symmetry, Eigen shear strain of the material element must be zero within any plane perpendicular to the reflection plane. The same applies to the most simple two-dimensional rotation symmetry, within any plane including the rotation axis. The corresponding reflection-rotation symmetry requires all the Eigen shear strains to be zero. Greater 2-d rotation symmetries require, in addition, normal eigenstrains perpendicular to the rotation axis to be equal, which means transverse isotropy of the eigenstrain tensor. Such a strain state complies with three-dimensional rotation symmetries, as long as not more than one of the symmetries is of order greater than 2. In such case all the normal eigenstrains must be equal, corresponding to isotropy of the eigenstrain tensor. Unlike two-dimensional symmetries, any three-dimensional reflection–rotation symmetry does not place more restrictions on the eigenstrain state than the corresponding rotation symmetry. There is, however, a three-dimensional symmetry which places no restriction on the eigenstrain state. Possible non-uniform eigenstrain states of macroscopic bodies are discussed. Eigendeformations of wood logs are illustrated as examples. It is found that one abstract symmetry group may correspond to several geometrical symmetry groups, and the geometrical symmetry group of a body may depend on the choice of co-ordinate system. Log symmetries translate into sawn goods provided the sawing pattern complies with the log symmetries. © RILEM 2011
abstractGer	Abstract Thermal and moisture expansion states available to material elements with particular symmetries, as well as macroscopic bodies with particular structural symmetries, are investigated in terms of Group Theory and Curie’s principle. It is found that in the case of one-dimensional material symmetry, Eigen shear strain of the material element must be zero within any plane perpendicular to the reflection plane. The same applies to the most simple two-dimensional rotation symmetry, within any plane including the rotation axis. The corresponding reflection-rotation symmetry requires all the Eigen shear strains to be zero. Greater 2-d rotation symmetries require, in addition, normal eigenstrains perpendicular to the rotation axis to be equal, which means transverse isotropy of the eigenstrain tensor. Such a strain state complies with three-dimensional rotation symmetries, as long as not more than one of the symmetries is of order greater than 2. In such case all the normal eigenstrains must be equal, corresponding to isotropy of the eigenstrain tensor. Unlike two-dimensional symmetries, any three-dimensional reflection–rotation symmetry does not place more restrictions on the eigenstrain state than the corresponding rotation symmetry. There is, however, a three-dimensional symmetry which places no restriction on the eigenstrain state. Possible non-uniform eigenstrain states of macroscopic bodies are discussed. Eigendeformations of wood logs are illustrated as examples. It is found that one abstract symmetry group may correspond to several geometrical symmetry groups, and the geometrical symmetry group of a body may depend on the choice of co-ordinate system. Log symmetries translate into sawn goods provided the sawing pattern complies with the log symmetries. © RILEM 2011
abstract_unstemmed	Abstract Thermal and moisture expansion states available to material elements with particular symmetries, as well as macroscopic bodies with particular structural symmetries, are investigated in terms of Group Theory and Curie’s principle. It is found that in the case of one-dimensional material symmetry, Eigen shear strain of the material element must be zero within any plane perpendicular to the reflection plane. The same applies to the most simple two-dimensional rotation symmetry, within any plane including the rotation axis. The corresponding reflection-rotation symmetry requires all the Eigen shear strains to be zero. Greater 2-d rotation symmetries require, in addition, normal eigenstrains perpendicular to the rotation axis to be equal, which means transverse isotropy of the eigenstrain tensor. Such a strain state complies with three-dimensional rotation symmetries, as long as not more than one of the symmetries is of order greater than 2. In such case all the normal eigenstrains must be equal, corresponding to isotropy of the eigenstrain tensor. Unlike two-dimensional symmetries, any three-dimensional reflection–rotation symmetry does not place more restrictions on the eigenstrain state than the corresponding rotation symmetry. There is, however, a three-dimensional symmetry which places no restriction on the eigenstrain state. Possible non-uniform eigenstrain states of macroscopic bodies are discussed. Eigendeformations of wood logs are illustrated as examples. It is found that one abstract symmetry group may correspond to several geometrical symmetry groups, and the geometrical symmetry group of a body may depend on the choice of co-ordinate system. Log symmetries translate into sawn goods provided the sawing pattern complies with the log symmetries. © RILEM 2011
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title_short	Thermal and moisture expansion of material elements and macroscopic bodies with geometrical symmetries—wood logs and sawn goods as practical examples
url	https://dx.doi.org/10.1617/s11527-011-9795-9
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up_date	2024-07-03T16:53:27.912Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR020565526</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230330153215.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201006s2011 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1617/s11527-011-9795-9</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR020565526</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s11527-011-9795-9-e</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="100" ind1="1" ind2=" "><subfield code="a">Kärenlampi, Petri P.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Thermal and moisture expansion of material elements and macroscopic bodies with geometrical symmetries—wood logs and sawn goods as practical examples</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2011</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© RILEM 2011</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Thermal and moisture expansion states available to material elements with particular symmetries, as well as macroscopic bodies with particular structural symmetries, are investigated in terms of Group Theory and Curie’s principle. It is found that in the case of one-dimensional material symmetry, Eigen shear strain of the material element must be zero within any plane perpendicular to the reflection plane. The same applies to the most simple two-dimensional rotation symmetry, within any plane including the rotation axis. The corresponding reflection-rotation symmetry requires all the Eigen shear strains to be zero. Greater 2-d rotation symmetries require, in addition, normal eigenstrains perpendicular to the rotation axis to be equal, which means transverse isotropy of the eigenstrain tensor. Such a strain state complies with three-dimensional rotation symmetries, as long as not more than one of the symmetries is of order greater than 2. In such case all the normal eigenstrains must be equal, corresponding to isotropy of the eigenstrain tensor. Unlike two-dimensional symmetries, any three-dimensional reflection–rotation symmetry does not place more restrictions on the eigenstrain state than the corresponding rotation symmetry. There is, however, a three-dimensional symmetry which places no restriction on the eigenstrain state. Possible non-uniform eigenstrain states of macroscopic bodies are discussed. Eigendeformations of wood logs are illustrated as examples. It is found that one abstract symmetry group may correspond to several geometrical symmetry groups, and the geometrical symmetry group of a body may depend on the choice of co-ordinate system. 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