On the impossibility of linear Cauchy and Piola-Kirchhoff constitutive theories for stress in solids
The possibility of linear elasticity in elastic solids is examined with regard to an infinitesimal theory based on a genuinely linear response function which retains its validity even for finite deformations. It is concluded that an exact linear constitutive theory for elastic solids is impossible....
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| Published in | Journal of elasticity Vol. 9; no. 1; pp. 83 - 89 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
01.01.1979
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| Online Access | Get full text |
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| Summary: | The possibility of linear elasticity in elastic solids is examined with regard to an infinitesimal theory based on a genuinely linear response function which retains its validity even for finite deformations. It is concluded that an exact linear constitutive theory for elastic solids is impossible. This conclusion results from consideration of the definition of linearity, the notion of material frame indifference, and the domain of definition of the stress response function. The result is generalized to viscoelasticity theory where the stress response is dependent on deformation gradient histories. |
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| Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| ISSN: | 0374-3535 1573-2681 |
| DOI: | 10.1007/BF00040982 |