One-dimensional motion of a material with a strain theshold
We consider the one-dimensional shearing motion of a material exhibiting elastic behaviour when the stress is below some threshold. The threshold represents a limit to the deformability, i.e. no further deformation can occur on increasing the stress. The mathematical formulation leads to a free boun...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Università degli Studi di Catania
2007-12-01
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| Series: | Le Matematiche |
| Subjects: | |
| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/36 |
| Summary: | We consider the one-dimensional shearing motion of a material exhibiting elastic behaviour when the stress is below some threshold. The threshold represents a limit to the deformability, i.e. no further deformation can occur on increasing the stress. The mathematical formulation leads to a free boundary problem for the wave equation, whose structure depends on whether the stress (and the velocity) are continuous across the propagating interface for the strain threshold .<br />Local existence and uniqueness are proved for the continuous case (in which the interface propagation is subsonic). Some explicit solutions are calculated for another case (with a supersonic interface). It is shown that the model with strain threshold is never the limit of hyperelastic systems. |
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| ISSN: | 0373-3505 2037-5298 |