Analytical expressions for the two basic modes of surface displacement and overall deformation of a free-standing or elastically embedded sphere
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909252186013696 |
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| author | Fischer, Lukas Menzel, Andreas M. |
| author_facet | Fischer, Lukas Menzel, Andreas M. |
| contents | Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a homogeneous, isotropic, linearly elastic sphere. The modes under consideration correspond to overall changes in volume and to relative uniaxial elongation or contraction. Both situations of an elastic sphere embedded under no-slip conditions in a linearly elastic, homogeneous, isotropic, infinitely extended background medium and of a free-standing elastic sphere are considered. For example, our analytical expressions are important as a basis for computational material optimization in the context of spherical soft actuators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09291 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytical expressions for the two basic modes of surface displacement and overall deformation of a free-standing or elastically embedded sphere Fischer, Lukas Menzel, Andreas M. Soft Condensed Matter Mathematical Physics Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a homogeneous, isotropic, linearly elastic sphere. The modes under consideration correspond to overall changes in volume and to relative uniaxial elongation or contraction. Both situations of an elastic sphere embedded under no-slip conditions in a linearly elastic, homogeneous, isotropic, infinitely extended background medium and of a free-standing elastic sphere are considered. For example, our analytical expressions are important as a basis for computational material optimization in the context of spherical soft actuators. |
| title | Analytical expressions for the two basic modes of surface displacement and overall deformation of a free-standing or elastically embedded sphere |
| topic | Soft Condensed Matter Mathematical Physics |
| url | https://arxiv.org/abs/2407.09291 |