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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2601.03814 |
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| _version_ | 1866917187992682496 |
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| author | Yu, Xiang Šmejkal, Michal Horák, Martin |
| author_facet | Yu, Xiang Šmejkal, Michal Horák, Martin |
| contents | We develop a general incremental framework for hyperelastic solids whose surfaces exhibit both stretch-dependent and curvature-dependent elastic behavior. Building upon a variational formulation of curvature-dependent surface elasticity, we derive compact governing equations expressed in a coordinate-free Lagrangian setting that remain valid for arbitrary geometries. Linearization about an arbitrarily large finite deformation yields incremental bulk and surface balance laws that closely resemble the classical small-on-large theory, but are now extended to include surface-curvatureinduced stresses. The applicability of the general theory is demonstrated by analyzing the onset of periodic beading in a soft cylindrical substrate coated with a surface layer exhibiting stretching- or curvature-dependent behavior, illustrating how surface stretching and bending effects influence instability thresholds for both compressible and incompressible bulk. This unified formulation thus provides a foundation for studying stability phenomena in elasto-capillary systems where surface curvature plays a critical mechanical role. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03814 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Incremental equations in curvature-dependent surface elasticity Yu, Xiang Šmejkal, Michal Horák, Martin Mathematical Physics We develop a general incremental framework for hyperelastic solids whose surfaces exhibit both stretch-dependent and curvature-dependent elastic behavior. Building upon a variational formulation of curvature-dependent surface elasticity, we derive compact governing equations expressed in a coordinate-free Lagrangian setting that remain valid for arbitrary geometries. Linearization about an arbitrarily large finite deformation yields incremental bulk and surface balance laws that closely resemble the classical small-on-large theory, but are now extended to include surface-curvatureinduced stresses. The applicability of the general theory is demonstrated by analyzing the onset of periodic beading in a soft cylindrical substrate coated with a surface layer exhibiting stretching- or curvature-dependent behavior, illustrating how surface stretching and bending effects influence instability thresholds for both compressible and incompressible bulk. This unified formulation thus provides a foundation for studying stability phenomena in elasto-capillary systems where surface curvature plays a critical mechanical role. |
| title | Incremental equations in curvature-dependent surface elasticity |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2601.03814 |