Stacking faults in the limit of a discrete model for partial edge dislocations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914859417862144 |
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| author | Bach, Annika Cicalese, Marco Garroni, Adriana Orlando, Gianluca |
| author_facet | Bach, Annika Cicalese, Marco Garroni, Adriana Orlando, Gianluca |
| contents | In the limit of vanishing lattice spacing we provide a rigorous variational coarse-graining result for a next-to-nearest neighbor lattice model of a simple crystal. We show that the $Γ$-limit of suitable scaled versions of the model leads to an energy describing a continuum mechanical model depending on partial dislocations and stacking faults. Our result highlights the necessary multiscale character of the energies setting the groundwork for more comprehensive models that can better explain and predict the mechanical behavior of materials with complex defect structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03975 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stacking faults in the limit of a discrete model for partial edge dislocations Bach, Annika Cicalese, Marco Garroni, Adriana Orlando, Gianluca Analysis of PDEs 49J45, 70G75, 74C05, 58K45 In the limit of vanishing lattice spacing we provide a rigorous variational coarse-graining result for a next-to-nearest neighbor lattice model of a simple crystal. We show that the $Γ$-limit of suitable scaled versions of the model leads to an energy describing a continuum mechanical model depending on partial dislocations and stacking faults. Our result highlights the necessary multiscale character of the energies setting the groundwork for more comprehensive models that can better explain and predict the mechanical behavior of materials with complex defect structures. |
| title | Stacking faults in the limit of a discrete model for partial edge dislocations |
| topic | Analysis of PDEs 49J45, 70G75, 74C05, 58K45 |
| url | https://arxiv.org/abs/2407.03975 |