Solutions for a free-boundary problem modeling multilayer films with coherent and incoherent interfaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914654259773440 |
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| author | Llerena, Randy Piovano, Paolo |
| author_facet | Llerena, Randy Piovano, Paolo |
| contents | In this paper we introduce a variational model for the study of multilayer films that allows for the treatment of both coherent and incoherent interfaces between layers. The model is designed in the framework of the theory of Stress Driven Rearrangement Instabilities, which are characterized by the competition between elastic and surface energy effects. The surface of each film layer is assumed to satisfy an ''exterior graph condition'', under which in particular bulk cracks are allowed to be of non-graph type. By applying the direct method of calculus of variations under a constraint on the number of connected components of the cracks not connected to the surface of the film layers the existence of energy minimizers is established in dimension 2. As a byproduct of the analysis the state of art on the variational modeling of single-layered films deposited on a fixed substrate is advanced by letting the substrate surface free, by addressing the presence of multiple layers of various materials, and by including the possibility of delamination between the various film layers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solutions for a free-boundary problem modeling multilayer films with coherent and incoherent interfaces Llerena, Randy Piovano, Paolo Analysis of PDEs 49J10, 49Q15, 49Q20, 35R35, 74A45, 74A50, 74G65 In this paper we introduce a variational model for the study of multilayer films that allows for the treatment of both coherent and incoherent interfaces between layers. The model is designed in the framework of the theory of Stress Driven Rearrangement Instabilities, which are characterized by the competition between elastic and surface energy effects. The surface of each film layer is assumed to satisfy an ''exterior graph condition'', under which in particular bulk cracks are allowed to be of non-graph type. By applying the direct method of calculus of variations under a constraint on the number of connected components of the cracks not connected to the surface of the film layers the existence of energy minimizers is established in dimension 2. As a byproduct of the analysis the state of art on the variational modeling of single-layered films deposited on a fixed substrate is advanced by letting the substrate surface free, by addressing the presence of multiple layers of various materials, and by including the possibility of delamination between the various film layers. |
| title | Solutions for a free-boundary problem modeling multilayer films with coherent and incoherent interfaces |
| topic | Analysis of PDEs 49J10, 49Q15, 49Q20, 35R35, 74A45, 74A50, 74G65 |
| url | https://arxiv.org/abs/2401.14866 |