Homogenization of layered materials with rigid components in two-slip finite crystal plasticity
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910819564912640 |
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| author | Ishikawa, Akira Svadlenka, Karel |
| author_facet | Ishikawa, Akira Svadlenka, Karel |
| contents | This paper is an extension of the result by Christowiak and Kreisbeck (2017), which addresses the Gamma-convergence approach to a homogenization problem for composite materials consisting of two distinct types of parallel layers. In Christowiak et al. (2017), one of the layers of the material undergoes only local rotations while the other allows local rotation and plastic deformation along a single slip system. On the other hand, real materials show an interplay of multiple directions of slip. Here we obtain the Gamma-limit for the problem where the number of slip directions is increased to two. When the slip systems are orthogonal, we derive the full homogenized energy based on generalized convex envelopes of the original energy density. Since these envelopes are not completely known for angles between slip directions differing from the right angle, we present a partial, conditional homogenization result in this general case. The analysis is based on a modification of the classical construction of laminate microstructures but several nontrivial difficulties arise due to nonconvex constraints being present in the composite energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02912 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homogenization of layered materials with rigid components in two-slip finite crystal plasticity Ishikawa, Akira Svadlenka, Karel Analysis of PDEs Optimization and Control 49J45 (Primary) 74Q05, 74C15 (Secondary) This paper is an extension of the result by Christowiak and Kreisbeck (2017), which addresses the Gamma-convergence approach to a homogenization problem for composite materials consisting of two distinct types of parallel layers. In Christowiak et al. (2017), one of the layers of the material undergoes only local rotations while the other allows local rotation and plastic deformation along a single slip system. On the other hand, real materials show an interplay of multiple directions of slip. Here we obtain the Gamma-limit for the problem where the number of slip directions is increased to two. When the slip systems are orthogonal, we derive the full homogenized energy based on generalized convex envelopes of the original energy density. Since these envelopes are not completely known for angles between slip directions differing from the right angle, we present a partial, conditional homogenization result in this general case. The analysis is based on a modification of the classical construction of laminate microstructures but several nontrivial difficulties arise due to nonconvex constraints being present in the composite energy. |
| title | Homogenization of layered materials with rigid components in two-slip finite crystal plasticity |
| topic | Analysis of PDEs Optimization and Control 49J45 (Primary) 74Q05, 74C15 (Secondary) |
| url | https://arxiv.org/abs/2407.02912 |