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Precisely, we consider materials arranged into periodically alternating thin horizontal strips of an elastically rigid component and a softer one with one active slip system. The energies arising from these modeling assumptions are of integral form, featuring linear growth and non-convex differential constraints. We approach this non-standard homogenization problem via Gamma-convergence. A crucial first step in the asymptotic analysis is the characterization of rigidity properties of limits of admissible deformations in the space BV of functions of bounded variation. In particular, we prove that, under suitable assumptions, the two-dimensional body may split horizontally into finitely many pieces, each of which undergoes shear deformation and global rotation. This allows us to identify a potential candidate for the homogenized limit energy, which we show to be a lower bound on the Gamma-limit. In the framework of non-simple materials, we present a complete Gamma-convergence result, including an explicit homogenization formula, for a regularized model with an anisotropic penalization in the layer direction.<\/jats:p>","DOI":"10.1515\/acv-2019-0011","type":"journal-article","created":{"date-parts":[[2019,10,1]],"date-time":"2019-10-01T09:02:55Z","timestamp":1569920575000},"page":"441-473","source":"Crossref","is-referenced-by-count":10,"title":["Homogenization in BV of a model for layered composites in finite crystal plasticity"],"prefix":"10.1515","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1715-5004","authenticated-orcid":false,"given":"Elisa","family":"Davoli","sequence":"first","affiliation":[{"name":"Faculty of Mathematics , University of Vienna , Oskar-Morgenstern-Platz 1, 1090 Vienna , Austria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7169-9141","authenticated-orcid":false,"given":"Rita","family":"Ferreira","sequence":"additional","affiliation":[{"name":"King Abdullah University of Science and Technology (KAUST) , CEMSE Division , Thuwal 23955-6900 , Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4775-8666","authenticated-orcid":false,"given":"Carolin","family":"Kreisbeck","sequence":"additional","affiliation":[{"name":"Mathematisch Instituut , Universiteit Utrecht , Postbus 80010, 3508 TA Utrecht , The Netherlands"}]}],"member":"374","published-online":{"date-parts":[[2019,10,1]]},"reference":[{"key":"2023033110232383127_j_acv-2019-0011_ref_001","doi-asserted-by":"crossref","unstructured":"G. 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