{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T03:33:13Z","timestamp":1648956793361},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2010,1,1]],"date-time":"2010-01-01T00:00:00Z","timestamp":1262304000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Methods Appl. Math."],"published-print":{"date-parts":[[2010]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The paper deals with the numerical computation of a crack problem\nposed on microstructural heterogeneous materials containing multiple phases in the\nmicrostructure. The failure of such materials is a natural multi-scale effect since cracks\ntypically nucleate in regions of defects on the microscopic scale. The modeling strategy\nfor solving the crack problem concerns simultaneously the macroscopic and microscopic\nmodels. Our approach is based on an efficient combination of the homogenization technique\nand the mesh superposition method (s-version of the finite element method). The\nhomogenized model relies on a double-scale asymptotic expansion of the displacement\nfield. The mesh superposition method uses two independent (global and local) finite\nelement meshes and the concept of superposing the local mesh arbitrarily on the global\ncontinuous mesh. The crack is treated by the local mesh and the homogenized material\nmodel is considered on the global mesh. Numerical experiments for problems on\nbiomorphic microcellular ceramic templates with porous microstructures of different\nmaterials constituents are presented.<\/jats:p>","DOI":"10.2478\/cmam-2010-0003","type":"journal-article","created":{"date-parts":[[2013,4,15]],"date-time":"2013-04-15T15:48:24Z","timestamp":1366040904000},"page":"69-86","source":"Crossref","is-referenced-by-count":2,"title":["Multi-scale Method for the Crack Problem in Microstructural Materials"],"prefix":"10.2478","volume":"10","author":[{"given":"R. H. W.","family":"Hoppe","sequence":"first","affiliation":[{"name":"1Institute of Mathematics, University of Augsburg, D-86159 Augsburg, Germany; Department of Mathematics, University of Houston, Houston, TX 77204\u20133008, USA."}]},{"given":"S.I.","family":"Petrova","sequence":"additional","affiliation":[{"name":"2Department of Mathematics, University of Applied Sciences, D-33609 Bielefeld, Germany; Institute for Parallel Processing, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/10\/1\/article-p69.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2010-0003\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:21:34Z","timestamp":1619101294000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/10\/1\/article-p69.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"references-count":0,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2010-0003","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2010]]}}}