{"id":"https://openalex.org/W3148298578","doi":"https://doi.org/10.1007/s00332-021-09733-1","title":"Phase-Field Approximation of Functionals Defined on Piecewise-Rigid Maps","display_name":"Phase-Field Approximation of Functionals Defined on Piecewise-Rigid Maps","publication_year":2021,"publication_date":"2021-07-22","ids":{"openalex":"https://openalex.org/W3148298578","doi":"https://doi.org/10.1007/s00332-021-09733-1","mag":"3148298578"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-021-09733-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-021-09733-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-021-09733-1.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00332-021-09733-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Marco Cicalese","orcid":"https://orcid.org/0000-0003-3650-4078"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Marco Cicalese","raw_affiliation_strings":["Zentrum Mathematik - M7, Technische Universit\u00e4t M\u00fcnchen, Boltzmannstrasse 3, 85747, Garching, Germany"],"raw_orcid":"https://orcid.org/0000-0003-3650-4078","affiliations":[{"raw_affiliation_string":"Zentrum Mathematik - M7, Technische Universit\u00e4t M\u00fcnchen, Boltzmannstrasse 3, 85747, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Matteo Focardi","orcid":null},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Matteo Focardi","raw_affiliation_strings":["DiMaI \u201cU. Dini\u201d, Universit\u00e0 di Firenze, V.le G.B. Morgagni 67/A, 50134, Firenze, Italia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DiMaI \u201cU. Dini\u201d, Universit\u00e0 di Firenze, V.le G.B. Morgagni 67/A, 50134, Firenze, Italia","institution_ids":["https://openalex.org/I45084792"]}]},{"author_position":"last","author":{"id":null,"display_name":"Caterina Ida Zeppieri","orcid":null},"institutions":[{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Caterina Ida Zeppieri","raw_affiliation_strings":["Angewandte Mathematik, Universit\u00e4t M\u00fcnster, Einsteinstr. 62, 48149, M\u00fcnster, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Angewandte Mathematik, Universit\u00e4t M\u00fcnster, Einsteinstr. 62, 48149, M\u00fcnster, Germany","institution_ids":["https://openalex.org/I22465464"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.3302,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.4735457,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"31","issue":"5","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.23659999668598175,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.23659999668598175,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.19099999964237213,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.09000000357627869,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/elasticity","display_name":"Elasticity (physics)","score":0.592199981212616},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5625},{"id":"https://openalex.org/keywords/nonlinear-elasticity","display_name":"Nonlinear elasticity","score":0.4884999990463257},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4593000113964081},{"id":"https://openalex.org/keywords/approximation-theory","display_name":"Approximation theory","score":0.3183000087738037},{"id":"https://openalex.org/keywords/variational-method","display_name":"Variational method","score":0.3127000033855438},{"id":"https://openalex.org/keywords/linear-approximation","display_name":"Linear approximation","score":0.3070000112056732}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6075000166893005},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.592199981212616},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5625},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5083000063896179},{"id":"https://openalex.org/C2983365874","wikidata":"https://www.wikidata.org/wiki/Q193514","display_name":"Nonlinear elasticity","level":3,"score":0.4884999990463257},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4593000113964081},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.373199999332428},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.3183000087738037},{"id":"https://openalex.org/C64618476","wikidata":"https://www.wikidata.org/wiki/Q164296","display_name":"Variational method","level":2,"score":0.3127000033855438},{"id":"https://openalex.org/C160824197","wikidata":"https://www.wikidata.org/wiki/Q2071054","display_name":"Linear approximation","level":3,"score":0.3070000112056732},{"id":"https://openalex.org/C2988439775","wikidata":"https://www.wikidata.org/wiki/Q5120022","display_name":"Brittle fracture","level":3,"score":0.2994999885559082},{"id":"https://openalex.org/C136478896","wikidata":"https://www.wikidata.org/wiki/Q898288","display_name":"Brittleness","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C3161131","wikidata":"https://www.wikidata.org/wiki/Q14097093","display_name":"Linear elasticity","level":3,"score":0.28119999170303345},{"id":"https://openalex.org/C43369102","wikidata":"https://www.wikidata.org/wiki/Q2307625","display_name":"Fracture (geology)","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.2606000006198883}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00332-021-09733-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-021-09733-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-021-09733-1.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2104.00658","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.00658","pdf_url":"https://arxiv.org/pdf/2104.00658","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:flore.unifi.it:2158/1249148","is_oa":true,"landing_page_url":"https://link.springer.com/article/10.1007/s00332-021-09733-1","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1705193","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1705193","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s00332-021-09733-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-021-09733-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-021-09733-1.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1177974802","display_name":null,"funder_award_id":"EXC 2044-390685587","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G1652504919","display_name":null,"funder_award_id":"EXC 2044","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G2110285270","display_name":null,"funder_award_id":"2044-390685587","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G2817606592","display_name":null,"funder_award_id":"390685587","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5074471488","display_name":null,"funder_award_id":"Excellence Strategy EXC 2044-390685587","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6773318802","display_name":null,"funder_award_id":"TRR 109","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8055832297","display_name":null,"funder_award_id":"EXC 2044-390685587, Mathematics M\u00fcnster: Dynamics-Geometry-Structure","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320323383","display_name":"Technische Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/02kkvpp62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3148298578.pdf","grobid_xml":"https://content.openalex.org/works/W3148298578.grobid-xml"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W140204898","https://openalex.org/W1480714962","https://openalex.org/W1504810697","https://openalex.org/W1544809911","https://openalex.org/W1657273372","https://openalex.org/W1970124681","https://openalex.org/W1970594704","https://openalex.org/W1975418759","https://openalex.org/W1975664820","https://openalex.org/W1976023670","https://openalex.org/W1986629145","https://openalex.org/W1990541396","https://openalex.org/W2002918602","https://openalex.org/W2006668994","https://openalex.org/W2007458449","https://openalex.org/W2025599926","https://openalex.org/W2029924054","https://openalex.org/W2030579135","https://openalex.org/W2032176211","https://openalex.org/W2033882205","https://openalex.org/W2036957001","https://openalex.org/W2041551574","https://openalex.org/W2043784721","https://openalex.org/W2051299903","https://openalex.org/W2069506491","https://openalex.org/W2073603659","https://openalex.org/W2080219393","https://openalex.org/W2105340951","https://openalex.org/W2114487471","https://openalex.org/W2150307755","https://openalex.org/W2155280009","https://openalex.org/W2236857541","https://openalex.org/W2322402158","https://openalex.org/W2504943536","https://openalex.org/W2532696885","https://openalex.org/W2586172299","https://openalex.org/W2744340592","https://openalex.org/W2806639284","https://openalex.org/W2936704787","https://openalex.org/W2962711219","https://openalex.org/W2962864730","https://openalex.org/W2963200847","https://openalex.org/W3080189141","https://openalex.org/W3081899042","https://openalex.org/W3154589321","https://openalex.org/W4212957809","https://openalex.org/W4236261452","https://openalex.org/W4239097771","https://openalex.org/W4255105497","https://openalex.org/W4293874319"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1],"provide":[2],"a":[3],"variational":[4],"approximation":[5],"of":[6,13,22,28],"Ambrosio\u2013Tortorelli":[7],"type":[8],"for":[9],"brittle":[10],"fracture":[11],"energies":[12],"piecewise-rigid":[14],"solids.":[15],"Our":[16],"result":[17],"covers":[18],"both":[19],"the":[20],"case":[21],"geometrically":[23],"nonlinear":[24],"elasticity":[25],"and":[26],"that":[27],"linearised":[29],"elasticity.":[30]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2021-04-13T00:00:00"}