{"id":"https://openalex.org/W2058353383","doi":"https://doi.org/10.1137/110821718","title":"An Efficient Approach to the Numerical Solution of Rate-Independent Problems with Nonconvex Energies","display_name":"An Efficient Approach to the Numerical Solution of Rate-Independent Problems with Nonconvex Energies","publication_year":2011,"publication_date":"2011-07-01","ids":{"openalex":"https://openalex.org/W2058353383","doi":"https://doi.org/10.1137/110821718","mag":"2058353383"},"language":"en","primary_location":{"id":"doi:10.1137/110821718","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110821718","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017359935","display_name":"S\u00f6ren Bartels","orcid":null},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"S\u00f6ren Bartels","raw_affiliation_strings":["University of Bonn"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Bonn","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086331654","display_name":"Martin Kru\u017e\u00edk","orcid":"https://orcid.org/0000-0003-1558-5809"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martin Kru\u017e\u00edk","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4042,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.88979758,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"9","issue":"3","first_page":"1276","last_page":"1300"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9811999797821045,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6200994253158569},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6071323752403259},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5598153471946716},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5496255159378052},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49895668029785156},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4813135862350464},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.413772314786911},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18998104333877563},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07698750495910645}],"concepts":[{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6200994253158569},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6071323752403259},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5598153471946716},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5496255159378052},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49895668029785156},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4813135862350464},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.413772314786911},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18998104333877563},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07698750495910645},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/110821718","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110821718","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"},{"id":"pmh:oai:asep.lib.cas.cz:CavUnEpca/0364707","is_oa":false,"landing_page_url":"http://hdl.handle.net/11104/0200115","pdf_url":null,"source":{"id":"https://openalex.org/S7407055266","display_name":"ASEP","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8999999761581421}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1484024929","https://openalex.org/W1512048500","https://openalex.org/W1537639429","https://openalex.org/W1584259498","https://openalex.org/W1639449914","https://openalex.org/W1964765773","https://openalex.org/W1982631219","https://openalex.org/W1987063601","https://openalex.org/W1994484217","https://openalex.org/W1995681628","https://openalex.org/W1995953909","https://openalex.org/W2014212235","https://openalex.org/W2020413485","https://openalex.org/W2030579135","https://openalex.org/W2045069146","https://openalex.org/W2064045310","https://openalex.org/W2069241221","https://openalex.org/W2070997252","https://openalex.org/W2074190491","https://openalex.org/W2079951412","https://openalex.org/W2084759830","https://openalex.org/W2088703872","https://openalex.org/W2096165789","https://openalex.org/W2105151698","https://openalex.org/W2132090340","https://openalex.org/W2142463173","https://openalex.org/W2163679815","https://openalex.org/W2729559833","https://openalex.org/W3021237030","https://openalex.org/W3098853646","https://openalex.org/W3183315860","https://openalex.org/W4247424088"],"related_works":["https://openalex.org/W3214346900","https://openalex.org/W2356099978","https://openalex.org/W3202709773","https://openalex.org/W3011140979","https://openalex.org/W1977848887","https://openalex.org/W3129086539","https://openalex.org/W4380147916","https://openalex.org/W2363346090","https://openalex.org/W4230510080","https://openalex.org/W4285308861"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,40],"new":[3],"approach":[4],"to":[5,18],"the":[6,20,46],"numerical":[7,52],"treatment":[8],"of":[9,45],"non(quasi)convex":[10],"rate-independent":[11],"evolutionary":[12],"problems.":[13],"The":[14,43],"main":[15],"idea":[16],"is":[17,48],"replace":[19],"original":[21],"microscopic":[22],"energy":[23],"density":[24],"with":[25,50],"its":[26],"polyconvexification.":[27],"For":[28],"this":[29],"problem,":[30],"first-order":[31],"optimality":[32],"conditions":[33],"are":[34],"derived":[35],"and":[36],"used":[37],"in":[38],"finding":[39],"discrete":[41],"solution.":[42],"effectiveness":[44],"method":[47],"illustrated":[49],"some":[51],"experiments.":[53]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}