{"id":"https://openalex.org/W2803574278","doi":"https://doi.org/10.1186/s40323-018-0106-7","title":"A simple and unified implementation of phase field and gradient damage models","display_name":"A simple and unified implementation of phase field and gradient damage models","publication_year":2018,"publication_date":"2018-05-21","ids":{"openalex":"https://openalex.org/W2803574278","doi":"https://doi.org/10.1186/s40323-018-0106-7","mag":"2803574278"},"language":"en","primary_location":{"id":"doi:10.1186/s40323-018-0106-7","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40323-018-0106-7","pdf_url":"https://amses-journal.springeropen.com/track/pdf/10.1186/s40323-018-0106-7","source":{"id":"https://openalex.org/S3034486266","display_name":"Advanced Modeling and Simulation in Engineering Sciences","issn_l":"2213-7467","issn":["2213-7467"],"is_oa":true,"is_in_doaj":true,"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":"Advanced Modeling and Simulation in Engineering Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://amses-journal.springeropen.com/track/pdf/10.1186/s40323-018-0106-7","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072983163","display_name":"Erfan Azinpour","orcid":"https://orcid.org/0000-0003-1018-7123"},"institutions":[{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]},{"id":"https://openalex.org/I4210121509","display_name":"Institute of Mechanical Engineering and Industrial Mangement","ror":"https://ror.org/02pk7c879","country_code":"PT","type":"facility","lineage":["https://openalex.org/I182534213","https://openalex.org/I4210121509"]},{"id":"https://openalex.org/I4403386606","display_name":"Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial","ror":"https://ror.org/01jbxwn06","country_code":null,"type":"facility","lineage":["https://openalex.org/I4403386606","https://openalex.org/I88596544"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"E. Azinpour","raw_affiliation_strings":["INEGI-Institute of Science and Innovation in Mechanical and Industrial Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal","Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial (Campus da FEUP, Rua Dr. Roberto Frias, 400, 4200 - 465, Porto, Portugal - Portugal)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INEGI-Institute of Science and Innovation in Mechanical and Industrial Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal","institution_ids":["https://openalex.org/I4210121509","https://openalex.org/I182534213"]},{"raw_affiliation_string":"Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial (Campus da FEUP, Rua Dr. Roberto Frias, 400, 4200 - 465, Porto, Portugal - Portugal)","institution_ids":["https://openalex.org/I4210121509","https://openalex.org/I4403386606"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001239416","display_name":"Jo\u00e3o Ferreira","orcid":"https://orcid.org/0000-0003-4310-2915"},"institutions":[{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]},{"id":"https://openalex.org/I4210121509","display_name":"Institute of Mechanical Engineering and Industrial Mangement","ror":"https://ror.org/02pk7c879","country_code":"PT","type":"facility","lineage":["https://openalex.org/I182534213","https://openalex.org/I4210121509"]},{"id":"https://openalex.org/I4403386606","display_name":"Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial","ror":"https://ror.org/01jbxwn06","country_code":null,"type":"facility","lineage":["https://openalex.org/I4403386606","https://openalex.org/I88596544"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"J. P. S. Ferreira","raw_affiliation_strings":["INEGI-Institute of Science and Innovation in Mechanical and Industrial Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal","Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial (Campus da FEUP, Rua Dr. Roberto Frias, 400, 4200 - 465, Porto, Portugal - Portugal)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INEGI-Institute of Science and Innovation in Mechanical and Industrial Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal","institution_ids":["https://openalex.org/I4210121509","https://openalex.org/I182534213"]},{"raw_affiliation_string":"Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial (Campus da FEUP, Rua Dr. Roberto Frias, 400, 4200 - 465, Porto, Portugal - Portugal)","institution_ids":["https://openalex.org/I4210121509","https://openalex.org/I4403386606"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066364235","display_name":"Marco Parente","orcid":"https://orcid.org/0000-0002-3326-6345"},"institutions":[{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]},{"id":"https://openalex.org/I4210121509","display_name":"Institute of Mechanical Engineering and Industrial Mangement","ror":"https://ror.org/02pk7c879","country_code":"PT","type":"facility","lineage":["https://openalex.org/I182534213","https://openalex.org/I4210121509"]},{"id":"https://openalex.org/I4403386606","display_name":"Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial","ror":"https://ror.org/01jbxwn06","country_code":null,"type":"facility","lineage":["https://openalex.org/I4403386606","https://openalex.org/I88596544"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"M. P. L. Parente","raw_affiliation_strings":["INEGI-Institute of Science and Innovation in Mechanical and Industrial Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal","Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial (Campus da FEUP, Rua Dr. Roberto Frias, 400, 4200 - 465, Porto, Portugal - Portugal)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INEGI-Institute of Science and Innovation in Mechanical and Industrial Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal","institution_ids":["https://openalex.org/I4210121509","https://openalex.org/I182534213"]},{"raw_affiliation_string":"Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial (Campus da FEUP, Rua Dr. Roberto Frias, 400, 4200 - 465, Porto, Portugal - Portugal)","institution_ids":["https://openalex.org/I4210121509","https://openalex.org/I4403386606"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002414903","display_name":"J De","orcid":"https://orcid.org/0000-0002-1257-1754"},"institutions":[{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]},{"id":"https://openalex.org/I4210121509","display_name":"Institute of Mechanical Engineering and Industrial Mangement","ror":"https://ror.org/02pk7c879","country_code":"PT","type":"facility","lineage":["https://openalex.org/I182534213","https://openalex.org/I4210121509"]},{"id":"https://openalex.org/I4403386606","display_name":"Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial","ror":"https://ror.org/01jbxwn06","country_code":null,"type":"facility","lineage":["https://openalex.org/I4403386606","https://openalex.org/I88596544"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"J. Cesar de Sa","raw_affiliation_strings":["INEGI-Institute of Science and Innovation in Mechanical and Industrial Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal","Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial (Campus da FEUP, Rua Dr. Roberto Frias, 400, 4200 - 465, Porto, Portugal - Portugal)"],"raw_orcid":"https://orcid.org/0000-0002-1257-1754","affiliations":[{"raw_affiliation_string":"INEGI-Institute of Science and Innovation in Mechanical and Industrial Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal","institution_ids":["https://openalex.org/I4210121509","https://openalex.org/I182534213"]},{"raw_affiliation_string":"Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial (Campus da FEUP, Rua Dr. Roberto Frias, 400, 4200 - 465, Porto, Portugal - Portugal)","institution_ids":["https://openalex.org/I4210121509","https://openalex.org/I4403386606"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5072983163"],"corresponding_institution_ids":["https://openalex.org/I182534213","https://openalex.org/I4210121509","https://openalex.org/I4403386606"],"apc_list":{"value":990,"currency":"GBP","value_usd":1214},"apc_paid":{"value":990,"currency":"GBP","value_usd":1214},"fwci":3.7569,"has_fulltext":true,"cited_by_count":45,"citation_normalized_percentile":{"value":0.92947778,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"5","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":1.0,"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"}},{"id":"https://openalex.org/T10161","display_name":"Rock Mechanics and Modeling","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.9991000294685364,"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/regularization","display_name":"Regularization (linguistics)","score":0.6160621047019958},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5333248376846313},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.5240921378135681},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4861271381378174},{"id":"https://openalex.org/keywords/thermal-conduction","display_name":"Thermal conduction","score":0.483467161655426},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4780602753162384},{"id":"https://openalex.org/keywords/displacement-field","display_name":"Displacement field","score":0.46193209290504456},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.4523310959339142},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.44475528597831726},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.4178673326969147},{"id":"https://openalex.org/keywords/benchmarking","display_name":"Benchmarking","score":0.41342973709106445},{"id":"https://openalex.org/keywords/viscoplasticity","display_name":"Viscoplasticity","score":0.4127941131591797},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40187621116638184},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.3777753710746765},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.36529725790023804},{"id":"https://openalex.org/keywords/mechanical-engineering","display_name":"Mechanical engineering","score":0.30304068326950073},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.2373255491256714},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21825677156448364},{"id":"https://openalex.org/keywords/constitutive-equation","display_name":"Constitutive equation","score":0.20891183614730835},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20421898365020752},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1880837082862854},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.16221317648887634},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.1204155683517456},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1062164306640625},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.0897257924079895}],"concepts":[{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6160621047019958},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5333248376846313},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.5240921378135681},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4861271381378174},{"id":"https://openalex.org/C172100665","wikidata":"https://www.wikidata.org/wiki/Q7465774","display_name":"Thermal conduction","level":2,"score":0.483467161655426},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4780602753162384},{"id":"https://openalex.org/C29660869","wikidata":"https://www.wikidata.org/wiki/Q5282615","display_name":"Displacement field","level":3,"score":0.46193209290504456},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4523310959339142},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.44475528597831726},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.4178673326969147},{"id":"https://openalex.org/C86251818","wikidata":"https://www.wikidata.org/wiki/Q816754","display_name":"Benchmarking","level":2,"score":0.41342973709106445},{"id":"https://openalex.org/C55359492","wikidata":"https://www.wikidata.org/wiki/Q7935671","display_name":"Viscoplasticity","level":4,"score":0.4127941131591797},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40187621116638184},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3777753710746765},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36529725790023804},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.30304068326950073},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.2373255491256714},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21825677156448364},{"id":"https://openalex.org/C202973686","wikidata":"https://www.wikidata.org/wiki/Q1937401","display_name":"Constitutive equation","level":3,"score":0.20891183614730835},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20421898365020752},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1880837082862854},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.16221317648887634},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.1204155683517456},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1062164306640625},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0897257924079895},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C162853370","wikidata":"https://www.wikidata.org/wiki/Q39809","display_name":"Marketing","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1186/s40323-018-0106-7","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40323-018-0106-7","pdf_url":"https://amses-journal.springeropen.com/track/pdf/10.1186/s40323-018-0106-7","source":{"id":"https://openalex.org/S3034486266","display_name":"Advanced Modeling and Simulation in Engineering Sciences","issn_l":"2213-7467","issn":["2213-7467"],"is_oa":true,"is_in_doaj":true,"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":"Advanced Modeling and Simulation in Engineering Sciences","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04456111v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04456111","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"http://link.springer.com/article/10.1186/s40323-018-0106-7/fulltext.html","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:0b5b059c9ad54cbf817c656323660b80","is_oa":true,"landing_page_url":"https://doaj.org/article/0b5b059c9ad54cbf817c656323660b80","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Advanced Modeling and Simulation in Engineering Sciences, Vol 5, Iss 1, Pp 1-24 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1186/s40323-018-0106-7","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40323-018-0106-7","pdf_url":"https://amses-journal.springeropen.com/track/pdf/10.1186/s40323-018-0106-7","source":{"id":"https://openalex.org/S3034486266","display_name":"Advanced Modeling and Simulation in Engineering Sciences","issn_l":"2213-7467","issn":["2213-7467"],"is_oa":true,"is_in_doaj":true,"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":"Advanced Modeling and Simulation in Engineering Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4452676427","display_name":null,"funder_award_id":"NORTE-01-0145-FEDER-000022","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"}],"funders":[{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2803574278.pdf","grobid_xml":"https://content.openalex.org/works/W2803574278.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W584802033","https://openalex.org/W607404562","https://openalex.org/W1515532860","https://openalex.org/W1826123630","https://openalex.org/W1967070136","https://openalex.org/W1970499362","https://openalex.org/W1970913426","https://openalex.org/W1975664820","https://openalex.org/W1977188519","https://openalex.org/W1978537219","https://openalex.org/W1984826750","https://openalex.org/W2006078294","https://openalex.org/W2007167704","https://openalex.org/W2015574716","https://openalex.org/W2016463190","https://openalex.org/W2017476964","https://openalex.org/W2020242014","https://openalex.org/W2027019914","https://openalex.org/W2033137672","https://openalex.org/W2033882205","https://openalex.org/W2042211262","https://openalex.org/W2043784721","https://openalex.org/W2047048398","https://openalex.org/W2049689581","https://openalex.org/W2051556631","https://openalex.org/W2052638010","https://openalex.org/W2058739156","https://openalex.org/W2058914173","https://openalex.org/W2074300745","https://openalex.org/W2088676724","https://openalex.org/W2093256786","https://openalex.org/W2094299102","https://openalex.org/W2095069391","https://openalex.org/W2100865094","https://openalex.org/W2106667498","https://openalex.org/W2113788046","https://openalex.org/W2114207581","https://openalex.org/W2114487471","https://openalex.org/W2123556503","https://openalex.org/W2145995141","https://openalex.org/W2157258353","https://openalex.org/W2170133891","https://openalex.org/W2306166862","https://openalex.org/W2408353796","https://openalex.org/W2480229508","https://openalex.org/W2521715188","https://openalex.org/W2616056183","https://openalex.org/W3153565953","https://openalex.org/W4239097771"],"related_works":["https://openalex.org/W4238897586","https://openalex.org/W435179959","https://openalex.org/W2619091065","https://openalex.org/W2059640416","https://openalex.org/W1490753184","https://openalex.org/W2284465472","https://openalex.org/W2291782699","https://openalex.org/W1993948687","https://openalex.org/W2011676020","https://openalex.org/W2000169967"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"the":[3,17,36,52,65,71,76,81,84,88,91,97,110,121],"analogous":[4],"treatment":[5],"between":[6,83],"coupled":[7,41],"temperature\u2013displacement":[8,42],"problems":[9],"and":[10,29,59,87,102,120],"material":[11,57,66],"failure":[12],"models":[13,32,58],"is":[14,48,100],"explored":[15],"within":[16],"context":[18],"of":[19,55,90],"a":[20],"commercial":[21],"software":[22,37],"(Abaqus\u00ae).":[23],"The":[24,44],"implicit":[25],"gradient":[26],"Lemaitre":[27],"damage":[28],"phase":[30],"field":[31],"are":[33,61],"implemented":[34],"utilizing":[35],"underlying":[38],"capabilities":[39],"for":[40],"problems.":[43],"heat":[45],"conduction":[46],"equation":[47],"made":[49],"compatible":[50],"with":[51],"diffusive":[53,92],"regularization":[54],"such":[56,116],"calculations":[60],"carried":[62],"out":[63],"at":[64],"point":[67],"level.":[68],"This":[69],"bypasses":[70],"need":[72],"to":[73,123],"implement":[74],"explicitly":[75],"weak":[77],"form":[78],"resultant":[79],"from":[80,109],"coupling":[82],"momentum":[85],"conservation":[86],"evolution":[89],"field.":[93],"Throughout":[94],"benchmarking":[95],"examples,":[96],"proposed":[98],"methodology":[99],"assessed":[101],"validated":[103],"by":[104],"investigating":[105],"typical":[106],"issues":[107],"risen":[108],"considered":[111],"local":[112],"inelastic-based":[113],"deformation":[114],"models,":[115],"as":[117],"mesh":[118],"dependency":[119],"difficulties":[122],"predict":[124],"cracked":[125],"regions.":[126]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":3}],"updated_date":"2026-06-02T09:04:35.204637","created_date":"2025-10-10T00:00:00"}