{"id":"https://openalex.org/W7119523674","doi":"https://doi.org/10.1016/j.cnsns.2026.109718","title":"Proposing the enriched strain-based gradient as a general implicit method to solve time-independent constitutive equation","display_name":"Proposing the enriched strain-based gradient as a general implicit method to solve time-independent constitutive equation","publication_year":2026,"publication_date":"2026-01-09","ids":{"openalex":"https://openalex.org/W7119523674","doi":"https://doi.org/10.1016/j.cnsns.2026.109718"},"language":"en","primary_location":{"id":"doi:10.1016/j.cnsns.2026.109718","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cnsns.2026.109718","pdf_url":null,"source":{"id":"https://openalex.org/S39612629","display_name":"Communications in Nonlinear Science and Numerical Simulation","issn_l":"1007-5704","issn":["1007-5704","1878-7274"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Nonlinear Science and Numerical Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://eprints.gla.ac.uk/376555/2/376555.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119240013","display_name":"Ali Biglarifadafan","orcid":null},"institutions":[{"id":"https://openalex.org/I198873322","display_name":"Golestan University","ror":"https://ror.org/046nf9z89","country_code":"IR","type":"education","lineage":["https://openalex.org/I198873322"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Ali Biglarifadafan","raw_affiliation_strings":["Department of Civil Engineering, Faculty of Engineering, Golestan University, Gorgan, Iran"],"raw_orcid":"https://orcid.org/0000-0002-9616-1823","affiliations":[{"raw_affiliation_string":"Department of Civil Engineering, Faculty of Engineering, Golestan University, Gorgan, Iran","institution_ids":["https://openalex.org/I198873322"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023762244","display_name":"Philip G. Harrison","orcid":"https://orcid.org/0000-0002-5171-6506"},"institutions":[{"id":"https://openalex.org/I7882870","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53","country_code":"GB","type":"education","lineage":["https://openalex.org/I7882870"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Philip Harrison","raw_affiliation_strings":["School of Engineering, University of Glasgow, Glasgow G12 8QQ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering, University of Glasgow, Glasgow G12 8QQ","institution_ids":["https://openalex.org/I7882870"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5119240013"],"corresponding_institution_ids":["https://openalex.org/I198873322"],"apc_list":{"value":3460,"currency":"USD","value_usd":3460},"apc_paid":null,"fwci":2.4942,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.81234072,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"157","issue":null,"first_page":"109718","last_page":"109718"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.32710000872612,"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"}},"topics":[{"id":"https://openalex.org/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.32710000872612,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.1282999962568283,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.1257999986410141,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/uniqueness","display_name":"Uniqueness","score":0.6866000294685364},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6604999899864197},{"id":"https://openalex.org/keywords/constitutive-equation","display_name":"Constitutive equation","score":0.567300021648407},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5297999978065491},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4763000011444092},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.45500001311302185},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.4318999946117401},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.41999998688697815},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.40950000286102295}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6866000294685364},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6604999899864197},{"id":"https://openalex.org/C202973686","wikidata":"https://www.wikidata.org/wiki/Q1937401","display_name":"Constitutive equation","level":3,"score":0.567300021648407},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5396000146865845},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5360000133514404},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5297999978065491},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4763000011444092},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.45500001311302185},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.4318999946117401},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.41999998688697815},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.40950000286102295},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.384799987077713},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3837999999523163},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.37450000643730164},{"id":"https://openalex.org/C163892269","wikidata":"https://www.wikidata.org/wiki/Q15300737","display_name":"Finite strain theory","level":3,"score":0.3393999934196472},{"id":"https://openalex.org/C149393637","wikidata":"https://www.wikidata.org/wiki/Q5421265","display_name":"Explicit and implicit methods","level":5,"score":0.3287000060081482},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32199999690055847},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.303600013256073},{"id":"https://openalex.org/C79186407","wikidata":"https://www.wikidata.org/wiki/Q472074","display_name":"Plasticity","level":2,"score":0.30070000886917114},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C156413551","wikidata":"https://www.wikidata.org/wiki/Q7621123","display_name":"Strain hardening exponent","level":2,"score":0.2822999954223633},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2630000114440918},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2605000138282776},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2540000081062317}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/j.cnsns.2026.109718","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cnsns.2026.109718","pdf_url":null,"source":{"id":"https://openalex.org/S39612629","display_name":"Communications in Nonlinear Science and Numerical Simulation","issn_l":"1007-5704","issn":["1007-5704","1878-7274"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Nonlinear Science and Numerical Simulation","raw_type":"journal-article"},{"id":"pmh:oai:eprints.gla.ac.uk:376555","is_oa":true,"landing_page_url":"https://eprints.gla.ac.uk/376555/2/376555.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4210235606","display_name":"ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam)","issn_l":"2622-8912","issn":["2622-8912","2622-8920"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Articles"}],"best_oa_location":{"id":"pmh:oai:eprints.gla.ac.uk:376555","is_oa":true,"landing_page_url":"https://eprints.gla.ac.uk/376555/2/376555.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4210235606","display_name":"ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam)","issn_l":"2622-8912","issn":["2622-8912","2622-8920"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Articles"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F6929743351","display_name":"Golestan University","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W110592042","https://openalex.org/W1965456126","https://openalex.org/W1980145538","https://openalex.org/W1981375575","https://openalex.org/W1981884911","https://openalex.org/W1984653822","https://openalex.org/W1990678081","https://openalex.org/W1991777134","https://openalex.org/W1993413845","https://openalex.org/W1997332076","https://openalex.org/W1997574312","https://openalex.org/W2007559860","https://openalex.org/W2009780994","https://openalex.org/W2013780610","https://openalex.org/W2016323862","https://openalex.org/W2044458236","https://openalex.org/W2065721961","https://openalex.org/W2080830554","https://openalex.org/W2084464549","https://openalex.org/W2107510071","https://openalex.org/W2253200911","https://openalex.org/W2312324498","https://openalex.org/W2326361801","https://openalex.org/W2988518820","https://openalex.org/W3136174515","https://openalex.org/W4403138902","https://openalex.org/W4408749435"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2026-01-09T00:00:00"}