{"id":"https://openalex.org/W2070664741","doi":"https://doi.org/10.1137/080726215","title":"On Existence and Approximation for a 3D Model of Thermally Induced Phase Transformations in Shape-Memory Alloys","display_name":"On Existence and Approximation for a 3D Model of Thermally Induced Phase Transformations in Shape-Memory Alloys","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2070664741","doi":"https://doi.org/10.1137/080726215","mag":"2070664741"},"language":"en","primary_location":{"id":"doi:10.1137/080726215","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080726215","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00863759/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052253534","display_name":"Alexander Mielke","orcid":"https://orcid.org/0000-0002-4583-3888"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexander Mielke","raw_affiliation_strings":["Numerical Mathematics and Scientific Computing [WIAS] (Mohrenstr. 39 10117 Berlin - Germany)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Numerical Mathematics and Scientific Computing [WIAS] (Mohrenstr. 39 10117 Berlin - Germany)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060048917","display_name":"L\u00e6titia Paoli","orcid":"https://orcid.org/0000-0003-2217-4565"},"institutions":[{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Laetitia Paoli","raw_affiliation_strings":["ICJ - Institut Camille Jordan (B\u00e2t. Jean Braconnier 43 bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ICJ - Institut Camille Jordan (B\u00e2t. Jean Braconnier 43 bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX - France)","institution_ids":["https://openalex.org/I4210104796"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5104035023","display_name":"Adrien Petrov","orcid":"https://orcid.org/0009-0001-7699-5214"},"institutions":[{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Adrien Petrov","raw_affiliation_strings":["ICJ - Institut Camille Jordan (B\u00e2t. Jean Braconnier 43 bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ICJ - Institut Camille Jordan (B\u00e2t. Jean Braconnier 43 bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX - France)","institution_ids":["https://openalex.org/I4210104796"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4906,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.90139976,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"41","issue":"4","first_page":"1388","last_page":"1414"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10865","display_name":"Shape Memory Alloy Transformations","score":0.9994999766349792,"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/T10865","display_name":"Shape Memory Alloy Transformations","score":0.9994999766349792,"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9868999719619751,"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/T11525","display_name":"Piezoelectric Actuators and Control","score":0.9648000001907349,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/convexity","display_name":"Convexity","score":0.7851371169090271},{"id":"https://openalex.org/keywords/shape-memory-alloy","display_name":"Shape-memory alloy","score":0.5480397939682007},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5347959399223328},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5207438468933105},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5046340227127075},{"id":"https://openalex.org/keywords/microstructure","display_name":"Microstructure","score":0.5021181106567383},{"id":"https://openalex.org/keywords/thermal","display_name":"Thermal","score":0.4788934290409088},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.46886661648750305},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.46016451716423035},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4484015107154846},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43211954832077026},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.3779493272304535},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3666282892227173},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.24886047840118408},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21736833453178406},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1478005349636078},{"id":"https://openalex.org/keywords/metallurgy","display_name":"Metallurgy","score":0.09277048707008362}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7851371169090271},{"id":"https://openalex.org/C49097943","wikidata":"https://www.wikidata.org/wiki/Q898455","display_name":"Shape-memory alloy","level":2,"score":0.5480397939682007},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5347959399223328},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5207438468933105},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5046340227127075},{"id":"https://openalex.org/C87976508","wikidata":"https://www.wikidata.org/wiki/Q1498213","display_name":"Microstructure","level":2,"score":0.5021181106567383},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.4788934290409088},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.46886661648750305},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46016451716423035},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4484015107154846},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43211954832077026},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.3779493272304535},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3666282892227173},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.24886047840118408},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21736833453178406},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1478005349636078},{"id":"https://openalex.org/C191897082","wikidata":"https://www.wikidata.org/wiki/Q11467","display_name":"Metallurgy","level":1,"score":0.09277048707008362},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/080726215","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080726215","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00863759v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00863759","pdf_url":"https://hal.science/hal-00863759/document","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":"SIAM Journal on Mathematical Analysis, 2009, 41 (4), pp.1388-1414. ⟨10.1137/080726215⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00863759v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00863759","pdf_url":"https://hal.science/hal-00863759/document","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":"SIAM Journal on Mathematical Analysis, 2009, 41 (4), pp.1388-1414. ⟨10.1137/080726215⟩","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2070664741.pdf","grobid_xml":"https://content.openalex.org/works/W2070664741.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1571335561","https://openalex.org/W1974452981","https://openalex.org/W1974948403","https://openalex.org/W1989046305","https://openalex.org/W1991808661","https://openalex.org/W1993654840","https://openalex.org/W2004685222","https://openalex.org/W2014509830","https://openalex.org/W2035954383","https://openalex.org/W2038918367","https://openalex.org/W2042023814","https://openalex.org/W2045069146","https://openalex.org/W2047948718","https://openalex.org/W2052634382","https://openalex.org/W2056773849","https://openalex.org/W2083733493","https://openalex.org/W2096165789","https://openalex.org/W2132090340","https://openalex.org/W2137187711","https://openalex.org/W2167324113","https://openalex.org/W2170069250","https://openalex.org/W2963689079"],"related_works":["https://openalex.org/W569866225","https://openalex.org/W4317821343","https://openalex.org/W2900265245","https://openalex.org/W2056723064","https://openalex.org/W4248728923","https://openalex.org/W2058940780","https://openalex.org/W1964872188","https://openalex.org/W607830317","https://openalex.org/W3131570391","https://openalex.org/W653245379"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3],"a":[4,22],"three-dimensional":[5],"model":[6],"for":[7],"thermal":[8],"stress-induced":[9],"transformations":[10],"in":[11,64],"shape-memory":[12],"materials.":[13],"Microstructure,":[14],"like":[15],"twined":[16],"martensites,":[17],"is":[18,44,57,62],"described":[19],"mesoscopically":[20],"by":[21],"vector":[23],"of":[24,31,51,67,78],"internal":[25],"variables":[26],"containing":[27],"the":[28,37,48,65],"volume":[29],"fractions":[30],"each":[32],"phase.":[33],"We":[34,70],"assume":[35],"that":[36],"temperature":[38],"variations":[39],"are":[40],"prescribed.":[41],"The":[42],"problem":[43],"formulated":[45],"mathematically":[46],"within":[47],"energetic":[49],"framework":[50],"rate-independent":[52],"processes.":[53],"An":[54],"existence":[55],"result":[56],"proved":[58],"and":[59,75],"temporal":[60],"regularity":[61],"obtained":[63],"case":[66],"uniform":[68],"convexity.":[69],"also":[71],"study":[72],"space-time":[73],"discretizations":[74],"establish":[76],"convergence":[77],"these":[79],"approximations.":[80]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}