{"id":"https://openalex.org/W2077787938","doi":"https://doi.org/10.1137/s0036139993255327","title":"A Weakly Nonlinear Analysis of Elasto-plastic-Microstructure Models","display_name":"A Weakly Nonlinear Analysis of Elasto-plastic-Microstructure Models","publication_year":1995,"publication_date":"1995-02-01","ids":{"openalex":"https://openalex.org/W2077787938","doi":"https://doi.org/10.1137/s0036139993255327","mag":"2077787938"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139993255327","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5110244736","display_name":"Lianjun An","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lianjun An","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5034324891","display_name":"Anthony Peirce","orcid":"https://orcid.org/0000-0002-8437-7889"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Anthony Peirce","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.294,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":82,"citation_normalized_percentile":{"value":0.935182,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"55","issue":"1","first_page":"136","last_page":"155"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9996,"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"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9996,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.996,"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/T10514","display_name":"Numerical methods in engineering","score":0.9905,"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/microscale-chemistry","display_name":"Microscale chemistry","score":0.5890985},{"id":"https://openalex.org/keywords/length-scale","display_name":"Length scale","score":0.5419948},{"id":"https://openalex.org/keywords/dilatant","display_name":"Dilatant","score":0.540562},{"id":"https://openalex.org/keywords/flutter","display_name":"Flutter","score":0.42655858}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.67262703},{"id":"https://openalex.org/C179428855","wikidata":"https://www.wikidata.org/wiki/Q1069216","display_name":"Microscale chemistry","level":2,"score":0.5890985},{"id":"https://openalex.org/C11135259","wikidata":"https://www.wikidata.org/wiki/Q2477027","display_name":"Length scale","level":2,"score":0.5419948},{"id":"https://openalex.org/C74108042","wikidata":"https://www.wikidata.org/wiki/Q1225407","display_name":"Dilatant","level":2,"score":0.540562},{"id":"https://openalex.org/C87976508","wikidata":"https://www.wikidata.org/wiki/Q1498213","display_name":"Microstructure","level":2,"score":0.5169729},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.50364226},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.4454704},{"id":"https://openalex.org/C2777834885","wikidata":"https://www.wikidata.org/wiki/Q13417156","display_name":"Flutter","level":3,"score":0.42655858},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.42256516},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41532397},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.38695055},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.33715624},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.20431635},{"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/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C191897082","wikidata":"https://www.wikidata.org/wiki/Q11467","display_name":"Metallurgy","level":1,"score":0.0},{"id":"https://openalex.org/C13393347","wikidata":"https://www.wikidata.org/wiki/Q8424","display_name":"Aerodynamics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139993255327","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.44}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":14,"referenced_works":["https://openalex.org/W1975750849","https://openalex.org/W1978046243","https://openalex.org/W1985167223","https://openalex.org/W1986972713","https://openalex.org/W1988995266","https://openalex.org/W2037065062","https://openalex.org/W2038991247","https://openalex.org/W2083534834","https://openalex.org/W2083960709","https://openalex.org/W2151595449","https://openalex.org/W2342116053","https://openalex.org/W2409135459","https://openalex.org/W305332711","https://openalex.org/W4241042417"],"related_works":["https://openalex.org/W4286285965","https://openalex.org/W2465699412","https://openalex.org/W2386299817","https://openalex.org/W2381864073","https://openalex.org/W2381719493","https://openalex.org/W2378045033","https://openalex.org/W2184236617","https://openalex.org/W2092867183","https://openalex.org/W1979808816","https://openalex.org/W1565353949"],"abstract_inverted_index":{"At":[0],"certain":[1],"critical":[2],"values":[3],"of":[4,11,22,30,38,80,90,113,139,156,163,204,212,219,251],"the":[5,8,35,47,77,81,88,91,95,109,114,126,135,140,149,153,157,160,164,171,177,180,189,202,205,209,213,220,228,237,258,267,272,279,295,303],"hardening":[6],"modulus,":[7],"governing":[9],"equations":[10],"elasto-plastic":[12],"flow":[13],"may":[14],"lose":[15],"their":[16],"hyperbolicity":[17],"and":[18,25,55,83,94,119,159,208],"exhibit":[19],"two":[20],"modes":[21,29,39],"ill-posedness:":[23],"shear-band":[24],"flutter":[26],"ill-posedness.":[27],"These":[28,283],"ill-posedness":[31],"are":[32,129,263,276,286],"characterized":[33],"by":[34,134,278,288],"uncontrolled":[36],"growth":[37],"at":[40],"infinitely":[41],"fine":[42],"scales,":[43],"which":[44,147],"ultimately":[45],"violates":[46],"continuum":[48,66],"assumption.":[49],"In":[50,98],"previous":[51],"work":[52],"[L.":[53],"An":[54],"A.":[56],"Peirce,":[57],"SIAM":[58],"J.":[59],"Appl.":[60],"Math.,":[61],"54(1994),":[62],"pp.":[63],"708\u2013730],":[64],"a":[65,85,101,185,199,232,309],"model":[67],"accounting":[68],"for":[69,245],"microscale":[70],"deformations":[71,124],"was":[72],"built.":[73],"Linear":[74],"analysis":[75,104,218],"demonstrated":[76],"regularizing":[78],"effect":[79,155,162],"microstructure":[82,165,281],"provided":[84],"relationship":[86],"between":[87,152,201],"width":[89,203],"localized":[92],"instabilities":[93],"microlength":[96],"scale.":[97],"this":[99],"paper":[100],"weakly":[102,190],"nonlinear":[103,191,233],"is":[105,174,195,224],"used":[106,196,225],"to":[107,131,176,183,188,197,226,231,242,308],"explore":[108],"immediate":[110],"post-critical":[111,123],"behavior":[112],"solutions.":[115],"For":[116],"both":[117],"one-dimensional":[118],"anti-plane":[120],"shear":[121,206,316],"models,":[122],"in":[125,170,179,236,294],"plastic":[127,172],"regions":[128,182],"shown":[130],"be":[132,243],"governed":[133],"Boussinesq":[136],"equation":[137,235],"(one":[138],"completely":[141],"integrable":[142],"PDEs":[143],"having":[144],"soliton":[145,168],"solutions),":[146],"describes":[148],"essential":[150],"coupling":[151],"focusing":[154],"nonlinearity":[158],"dispersive":[161,280],"terms.":[166,282],"The":[167],"solution":[169,178,187,194,223],"region":[173],"patched":[175],"elastic":[181],"provide":[184],"special":[186,254],"system.":[192],"This":[193,291],"derive":[198],"relation":[200],"band":[207],"length":[210],"scale":[211,217],"microstructure.":[214],"A":[215],"multiple":[216],"constant":[221],"displacement":[222],"reduce":[227],"perturbed":[229],"problem":[230],"Schr\u00f6dinger":[234],"amplitude":[238],"functions\u2014which":[239],"turn":[240],"out":[241],"unstable":[244,264],"large":[246],"time":[247,269],"scales.":[248],"Stability":[249],"analyses":[250],"more":[252],"complicated":[253],"solutions":[255,262],"show":[256],"that":[257,302],"low":[259],"wave":[260,274],"number":[261],"even":[265],"on":[266],"fast":[268],"scales":[270],"while":[271],"high":[273],"numbers":[275],"damped":[277],"theoretical":[284],"results":[285],"corroborated":[287],"numerical":[289],"evidence.":[290],"pervasive":[292],"instability":[293],"strain-softening":[296],"regime":[297],"immediately":[298],"after":[299],"failure,":[300],"indicates":[301],"material":[304],"will":[305],"rapidly":[306],"move":[307],"lower":[310],"residual":[311],"stress":[312],"state":[313],"with":[314],"well-defined":[315],"bands.":[317]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2077787938","counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":5}],"updated_date":"2024-12-11T01:59:48.352921","created_date":"2016-06-24"}
