Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2029838791', 'doi': 'https://doi.org/10.1002/nag.213', 'title': 'Self‐similar solution of a plane‐strain fracture driven by a power‐law fluid', 'display_name': 'Self‐similar solution of a plane‐strain fracture driven by a power‐law fluid', 'publication_year': 2002, 'publication_date': '2002-03-25', 'ids': {'openalex': 'https://openalex.org/W2029838791', 'doi': 'https://doi.org/10.1002/nag.213', 'mag': '2029838791'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1002/nag.213', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S10012645', 'display_name': 'International Journal for Numerical and Analytical Methods in Geomechanics', 'issn_l': '0363-9061', 'issn': ['0363-9061', '1096-9853'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320595', 'host_organization_name': 'Wiley', 'host_organization_lineage': ['https://openalex.org/P4310320595'], 'host_organization_lineage_names': ['Wiley'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, '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': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5084540378', 'display_name': 'José Adachi', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I130238516', 'display_name': 'University of Minnesota', 'ror': 'https://ror.org/017zqws13', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I130238516']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'J. I. Adachi', 'raw_affiliation_strings': ['Department of Civil Engineering, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A.'], 'affiliations': [{'raw_affiliation_string': 'Department of Civil Engineering, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A.', 'institution_ids': ['https://openalex.org/I130238516']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5035412488', 'display_name': 'Emmanuel Detournay', 'orcid': 'https://orcid.org/0000-0003-3698-7575'}, 'institutions': [{'id': 'https://openalex.org/I130238516', 'display_name': 'University of Minnesota', 'ror': 'https://ror.org/017zqws13', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I130238516']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'E. Detournay', 'raw_affiliation_strings': ['Department of Civil Engineering, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A.'], 'affiliations': [{'raw_affiliation_string': 'Department of Civil Engineering, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A.', 'institution_ids': ['https://openalex.org/I130238516']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': {'value': 4530, 'currency': 'USD', 'value_usd': 4530, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 6.103, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 191, 'citation_normalized_percentile': {'value': 0.999952, 'is_in_top_1_percent': True, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 98, 'max': 99}, 'biblio': {'volume': '26', 'issue': '6', 'first_page': '579', 'last_page': '604'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10635', 'display_name': 'Hydraulic Fracturing and Reservoir Analysis', 'score': 0.9998, 'subfield': {'id': 'https://openalex.org/subfields/2210', 'display_name': 'Mechanical 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/T10635', 'display_name': 'Hydraulic Fracturing and Reservoir Analysis', 'score': 0.9998, 'subfield': {'id': 'https://openalex.org/subfields/2210', 'display_name': 'Mechanical 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/T10892', 'display_name': 'Drilling and Well Engineering', 'score': 0.996, 'subfield': {'id': 'https://openalex.org/subfields/2212', 'display_name': 'Ocean 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/T10514', 'display_name': 'Numerical methods in engineering', 'score': 0.9945, '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/herschel–bulkley-fluid', 'display_name': 'Herschel–Bulkley fluid', 'score': 0.5277363}, {'id': 'https://openalex.org/keywords/power-law-fluid', 'display_name': 'Power-law fluid', 'score': 0.49588546}], 'concepts': [{'id': 'https://openalex.org/C43369102', 'wikidata': 'https://www.wikidata.org/wiki/Q2307625', 'display_name': 'Fracture (geology)', 'level': 2, 'score': 0.5694325}, {'id': 'https://openalex.org/C57879066', 'wikidata': 'https://www.wikidata.org/wiki/Q41217', 'display_name': 'Mechanics', 'level': 1, 'score': 0.5614865}, {'id': 'https://openalex.org/C97549433', 'wikidata': 'https://www.wikidata.org/wiki/Q911969', 'display_name': 'Fracture toughness', 'level': 2, 'score': 0.5324313}, {'id': 'https://openalex.org/C191236761', 'wikidata': 'https://www.wikidata.org/wiki/Q10862968', 'display_name': 'Herschel–Bulkley fluid', 'level': 3, 'score': 0.5277363}, {'id': 'https://openalex.org/C84655787', 'wikidata': 'https://www.wikidata.org/wiki/Q8067817', 'display_name': 'Compressibility', 'level': 2, 'score': 0.5224687}, {'id': 'https://openalex.org/C192562407', 'wikidata': 'https://www.wikidata.org/wiki/Q228736', 'display_name': 'Materials science', 'level': 0, 'score': 0.50718594}, {'id': 'https://openalex.org/C47681835', 'wikidata': 'https://www.wikidata.org/wiki/Q970142', 'display_name': 'Power-law fluid', 'level': 3, 'score': 0.49588546}, {'id': 'https://openalex.org/C90278072', 'wikidata': 'https://www.wikidata.org/wiki/Q216320', 'display_name': 'Fluid dynamics', 'level': 2, 'score': 0.45457596}, {'id': 'https://openalex.org/C200990466', 'wikidata': 'https://www.wikidata.org/wiki/Q271707', 'display_name': 'Rheology', 'level': 2, 'score': 0.44525063}, {'id': 'https://openalex.org/C54303661', 'wikidata': 'https://www.wikidata.org/wiki/Q1754376', 'display_name': 'Stress intensity factor', 'level': 3, 'score': 0.444577}, {'id': 'https://openalex.org/C184608416', 'wikidata': 'https://www.wikidata.org/wiki/Q1455803', 'display_name': 'Lubrication', 'level': 2, 'score': 0.44005963}, {'id': 'https://openalex.org/C59085676', 'wikidata': 'https://www.wikidata.org/wiki/Q957852', 'display_name': 'Fracture mechanics', 'level': 2, 'score': 0.43019903}, {'id': 'https://openalex.org/C38349280', 'wikidata': 'https://www.wikidata.org/wiki/Q1434290', 'display_name': 'Flow (mathematics)', 'level': 2, 'score': 0.36808577}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.33756298}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.22686625}, {'id': 'https://openalex.org/C159985019', 'wikidata': 'https://www.wikidata.org/wiki/Q181790', 'display_name': 'Composite material', 'level': 1, 'score': 0.17034698}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1002/nag.213', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S10012645', 'display_name': 'International Journal for Numerical and Analytical Methods in Geomechanics', 'issn_l': '0363-9061', 'issn': ['0363-9061', '1096-9853'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320595', 'host_organization_name': 'Wiley', 'host_organization_lineage': ['https://openalex.org/P4310320595'], 'host_organization_lineage_names': ['Wiley'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 28, 'referenced_works': ['https://openalex.org/W1552522682', 'https://openalex.org/W1596035524', 'https://openalex.org/W1606871564', 'https://openalex.org/W1609413062', 'https://openalex.org/W1976240542', 'https://openalex.org/W1980905255', 'https://openalex.org/W2003115626', 'https://openalex.org/W2003952276', 'https://openalex.org/W2005447590', 'https://openalex.org/W2007260247', 'https://openalex.org/W2014097614', 'https://openalex.org/W2028783611', 'https://openalex.org/W2056641273', 'https://openalex.org/W2072740827', 'https://openalex.org/W2083889911', 'https://openalex.org/W2120062331', 'https://openalex.org/W2143738823', 'https://openalex.org/W2157005274', 'https://openalex.org/W2313278888', 'https://openalex.org/W231449510', 'https://openalex.org/W2322916628', 'https://openalex.org/W2973130369', 'https://openalex.org/W2989128237', 'https://openalex.org/W3016843226', 'https://openalex.org/W3119264854', 'https://openalex.org/W4242849907', 'https://openalex.org/W4255449311', 'https://openalex.org/W4295022726'], 'related_works': ['https://openalex.org/W2728620038', 'https://openalex.org/W253201199', 'https://openalex.org/W2359066344', 'https://openalex.org/W2098067939', 'https://openalex.org/W2081266530', 'https://openalex.org/W2038349340', 'https://openalex.org/W2001346919', 'https://openalex.org/W1993085275', 'https://openalex.org/W1983340862', 'https://openalex.org/W1140262705'], 'abstract_inverted_index': {'Abstract': [0], 'This': [1, 119], 'paper': [2], 'analyses': [3], 'the': [4, 40, 43, 50, 56, 61, 66, 70, 80, 84, 87, 98, 102, 105, 110, 115, 126, 136, 148, 153], 'problem': [5, 88], 'of': [6, 24, 39, 58, 73, 132, 147], 'a': [7, 130, 141], 'hydraulically': [8], 'driven': [9, 21], 'fracture,': [10], 'propagating': [11], 'in': [12, 129, 152], 'an': [13, 25], 'impermeable,': [14], 'linear': [15], 'elastic': [16, 51], 'medium.': [17], 'The': [18, 37, 145], 'fracture': [19, 41, 103, 127], 'is': [20, 63, 89, 117, 122, 156], 'by': [22, 124], 'injection': [23], 'incompressible,': [26], 'viscous': [27], 'fluid': [28, 45, 59, 81, 107, 111, 149], 'with': [29, 135], 'power‐law': [30], 'rheology': [31], 'and': [32, 42, 55, 76, 83, 109], 'behaviour': [33], 'index': [34, 150], 'n': [35, 151], '⩾0.': [36], 'opening': [38, 128], 'internal': [44], 'pressure': [46, 108], 'are': [47], 'related': [48], 'through': [49], 'singular': [52], 'integral': [53], 'equation,': [54], 'flow': [57, 112], 'inside': [60, 114], 'crack': [62, 85, 99, 116, 154], 'modelled': [64], 'using': [65, 140], 'lubrication': [67], 'theory.': [68], 'Under': [69], 'additional': [71], 'assumptions': [72], 'negligible': [74], 'toughness': [75], 'no': [77], 'lag': [78], 'between': [79], 'front': [82], 'tip,': [86], 'reduced': [90], 'to': [91], 'self‐similar': [92, 120], 'form.': [93], 'A': [94], 'solution': [95, 121], 'that': [96], 'describes': [97], 'length': [100], 'evolution,': [101], 'opening,': [104], 'net': [106], 'rate': [113], 'presented.': [118], 'obtained': [123], 'expanding': [125], 'series': [131, 137], 'Gegenbauer': [133], 'polynomials,': [134], 'coefficients': [138], 'calculated': [139], 'numerical': [142], 'minimization': [143], 'procedure.': [144], 'influence': [146], 'propagation': [155], 'also': [157], 'analysed.': [158], 'Copyright': [159], '©': [160], '2002': [161], 'John': [162], 'Wiley': [163], '&': [164], 'Sons,': [165], 'Ltd.': [166]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2029838791', 'counts_by_year': [{'year': 2024, 'cited_by_count': 4}, {'year': 2023, 'cited_by_count': 12}, {'year': 2022, 'cited_by_count': 13}, {'year': 2021, 'cited_by_count': 12}, {'year': 2020, 'cited_by_count': 15}, {'year': 2019, 'cited_by_count': 8}, {'year': 2018, 'cited_by_count': 18}, {'year': 2017, 'cited_by_count': 13}, {'year': 2016, 'cited_by_count': 14}, {'year': 2015, 'cited_by_count': 10}, {'year': 2014, 'cited_by_count': 14}, {'year': 2013, 'cited_by_count': 13}, {'year': 2012, 'cited_by_count': 5}], 'updated_date': '2025-01-10T10:10:25.435211', 'created_date': '2016-06-24'}