{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T04:27:38Z","timestamp":1781152058886,"version":"3.54.1"},"reference-count":64,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T00:00:00Z","timestamp":1682294400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T00:00:00Z","timestamp":1682294400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/V049259\/1"],"award-info":[{"award-number":["EP\/V049259\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014013","name":"UK Research and Innovation","doi-asserted-by":"publisher","award":["MR\/V024124\/1"],"award-info":[{"award-number":["MR\/V024124\/1"]}],"id":[{"id":"10.13039\/100014013","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["REQ2021-A-30"],"award-info":[{"award-number":["REQ2021-A-30"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000288","name":"Royal Society","doi-asserted-by":"publisher","award":["RGS\/R1\/231417"],"award-info":[{"award-number":["RGS\/R1\/231417"]}],"id":[{"id":"10.13039\/501100000288","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2023,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper investigates the effect of moisture content upon the degradation behaviour of composite materials. A coupled phase field framework considering moisture diffusion, hygroscopic expansion, and fracture behaviour is developed. This multi-physics framework is used to explore the damage evolution of composite materials, spanning the micro-, meso- and macro-scales. The micro-scale unit-cell model shows how the mismatch between the hygroscopic expansion of fibre and matrix leads to interface debonding. From the meso-scale ply-level model, we learn that the distribution of fibres has a minor influence on the material properties, while increasing moisture content facilitates interface debonding. The macro-scale laminate-level model shows that moisture induces a higher degree of damage on the longitudinal ply relative to the transverse ply. This work opens a new avenue to understand and predict environmentally assisted degradation in composite materials.<\/jats:p>","DOI":"10.1007\/s00366-023-01820-z","type":"journal-article","created":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T17:03:39Z","timestamp":1682355819000},"page":"3847-3864","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Hygroscopic phase field fracture modelling of composite materials"],"prefix":"10.1007","volume":"39","author":[{"given":"Kit","family":"Au-Yeung","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adria","family":"Quintanas-Corominas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Emilio","family":"Mart\u00ednez-Pa\u00f1eda","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6380-9259","authenticated-orcid":false,"given":"Wei","family":"Tan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,4,24]]},"reference":[{"key":"1820_CR1","volume":"36","author":"R Barbi\u00e8re","year":"2020","unstructured":"Barbi\u00e8re R, Touchard F, Chocinski-Arnault L, Mellier D (2020) Influence of moisture and drying on fatigue damage mechanisms in a woven hemp\/epoxy composite: Acoustic emission and micro-ct analysis. Int J Fatigue 36:105593","journal-title":"Int J Fatigue"},{"key":"1820_CR2","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.compstruct.2018.08.037","volume":"206","author":"A Chilali","year":"2018","unstructured":"Chilali A, Assarar M, Zouari W, Kebir H, Ayad R (2018) Analysis of the hydro-mechanical behaviour of flax fibre-reinforced composites: assessment of hygroscopic expansion and its impact on internal stress. Composite Struct 206:177\u2013184","journal-title":"Composite Struct"},{"key":"1820_CR3","doi-asserted-by":"crossref","DOI":"10.1016\/j.compositesa.2020.105914","volume":"136","author":"M Abida","year":"2020","unstructured":"Abida M, Gehring F, Mars J, Vivet A, Dammak F, Haddar M (2020) Hygro-mechanical coupling and multiscale swelling coefficients assessment of flax yarns and flax \/ epoxy composites. Composites Part A 136:105914","journal-title":"Composites Part A"},{"issue":"7","key":"1820_CR4","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1016\/S1359-835X(00)00036-1","volume":"31","author":"FU Buehler","year":"2000","unstructured":"Buehler FU, Seferis JC (2000) Effect of reinforcement and solvent content on moisture absorption in epoxy composite materials. Composites Part A 31(7):741\u2013748","journal-title":"Composites Part A"},{"issue":"4\u20135","key":"1820_CR5","first-page":"2902","volume":"2","author":"N Sateesh","year":"2015","unstructured":"Sateesh N, Sampath Rao P, Ravishanker DV, Satyanarayana K (2015) Effect of moisture on gfrp composite materials. Materials Today 2(4\u20135):2902\u20132908","journal-title":"Materials Today"},{"key":"1820_CR6","unstructured":"Li M (2020) Temperature and moisture effects on composite materials for wind turbine blades"},{"key":"1820_CR7","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1023\/A:1009838128526","volume":"4","author":"YJ Weitsman","year":"2000","unstructured":"Weitsman YJ, Elahi M (2000) Effects of fluids on the deformation, strength and durability of polymeric composites\u2014an overview. Mech Time-Dependent Mater 4:107\u2013126","journal-title":"Mech Time-Dependent Mater"},{"key":"1820_CR8","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1163\/156855401753255422","volume":"8","author":"AK Mohanty","year":"2012","unstructured":"Mohanty AK, Misra M, Drzal T (2012) Surface modifications of natural fibers and performance of the resulting biocomposites: An overview. Composite Interfaces 8:313\u2013343","journal-title":"Composite Interfaces"},{"key":"1820_CR9","doi-asserted-by":"crossref","first-page":"1123","DOI":"10.1016\/j.eurpolymj.2004.11.029","volume":"41","author":"B Yang","year":"2004","unstructured":"Yang B, Huang WM, Li C, Chor JH (2004) Effects of moisture on the glass transition temperature of polyurethane shape memory polymer filled with nano-carbon powder. Euro Polymer J 41:1123\u20131128","journal-title":"Euro Polymer J"},{"key":"1820_CR10","volume":"231","author":"MM Lu","year":"2022","unstructured":"Lu MM, Fuentes CA, Willem A, Vuure V (2022) Moisture sorption and swelling of flax fibre and flax fibre composites. Composites Part B 231:109538","journal-title":"Composites Part B"},{"issue":"1","key":"1820_CR11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s12046-020-01514-y","volume":"45","author":"M Sathiyamoorthy","year":"2020","unstructured":"Sathiyamoorthy M, Senthilkumar S (2020) Mechanical, thermal, and water absorption behaviour of jute\/carbon reinforced hybrid composites. S\u0101dhan\u0101 45(1):1\u201312","journal-title":"S\u0101dhan\u0101"},{"issue":"1","key":"1820_CR12","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s40870-020-00260-w","volume":"7","author":"R Chavez Morales","year":"2021","unstructured":"Chavez Morales R, Eliasson V (2021) The effect of moisture intake on the mode-ii dynamic fracture behavior of carbon fiber\/epoxy composites. J Dyn Behavi Mater 7(1):21\u201333","journal-title":"J Dyn Behavi Mater"},{"issue":"15","key":"1820_CR13","doi-asserted-by":"crossref","first-page":"2043","DOI":"10.1177\/0021998320984237","volume":"55","author":"ZA Oguz","year":"2021","unstructured":"Oguz ZA, Erklig A, Bozkurt \u00d6Y (2021) Degradation of hybrid aramid\/glass\/epoxy composites hydrothermally aged in distilled water. J Composite Mater 55(15):2043\u20132060","journal-title":"J Composite Mater"},{"key":"1820_CR14","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.compositesa.2015.11.017","volume":"81","author":"LR LeBlanc","year":"2016","unstructured":"LeBlanc LR, LaPlante G (2016) Experimental investigation and finite element modeling of mixed-mode delamination in a moisture-exposed carbon\/epoxy composite. Composites Part A 81:202\u2013213","journal-title":"Composites Part A"},{"key":"1820_CR15","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.ijsolstr.2017.05.045","volume":"154","author":"Y Sinchuk","year":"2018","unstructured":"Sinchuk Y, Pannier Y, Gueguen M, Tandiang D, Gigliotti M (2018) Computed-tomography based modeling and simulation of moisture diffusion and induced swelling in textile composite materials. Int J Solids Struct 154:88\u201396","journal-title":"Int J Solids Struct"},{"key":"1820_CR16","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1016\/j.ijsolstr.2018.09.009","volume":"158","author":"AI Gagani","year":"2019","unstructured":"Gagani AI, Echtermeyer AT (2019) Influence of delaminations on fluid diffusion in multidirectional composite laminates\u2014theory and experiments. Int J Solids Struct 158:232\u2013242","journal-title":"Int J Solids Struct"},{"issue":"15","key":"1820_CR17","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1177\/0731684419845479","volume":"38","author":"H Bourennane","year":"2019","unstructured":"Bourennane H, Gueribiz D, Fr\u00e9our S, Jacquemin F (2019) Modeling the effect of damage on diffusive behavior in a polymeric matrix composite material. J Reinforced Plastics Composites 38(15):711\u2013733","journal-title":"J Reinforced Plastics Composites"},{"issue":"3","key":"1820_CR18","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1109\/TEPM.2002.804613","volume":"25","author":"EH Wong","year":"2002","unstructured":"Wong EH, Koh SW, Lee KH, Rajoo R (2002) Comprehensive treatment of moisture induced failure-recent advances. IEEE Trans Electron Packaging Manuf 25(3):223\u2013230","journal-title":"IEEE Trans Electron Packaging Manuf"},{"issue":"3","key":"1820_CR19","doi-asserted-by":"crossref","first-page":"904","DOI":"10.1002\/pc.24017","volume":"39","author":"X Cheng","year":"2016","unstructured":"Cheng X, Liu S, Zhang J, Guo X, Bao J (2016) Hygrothermal effects on mechanical behavior of scarf repaired carbon-epoxy laminates subject to axial compression loads: Experiment and numerical simulation. Polymer Composites 39(3):904\u2013914","journal-title":"Polymer Composites"},{"key":"1820_CR20","doi-asserted-by":"crossref","unstructured":"Griffith A (1921) Vi. the phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character 221, 163\u2013198","DOI":"10.1098\/rsta.1921.0006"},{"key":"1820_CR21","volume":"376","author":"F Fei","year":"2021","unstructured":"Fei F, Choo J (2021) Double-phase-field formulation for mixed-mode fracture in rocks. Comput Methods Appl Mech Eng 376:113655","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1820_CR22","volume":"121","author":"Y Navidtehrani","year":"2022","unstructured":"Navidtehrani Y, Beteg\u00f3n C, Mart\u00ednez-Pa\u00f1eda E (2022) A general framework for decomposing the phase field fracture driving force, particularised to a drucker-prager failure surface. Theo Appl Fracture Mech 121:103555","journal-title":"Theo Appl Fracture Mech"},{"key":"1820_CR23","doi-asserted-by":"crossref","unstructured":"Carollo V, Reinoso J, Paggi M (2018) Modeling complex crack paths in ceramic laminates: A novel variational framework combining the phase field method of fracture and the cohesive zone model. Journal of the European Ceramic Society 38(8), 2994\u20133003. Cermodel 2017: Modelling and Simulation Meet Innovation in Ceramics Technology","DOI":"10.1016\/j.jeurceramsoc.2018.01.035"},{"issue":"1","key":"1820_CR24","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1016\/j.ceramint.2020.08.191","volume":"47","author":"W Li","year":"2021","unstructured":"Li W, Shirvan K (2021) Multiphysics phase-field modeling of quasi-static cracking in Urania ceramic nuclear fuel. Ceramics Int 47(1):793\u2013810","journal-title":"Ceramics Int"},{"issue":"5","key":"1820_CR25","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1007\/s00466-015-1151-4","volume":"55","author":"M Ambati","year":"2015","unstructured":"Ambati M, Gerasimov T, De Lorenzis L (2015) Phase-field modeling of ductile fracture. Comput Mech 55(5):1017\u20131040","journal-title":"Comput Mech"},{"key":"1820_CR26","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.cma.2018.07.029","volume":"342","author":"M Dittmann","year":"2018","unstructured":"Dittmann M, Aldakheel F, Schulte J, Wriggers P, Hesch C (2018) Variational phase-field formulation of non-linear ductile fracture. Comput Methods Appl Mech Eng 342:71\u201394","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1820_CR27","doi-asserted-by":"crossref","unstructured":"Hirshikesh Natarajan S, Annabattula RK, Mart\u00ednez-Pa\u00f1eda E (2019) Phase field modelling of crack propagation in functionally graded materials. Composites Part B 169, 239\u2013248","DOI":"10.1016\/j.compositesb.2019.04.003"},{"key":"1820_CR28","doi-asserted-by":"crossref","unstructured":"Nguyen KD, Thanh C-L, Nguyen-Xuan H, Abdel-Wahab M (2021) A hybrid phase-field isogeometric analysis to crack propagation in porous functionally graded structures. Eng Comput","DOI":"10.1007\/s00366-021-01518-0"},{"key":"1820_CR29","doi-asserted-by":"crossref","unstructured":"He B, Vo T, Newell P (2022) Investigation of fracture in porous materials: a phase-field fracture study informed by reaxff. Eng Comput","DOI":"10.1007\/s00366-022-01708-4"},{"key":"1820_CR30","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.cma.2019.03.001","volume":"350","author":"S Zhou","year":"2019","unstructured":"Zhou S, Zhuang X, Rabczuk T (2019) Phase-field modeling of fluid-driven dynamic cracking in porous media. Comput Methods Appl Mech Eng 350:169\u2013198","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1820_CR31","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2020.113504","volume":"373","author":"M Simoes","year":"2021","unstructured":"Simoes M, Mart\u00ednez-Pa\u00f1eda E (2021) Phase field modelling of fracture and fatigue in shape memory alloys. Comput Methods Appl Mech Eng 373:113504","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1820_CR32","doi-asserted-by":"crossref","DOI":"10.1016\/j.commatsci.2022.111844","volume":"216","author":"A Lotfolahpour","year":"2023","unstructured":"Lotfolahpour A, Huber W, Asle Zaeem M (2023) A phase-field model for interactive evolution of phase transformation and cracking in superelastic shape memory ceramics. Comput Materials Sci 216:111844","journal-title":"Comput Materials Sci"},{"key":"1820_CR33","doi-asserted-by":"crossref","DOI":"10.1016\/j.engfracmech.2022.108693","volume":"272","author":"T Clayton","year":"2022","unstructured":"Clayton T, Duddu R, Siegert M, Mart\u00ednez-Pa\u00f1eda E (2022) A stress-based poro-damage phase field model for hydrofracturing of creeping glaciers and ice shelves. Eng Fracture Mech 272:108693","journal-title":"Eng Fracture Mech"},{"key":"1820_CR34","volume":"45","author":"X Sun","year":"2021","unstructured":"Sun X, Duddu R (2021) Hirshikesh: a poro-damage phase field model for hydrofracturing of glacier crevasses. Extreme Mech Lett 45:101277","journal-title":"Extreme Mech Lett"},{"key":"1820_CR35","doi-asserted-by":"crossref","DOI":"10.1016\/j.compositesb.2022.109788","volume":"236","author":"L Quinteros","year":"2022","unstructured":"Quinteros L, Garc\u00eda-Mac\u00edas E, Mart\u00ednez-Pa\u00f1eda E (2022) Micromechanics-based phase field fracture modelling of cnt composites. Composites Part B 236:109788","journal-title":"Composites Part B"},{"key":"1820_CR36","doi-asserted-by":"crossref","first-page":"899","DOI":"10.1016\/j.compstruct.2019.02.007","volume":"220","author":"A Quintanas-Corominas","year":"2019","unstructured":"Quintanas-Corominas A, Reinoso J, Casoni E, Turon A, Mayugo JA (2019) A phase field approach to simulate intralaminar and translaminar fracture in long fiber composite materials. Composite Struct 220:899\u2013911","journal-title":"Composite Struct"},{"key":"1820_CR37","volume":"202","author":"W Tan","year":"2021","unstructured":"Tan W, Mart\u00ednez-Pa\u00f1eda E (2021) Phase field predictions of microscopic fracture and r-curve behaviour of fibre-reinforced composites. Composites Sci Technol 202:108539","journal-title":"Composites Sci Technol"},{"key":"1820_CR38","volume":"286","author":"W Tan","year":"2022","unstructured":"Tan W, Mart\u00ednez-Pa\u00f1eda E (2022) Phase field fracture predictions of microscopic bridging behaviour of composite materials. Composite Struct 286:115242","journal-title":"Composite Struct"},{"key":"1820_CR39","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1016\/j.cma.2018.07.021","volume":"342","author":"E Mart\u00ednez-Pa\u00f1eda","year":"2018","unstructured":"Mart\u00ednez-Pa\u00f1eda E, Golahmar A, Niordson CF (2018) A phase field formulation for hydrogen assisted cracking. Comput Methods Appl Mech Eng 342:742\u2013761","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"75","key":"1820_CR40","doi-asserted-by":"crossref","first-page":"32235","DOI":"10.1016\/j.ijhydene.2022.07.117","volume":"47","author":"A Valverde-Gonz\u00e1lez","year":"2022","unstructured":"Valverde-Gonz\u00e1lez A, Mart\u00ednez-Pa\u00f1eda E, Quintanas-Corominas A, Reinoso J, Paggi M (2022) Computational modelling of hydrogen assisted fracture in polycrystalline materials. Int J Hydrogen Energy 47(75):32235\u201332251","journal-title":"Int J Hydrogen Energy"},{"key":"1820_CR41","doi-asserted-by":"crossref","DOI":"10.1016\/j.jpowsour.2022.231119","volume":"526","author":"AM Boyce","year":"2022","unstructured":"Boyce AM, Mart\u00ednez-Pa\u00f1eda E, Wade A, Zhang YS, Bailey JJ, Heenan TMM, Brett DJL, Shearing PR (2022) Cracking predictions of lithium-ion battery electrodes by x-ray computed tomography and modelling. J Power Sources 526:231119","journal-title":"J Power Sources"},{"key":"1820_CR42","doi-asserted-by":"crossref","unstructured":"Zhao Y, Xu B-X, Stein P, Gross D (2016) Phase-field study of electrochemical reactions at exterior and interior interfaces in li-ion battery electrode particles. Comput Methods Appl Mech Eng 312, 428\u2013446. Phase Field Approaches to Fracture","DOI":"10.1016\/j.cma.2016.04.033"},{"key":"1820_CR43","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2020.113648","volume":"376","author":"TK Mandal","year":"2021","unstructured":"Mandal TK, Nguyen VP, Wu J-Y, Nguyen-Thanh C, de Vaucorbeil A (2021) Fracture of thermo-elastic solids: phase-field modeling and new results with an efficient monolithic solver. Comput Methods Appl Mech Eng 376:113648","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1820_CR44","doi-asserted-by":"crossref","unstructured":"Asur Vijaya Kumar PK, Dean A, Reinoso J, Paggi M (2022) Nonlinear thermo-elastic phase-field fracture of thin-walled structures relying on solid shell concepts. Comput Methods Appl Mech Eng 396, 115096","DOI":"10.1016\/j.cma.2022.115096"},{"key":"1820_CR45","volume":"166","author":"C Cui","year":"2022","unstructured":"Cui C, Ma R, Mart\u00ednez-Pa\u00f1eda E (2022) A generalised, multi-phase-field theory for dissolution-driven stress corrosion cracking and hydrogen embrittlement. J Mech Phys Solids 166:104951","journal-title":"J Mech Phys Solids"},{"key":"1820_CR46","doi-asserted-by":"crossref","unstructured":"Ansari TQ, Huang H, Shi S-Q (2021) Phase field modeling for the morphological and microstructural evolution of metallic materials under environmental attack. npj Comput Materials 7(1), 143","DOI":"10.1038\/s41524-021-00612-7"},{"key":"1820_CR47","doi-asserted-by":"crossref","unstructured":"Arash B, Exner W, Rolfes R (2022) Effect of moisture on the nonlinear viscoelastic fracture behavior of polymer nanocompsites: a finite deformation phase-field model. Eng Comput","DOI":"10.1007\/s00366-022-01670-1"},{"key":"1820_CR48","volume":"388","author":"J-Y Ye","year":"2022","unstructured":"Ye J-Y, Zhang L-W (2022) Damage evolution of polymer-matrix multiphase composites under coupled moisture effects. Comput Methods Appl Mech Eng 388:114213","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"8","key":"1820_CR49","doi-asserted-by":"crossref","first-page":"1319","DOI":"10.1016\/S0022-5096(98)00034-9","volume":"46","author":"GA Francfort","year":"1998","unstructured":"Francfort GA, Marigo J-J (1998) Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids 46(8):1319\u20131342","journal-title":"J Mech Phys Solids"},{"issue":"4","key":"1820_CR50","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1016\/S0022-5096(99)00028-9","volume":"48","author":"B Bourdin","year":"2000","unstructured":"Bourdin B, Francfort GA, Marigo J-J (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48(4):797\u2013826","journal-title":"J Mech Phys Solids"},{"issue":"2203","key":"1820_CR51","doi-asserted-by":"crossref","first-page":"20210021","DOI":"10.1098\/rsta.2021.0021","volume":"379","author":"PK Kristensen","year":"2021","unstructured":"Kristensen PK, Niordson CF, Mart\u00ednez-Pa\u00f1eda E (2021) An assessment of phase field fracture: crack initiation and growth. Philosoph Trans R Soc A 379(2203):20210021","journal-title":"Philosoph Trans R Soc A"},{"key":"1820_CR52","doi-asserted-by":"crossref","first-page":"1209","DOI":"10.1016\/j.jmps.2009.04.011","volume":"57","author":"H Amor","year":"2009","unstructured":"Amor H, Marigo JJ, Maurini C (2009) Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments. J Mech Phys Solids 57:1209\u20131229","journal-title":"J Mech Phys Solids"},{"issue":"45\u201348","key":"1820_CR53","doi-asserted-by":"crossref","first-page":"2765","DOI":"10.1016\/j.cma.2010.04.011","volume":"199","author":"C Miehe","year":"2010","unstructured":"Miehe C, Hofacker M, Welschinger F (2010) A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng 199(45\u201348):2765\u20132778","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1820_CR54","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1016\/j.compstruct.2012.09.044","volume":"97","author":"Y Joliff","year":"2013","unstructured":"Joliff Y, Belec L, Chailan JN (2013) Modified water diffusion kinetics in an unidirectional glass\/fibre composite due to the interphase area: experimental, analytical and numerical approach. Composite Struct 97:296\u2013303","journal-title":"Composite Struct"},{"key":"1820_CR55","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/j.compstruct.2014.05.026","volume":"116","author":"T Peret","year":"2014","unstructured":"Peret T, Clement A, Freour S, Jacquemin F (2014) Numerical transient hygro-elastic analyses of reinforced fickian and non-fickian polymers. Composite Struct 116:395\u2013403","journal-title":"Composite Struct"},{"key":"1820_CR56","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1002\/app.39148","volume":"130","author":"A C\u00e9lino","year":"2013","unstructured":"C\u00e9lino A, Fr\u00e9our S, Jacquemin F, Casari P (2013) Characterization and modeling of the moisture diffusion behavior of natural fibers. J Appl Polymer Sci 130:297\u2013306","journal-title":"J Appl Polymer Sci"},{"key":"1820_CR57","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/j.polymdegradstab.2016.11.006","volume":"134","author":"S Sugiman","year":"2016","unstructured":"Sugiman S, Putra IKP, Setyawan PD (2016) Effects of the media and ageing condition on the tensile properties and fracture toughness of epoxy resin. Polymer Degradation Stab 134:311\u2013321","journal-title":"Polymer Degradation Stab"},{"issue":"1","key":"1820_CR58","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1002\/app.39148","volume":"130","author":"A C\u00e9lino","year":"2013","unstructured":"C\u00e9lino A, Fr\u00e9our S, Jacquemin F, Casari P (2013) Characterization and modeling of the moisture diffusion behavior of natural fibers. J Appl Polymer Sci 130(1):297\u2013306","journal-title":"J Appl Polymer Sci"},{"key":"1820_CR59","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2022.114880","volume":"395","author":"D Phansalkar","year":"2022","unstructured":"Phansalkar D, Weinberg K, Ortiz M, Leyendecker S (2022) A spatially adaptive phase-field model of fracture. Comput Methods Appl Mech Eng 395:114880","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"1","key":"1820_CR60","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.dt.2020.03.004","volume":"17","author":"E Mart\u00ednez-Pa\u00f1eda","year":"2021","unstructured":"Mart\u00ednez-Pa\u00f1eda E, Natarajan S et al (2021) Adaptive phase field modelling of crack propagation in orthotropic functionally graded materials. Defence Technol 17(1):185\u2013195","journal-title":"Defence Technol"},{"key":"1820_CR61","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2021.113874","volume":"383","author":"H Hirshikesh","year":"2021","unstructured":"Hirshikesh H, Pramod A, Waisman H, Natarajan S (2021) Adaptive phase field method using novel physics based refinement criteria. Comput Methods Appl Mech Eng 383:113874","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1820_CR62","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1016\/j.cma.2019.06.002","volume":"355","author":"A Pramod","year":"2019","unstructured":"Pramod A, Annabattula R, Ooi E, Song C, Natarajan S et al (2019) Adaptive phase-field modeling of brittle fracture using the scaled boundary finite element method. Comput Methods Appl Mech Eng 355:284\u2013307","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1820_CR63","volume":"6","author":"Y Navidtehrani","year":"2021","unstructured":"Navidtehrani Y, Beteg\u00f3n C, Mart\u00ednez-Pa\u00f1eda E (2021) A simple and robust abaqus implementation of the phase field fracture method. Appl Eng Sci 6:100050","journal-title":"Appl Eng Sci"},{"key":"1820_CR64","doi-asserted-by":"crossref","unstructured":"Navidtehrani Y, Beteg\u00f3n C, Mart\u00ednez-Pa\u00f1eda E (2021) A unified abaqus implementation of the phase field fracture method using only a user material subroutine 14(8)","DOI":"10.3390\/ma14081913"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-023-01820-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-023-01820-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-023-01820-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,20]],"date-time":"2023-12-20T03:05:01Z","timestamp":1703041501000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-023-01820-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,24]]},"references-count":64,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["1820"],"URL":"https:\/\/doi.org\/10.1007\/s00366-023-01820-z","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,24]]},"assertion":[{"value":"2 December 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 April 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 April 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}