{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T11:06:59Z","timestamp":1776424019316,"version":"3.51.2"},"reference-count":55,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2016,9,22]],"date-time":"2016-09-22T00:00:00Z","timestamp":1474502400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Mech"],"published-print":{"date-parts":[[2016,12]]},"DOI":"10.1007\/s00466-016-1328-5","type":"journal-article","created":{"date-parts":[[2016,9,22]],"date-time":"2016-09-22T19:03:42Z","timestamp":1474571022000},"page":"1003-1018","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":62,"title":["A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement"],"prefix":"10.1007","volume":"58","author":[{"given":"P.","family":"Areias","sequence":"first","affiliation":[]},{"given":"T.","family":"Rabczuk","sequence":"additional","affiliation":[]},{"given":"J. C\u00e9sar","family":"de S\u00e1","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,9,22]]},"reference":[{"key":"1328_CR1","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1002\/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J","volume":"46","author":"N Mo\u00ebs","year":"1999","unstructured":"Mo\u00ebs N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131\u2013150","journal-title":"Int J Numer Methods Eng"},{"key":"1328_CR2","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/BF00356478","volume":"17","author":"J Oliver","year":"1995","unstructured":"Oliver J (1995) Continuum modelling of strong discontinuities in solid mechanics using damage models. Comput Mech 17:49\u201361","journal-title":"Comput Mech"},{"key":"1328_CR3","doi-asserted-by":"crossref","first-page":"1727","DOI":"10.1002\/nme.1620090302","volume":"9","author":"RD Henshell","year":"1975","unstructured":"Henshell RD, Shaw KG (1975) Crack tip elements are unnecessary. Int J Numer Methods Eng 9:1727\u20131742","journal-title":"Int J Numer Methods Eng"},{"key":"1328_CR4","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1016\/0020-7683(88)90059-5","volume":"24","author":"D Lasry","year":"1988","unstructured":"Lasry D, Belytschko T (1988) Localization limiters in transient problems. Int J Solids Struct 24:581\u2013597","journal-title":"Int J Solids Struct"},{"issue":"2","key":"1328_CR5","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/0013-7944(95)00247-2","volume":"55","author":"TN Bittencourt","year":"1996","unstructured":"Bittencourt TN, Wawrzynek PA, Ingraffea AR, Sousa JL (1996) Quasi-automatic simulation of crack propagation for 2D LEFM problems. Eng Fract Mech 55(2):321\u2013334","journal-title":"Eng Fract Mech"},{"key":"1328_CR6","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1016\/j.engfracmech.2005.08.007","volume":"73","author":"D Colombo","year":"2006","unstructured":"Colombo D, Giglio M (2006) A methodology for automatic crack propagation modelling in planar and shell fe models. Eng Fract Mech 73:490\u2013504","journal-title":"Eng Fract Mech"},{"key":"1328_CR7","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/S0045-7949(02)00431-5","volume":"81","author":"BL Karihaloo","year":"2003","unstructured":"Karihaloo BL, Xiao QZ (2003) Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review. Comput Struct 81:119\u2013129","journal-title":"Comput Struct"},{"key":"1328_CR8","doi-asserted-by":"crossref","first-page":"1466","DOI":"10.1002\/nme.2001","volume":"71","author":"S Loehnert","year":"2007","unstructured":"Loehnert S, Belytschko T (2007) A multiscale projection method for macro\/microcrack simulations. Int J Numer Methods Eng 71:1466\u20131482","journal-title":"Int J Numer Methods Eng"},{"key":"1328_CR9","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1016\/S0013-7944(01)00128-X","volume":"69","author":"N Mo\u00ebs","year":"2002","unstructured":"Mo\u00ebs N, Belytschko T (2002) Extended finite element method for cohesive crack growth. Eng Fract Mech 69:813\u2013833","journal-title":"Eng Fract Mech"},{"key":"1328_CR10","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.engfracmech.2012.01.001","volume":"84","author":"H Nguyen-Xuan","year":"2012","unstructured":"Nguyen-Xuan H, Liu GR, Nourbakhshnia N, Chen L (2012) A novel singular ES-FEM for crack growth simulation. Eng Fract Mech 84:41\u201366","journal-title":"Eng Fract Mech"},{"key":"1328_CR11","unstructured":"Pierard O, Jin Y, Wyart E, Dompierre B, Bechet E (2016) Simulation of contact on crack lips and its influence on fatigue life prediction. In: Carpintieri A, Fatemi A, Navarro C (eds) International Conference on Multiaxial Fatigue and Fracture, ICMFF11, Seville. Fracture and structural integrity"},{"key":"1328_CR12","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1016\/S0013-7944(01)00108-4","volume":"69","author":"J Alfaiate","year":"2002","unstructured":"Alfaiate J, Wells GN, Sluys LJ (2002) On the use of embedded discontinuity elements with crack path continuity for mode-I and mixed-mode fracture. Eng Fract Mech 69:661\u2013686","journal-title":"Eng Fract Mech"},{"key":"1328_CR13","doi-asserted-by":"crossref","first-page":"3523","DOI":"10.1016\/j.cma.2003.12.041","volume":"193","author":"A Hansbo","year":"2004","unstructured":"Hansbo A, Hansbo P (2004) A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput Methods Appl Mech Eng 193:3523\u20133540","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1328_CR14","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1002\/nme.4477","volume":"94","author":"P Areias","year":"2013","unstructured":"Areias P, Rabczuk T (2013) Finite strain fracture of plates and shells with configurational forces and edge rotations. Int J Numer Methods Eng 94:1099\u20131122","journal-title":"Int J Numer Methods Eng"},{"key":"1328_CR15","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1002\/nme.1999","volume":"72","author":"C Miehe","year":"2007","unstructured":"Miehe C, G\u00fcrses E (2007) A robust algorithm for configurational-force-driven brittle crack propagation with $$r-$$ r - adaptive mesh alignment. Int J Numer Methods Eng 72:127\u2013155","journal-title":"Int J Numer Methods Eng"},{"key":"1328_CR16","doi-asserted-by":"crossref","first-page":"1945","DOI":"10.1002\/nme.948","volume":"59","author":"M Duflot","year":"2004","unstructured":"Duflot M, Nguyen-Dang H (2004) A meshless method with enriched weight functions for fatigue. Int J Numer Methods Eng 59:1945\u20131961","journal-title":"Int J Numer Methods Eng"},{"issue":"2","key":"1328_CR17","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s00466-013-0910-3","volume":"53","author":"E Barbieri","year":"2014","unstructured":"Barbieri E, Petrinic N (2014) Three-dimensional crack propagation with distance-based discontinuous kernels in meshfree methods. Comput Mech 53(2):325\u2013342","journal-title":"Comput Mech"},{"key":"1328_CR18","doi-asserted-by":"crossref","unstructured":"Peng X, Atroshchenko E, Kerfriden P, Bordas SPA (2016) Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth. Comput Methods Appl Mech Eng (in press)","DOI":"10.1016\/j.cma.2016.05.038"},{"key":"1328_CR19","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1007\/s00371-015-1123-x","volume":"31","author":"CJ Paulus","year":"2015","unstructured":"Paulus CJ, Untereiner L, Courtecuisse H, Cotin S, Cazier D (2015) Virtual cutting of deformable objects based on efficient topological operations. Vis Comput 31:831\u2013841","journal-title":"Vis Comput"},{"issue":"35\u201336","key":"1328_CR20","doi-asserted-by":"crossref","first-page":"3887","DOI":"10.1016\/S0045-7825(03)00391-8","volume":"192","author":"PO Bouchard","year":"2003","unstructured":"Bouchard PO, Bay F, Chastel Y (2003) Numerical modeling of crack propagation\u2014implementation, techniques and comparison of different criteria. Comp Methods Appl Mech Eng 192(35\u201336):3887\u20133908","journal-title":"Comp Methods Appl Mech Eng"},{"key":"1328_CR21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.finel.2012.04.006","volume":"59","author":"R Khaoulani El","year":"2012","unstructured":"El Khaoulani R, Bouchard PO (2012) An anisotropic mesh adaptation strategy for damage and failure in ductile materials. Finite Elem Anal Des 59:1\u201310","journal-title":"Finite Elem Anal Des"},{"key":"1328_CR22","doi-asserted-by":"crossref","first-page":"1653","DOI":"10.1016\/j.engfracmech.2006.01.009","volume":"73","author":"X Teng","year":"2006","unstructured":"Teng X, Wierzbicki T (2006) Evaluation of six fracture models in high velocity perforation. Eng Fract Mech 73:1653\u20131678","journal-title":"Eng Fract Mech"},{"key":"1328_CR23","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1002\/nme.1620280214","volume":"28","author":"J Oliver","year":"1989","unstructured":"Oliver J (1989) A consistent characteristic length for smeared cracking models. Int J Numer Methods Eng 28:461\u2013474","journal-title":"Int J Numer Methods Eng"},{"key":"1328_CR24","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1061\/(ASCE)0733-9399(1999)125:1(60)","volume":"125","author":"G Etse","year":"1999","unstructured":"Etse G, Willam K (1999) Failure analysis of elastoviscoplastic material models. J Eng Mech 125:60\u201369","journal-title":"J Eng Mech"},{"key":"1328_CR25","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1115\/1.3171860","volume":"53","author":"HL Schreyer","year":"1986","unstructured":"Schreyer HL, Chen Z (1986) One-dimensional softening with localization. J Appl Mech 53:791\u2013797","journal-title":"J Appl Mech"},{"key":"1328_CR26","unstructured":"Areias P. Simplas. http:\/\/home.uevora.pt\/~pmaa\/SimplasWebsite\/Simplas.html"},{"key":"1328_CR27","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-18255-6","volume-title":"A course on damage mechanics","author":"J Lemaitre","year":"1996","unstructured":"Lemaitre J (1996) A course on damage mechanics, 2nd edn. Springer, New York","edition":"2"},{"key":"1328_CR28","volume-title":"Theoretical mechanics of particles and continua","author":"AL Fetter","year":"2003","unstructured":"Fetter AL, Walecka JD (2003) Theoretical mechanics of particles and continua. Courier Dover, New York"},{"key":"1328_CR29","volume-title":"Non-linear elastic deformations","author":"RW Ogden","year":"1997","unstructured":"Ogden RW (1997) Non-linear elastic deformations. Dover Publications, New York"},{"key":"1328_CR30","unstructured":"Mazars J (1984) Application de la m\u00e9canique de l\u2019endommagement au comportement non lin\u00e9aire et \u00e0 la rupture du b\u00e9ton de structure. Th\u00e8se de Doctorat d\u2019Etat, Universit\u00e9 Paris VI, Paris"},{"key":"1328_CR31","doi-asserted-by":"crossref","first-page":"3391","DOI":"10.1002\/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D","volume":"39","author":"RHJ Peerlings","year":"1996","unstructured":"Peerlings RHJ, de Borst R, Brekelmans WAM, de Vree JHP (1996) Gradient enhanced damage for quasi-brittle materials. Int J Numer Methods Eng 39:3391\u20133403","journal-title":"Int J Numer Methods Eng"},{"key":"1328_CR32","doi-asserted-by":"crossref","unstructured":"Areias P, Dias-da-Costa D, Alfaiate J, J\u00falio E (2009) Arbitrary bi-dimensional finite strain cohesive crack propagation. Comput Mech 45(1):61\u201375","DOI":"10.1007\/s00466-009-0418-z"},{"key":"1328_CR33","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1016\/S0168-874X(02)00164-6","volume":"39","author":"PMA Areias","year":"2003","unstructured":"Areias PMA, C\u00e9sar de S\u00e1 JMA, Concei\u00e7\u00e3o CA (2003) A gradient model for finite strain elastoplasticity coupled with damage. Finite Elem Anal Des 39:1191\u20131235","journal-title":"Finite Elem Anal Des"},{"key":"1328_CR34","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1016\/S0997-7538(99)00114-X","volume":"18","author":"R Borst de","year":"1999","unstructured":"de Borst R, Pamin J, Geers MGD (1999) On coupled gradient-dependent plasticity and damage theories with a view to localization analysis. Eur J Mech A 18:939\u2013962","journal-title":"Eur J Mech A"},{"key":"1328_CR35","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/S0045-7825(98)80011-X","volume":"160","author":"MGD Geers","year":"1998","unstructured":"Geers MGD, de Borst R, Brekelmans WAM, Peerlings RHJ (1998) Strain-based transient-gradient damage model for failure analysis. Comput Methods Appl Mech Eng 160:133\u2013153","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1328_CR36","unstructured":"Wolfram Research Inc. Mathematica (2007)"},{"issue":"4","key":"1328_CR37","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1007\/s003660200028","volume":"18","author":"J Korelc","year":"2002","unstructured":"Korelc J (2002) Multi-language and multi-environment generation of nonlinear finite element codes. Eng Comput 18(4):312\u2013327","journal-title":"Eng Comput"},{"key":"1328_CR38","volume-title":"Nonlinear finite elements for continua and structures","author":"T Belytschko","year":"2000","unstructured":"Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, New York"},{"key":"1328_CR39","volume-title":"Mesh generation: application to finite elements","author":"PJ Frey","year":"2000","unstructured":"Frey PJ, George P-L (2000) Mesh generation: application to finite elements. Hermes Science, Oxford"},{"key":"1328_CR40","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1007\/s00466-011-0588-3","volume":"48","author":"P Areias","year":"2011","unstructured":"Areias P, Gar\u00e7\u00e3o J, Pires EB, Barbosa JI (2011) Exact corotational shell for finite strains and fracture. Comput Mech 48:385\u2013406","journal-title":"Comput Mech"},{"key":"1328_CR41","unstructured":"Winkler BJ (2001) Traglastuntersuchungen von unbewehrten und bew. Betonstrukturen auf der Grundlage eines objektiven Werkstoffgesetzes f\u00fcr Beton. PhD thesis, University of Innsbruck, Innrain 52, 6020 Innsbruck"},{"key":"1328_CR42","doi-asserted-by":"crossref","unstructured":"Most T, Bucher C (2006) Energy-based simulation of concrete cracking using an improved mixed-mode cohesive crack model within a meshless discretization. Int J Numer Anal Met 31:285\u2013305","DOI":"10.1002\/nag.536"},{"key":"1328_CR43","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1002\/nag.560","volume":"31","author":"P Dumstorff","year":"2007","unstructured":"Dumstorff P, Meschke G (2007) Crack propagation criteria. Int J Numer Anal Met 31:239\u2013259","journal-title":"Int J Numer Anal Met"},{"key":"1328_CR44","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1115\/1.3656897","volume":"85","author":"F Erdogan","year":"1963","unstructured":"Erdogan F, Sih GC (1963) On the crack extension in plates under plane loading and transverse shear. J Bas Eng 85:519\u2013527","journal-title":"J Bas Eng"},{"key":"1328_CR45","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.engfracmech.2015.10.042","volume":"158","author":"P Areias","year":"2016","unstructured":"Areias P, Msekh MA, Rabczuk T (2016) Damage and fracture algorithm using the screened poisson equation and local remeshing. Eng Fract Mech 158:116\u2013143","journal-title":"Eng Fract Mech"},{"key":"1328_CR46","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1061\/(ASCE)0733-9399(1997)123:8(765)","volume":"123","author":"I Carol","year":"1997","unstructured":"Carol I, Prat PC, L\u00f3pez CM (1997) Normal\/shear cracking model: application to discrete crack analysis. J Eng Mech 123:765\u2013773","journal-title":"J Eng Mech"},{"key":"1328_CR47","unstructured":"Schlangen E (1993) Experimental and numerical analysis of fracture processes in concrete. PhD thesis, Delft"},{"key":"1328_CR48","unstructured":"Alfaiate J, Simone A, Sluys LJ (2003) A new approach to strong embedded discontinuities. In: Bicanic N, de Borst R, Mang H, Meschke G (eds) Computational Modelling of Concrete Structures, EURO-C 2003. St. Johann im Pongau"},{"key":"1328_CR49","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1007\/s00466-004-0603-z","volume":"35","author":"PMA Areias","year":"2004","unstructured":"Areias PMA, C\u00e9sar de S\u00e1 JMA, Concei\u00e7\u00e3o Ant\u00f3nio CA, Carneiro JASAO, Teixeira VMP (2004) Strong displacement discontinuities and Lagrange multipliers in the analysis of finite displacement fracture problems. Comput Mech 35:54\u201371","journal-title":"Comput Mech"},{"issue":"9","key":"1328_CR50","doi-asserted-by":"crossref","first-page":"1176","DOI":"10.1016\/j.engfracmech.2009.01.011","volume":"76","author":"D Dias-da-Costa","year":"2009","unstructured":"Dias-da-Costa D, Alfaiate J, Sluys LJ, J\u00falio E (2009) A discrete strong discontinuity approach. Eng Fract Mech 76(9):1176\u20131201","journal-title":"Eng Fract Mech"},{"key":"1328_CR51","unstructured":"Arrea M, Ingraffea RA (1982) Mixed-mode crack propagation in mortar and concrete. Technical Report Report 81-13, Cornell University, Department of Structural Engineering"},{"key":"1328_CR52","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1002\/nme.1305","volume":"63","author":"PMA Areias","year":"2005","unstructured":"Areias PMA, Belytschko T (2005) Analysis of three-dimensional crack initiation and propagation using the extended finite element method. Int J Numer Methods Eng 63:760\u2013788","journal-title":"Int J Numer Methods Eng"},{"issue":"9","key":"1328_CR53","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1016\/0020-7683(91)90115-V","volume":"27","author":"P Bocca","year":"1991","unstructured":"Bocca P, Carpinteri A, Valente S (1991) Mixed mode fracture of concrete. Int J Solids Struct 27(9):1139\u20131153","journal-title":"Int J Solids Struct"},{"key":"1328_CR54","doi-asserted-by":"crossref","first-page":"2316","DOI":"10.1002\/nme.1151","volume":"61","author":"T Rabczuk","year":"2004","unstructured":"Rabczuk T, Belytschko T (2004) Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Methods Eng 61:2316\u20132343","journal-title":"Int J Numer Methods Eng"},{"key":"1328_CR55","series-title":"Applications and numerics","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/978-3-662-03567-2_5","volume-title":"Mathematical visualization: algorithms","author":"D Ruprecht","year":"1998","unstructured":"Ruprecht D, M\u00fcller H (1998) A scheme for edge-based adaptive tetrahedron subdivision. In: Hege H-C, Polthier K (eds) Mathematical visualization: algorithms., Applications and numericsSpringer, Berlin, pp 61\u201370"}],"container-title":["Computational Mechanics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00466-016-1328-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00466-016-1328-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00466-016-1328-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,24]],"date-time":"2017-06-24T19:30:43Z","timestamp":1498332643000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00466-016-1328-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,22]]},"references-count":55,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2016,12]]}},"alternative-id":["1328"],"URL":"https:\/\/doi.org\/10.1007\/s00466-016-1328-5","relation":{},"ISSN":["0178-7675","1432-0924"],"issn-type":[{"value":"0178-7675","type":"print"},{"value":"1432-0924","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,9,22]]}}}