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Mesh-independent matrix cracking and delamination modeling in laminated composites. (English) Zbl 1242.74126
Summary: The initiation and evolution of transverse matrix cracks and delaminations are predicted within a mesh-independent cracking (MIC) framework. MIC is a regularized extended finite element method (x-FEM) that allows the insertion of cracks in directions that are independent of the mesh orientation. The Heaviside step function that is typically used to introduce a displacement discontinuity across a crack surface is replaced by a continuous function approximated by using the original displacement shape functions. Such regularization allows the preservation of the Gaussian integration schema regardless of the enrichment required to model cracking in an arbitrary direction. The interaction between plies is anchored on the integration point distribution, which remains constant through the entire simulation. Initiation and propagation of delaminations between plies as well as intra-ply MIC opening is implemented by using a mixed-mode cohesive formulation in a fully three-dimensional model that includes residual thermal stresses. The validity of the proposed methodology was tested against a variety of problems ranging from simple evolution of delamination from existing transverse cracks to strength predictions of complex laminates withouttextita priori knowledge of damage location or initiation. Good agreement with conventional numerical solutions and/or experimental data was observed in all the problems considered.

##### MSC:
 74S05 Finite element methods applied to problems in solid mechanics 74R10 Brittle fracture 74E30 Composite and mixture properties
##### Keywords:
composite; mesh independent cracking; delamination; failure
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##### References:
 [1] Maimí, A continuum damage model for composite laminates: part I-constitutive model, Mechanics of Materials 39 pp 897– (2007) · doi:10.1016/j.mechmat.2007.03.005 [2] Maimí, A continuum damage model for composite laminates: part II-computational implementation and validation, Mechanics of Materials 39 pp 909– (2007) · doi:10.1016/j.mechmat.2007.03.006 [3] Alfano, Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues, International Journal for Numerical Methods in Engineering 50 pp 1701– (2001) · Zbl 1011.74066 · doi:10.1002/nme.93 [4] Jiang, A concise interface constitutive law and its application to scaled notched tensile specimens, International Journal for Numerical Methods in Engineering 69 pp 1982– (2007) · Zbl 1194.74342 · doi:10.1002/nme.1842 [5] Turon, A damage model for the simulation of delamination in advanced composites under variable-mode loading, Mechanics of Materials 38 pp 1072– (2006) · doi:10.1016/j.mechmat.2005.10.003 [6] Krueger R The virtual crack closure technique: history, approach and applications 2002 [7] Deobald LR Mabson GE Dopker B Hoyt DM Baylor J Greasser D Interlaminar fatigue elements for crack growth based on virtual crack closure technique [8] Iarve, Theoretical and experimental investigation of stress redistribution in open hole composite laminates due to damage accumulation, Composites Part A 36 pp 163– (2005) · doi:10.1016/j.compositesa.2004.06.011 [9] Hallett, Modeling the interaction between matrix crack and delamination damage in scaled quasi-isotropic specimens, Composites Science and Technology 68 pp 80– (2008) · doi:10.1016/j.compscitech.2007.05.038 [10] Van der Meer, Continuum models for the analysis of progressive failure in composite laminates, Journal of Composite Materials 40 pp 2131– (2009) · doi:10.1177/0021998309343054 [11] Allix, Analyse de la Tenue aux Impacts à Faible Vitesse et Faible Énergie des Stratifiés Composites par la Mécanique de l’Endommagement, Mécanique and Industries 1 (1) pp 27– (2000) · doi:10.1016/S1296-2139(00)00105-6 [12] Ladevèze, Towards a bridge between the micro-and mesomechanics of delamination for laminated composites, Composites Science and Technology 66 pp 698– (2006) · doi:10.1016/j.compscitech.2004.12.026 [13] Lubineau, Construction of a micromechanics-based intralaminar mesomodel, and illustrations in ABAQUS/Standard Computational, Materials Science 43 pp 137– (2008) [14] Wawrzynek, An interactive approach to local remeshing around a crack tip, Finite Elements in Analysis and Design 5 (1) pp 87– (1989) · doi:10.1016/0168-874X(89)90008-5 [15] Fish, The s-method of the finite element method for multilayered laminates, International Journal for Numerical Methods in Engineering 33 pp 1081– (1992) · Zbl 0775.73247 · doi:10.1002/nme.1620330512 [16] Iarve EV Three-dimensional stress analysis in open hole composite laminates containing matrix cracks 1998 [17] Moës, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering 46 pp 601– (1999) · Zbl 0955.74066 · doi:10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J [18] Belytschko, Structured extended finite element methods for solids defined by implicit boundaries, International Journal for Numerical Methods in Engineering 56 pp 609– (2003) · Zbl 1038.74041 · doi:10.1002/nme.686 [19] Huynh, The extended finite element method for fracture in composite materials, International Journal for Numerical Methods in Engineering 77 pp 214– (2009) · Zbl 1257.74153 · doi:10.1002/nme.2411 [20] Van der Meer, A phantom node formulation with mixed mode cohesive law for splitting in laminates, International Journal of Fracture 158 (2) pp 107– (2009) · Zbl 1400.74106 · doi:10.1007/s10704-009-9344-5 [21] Ling, An augmented finite element method for modeling arbitrary discontinuities in composite materials, International Journal of Fracture 156 pp 53– (2009) · Zbl 1273.74540 · doi:10.1007/s10704-009-9347-2 [22] Hansbo, An unfitted finite element method for the simulation of strong and weak discontinuities in solid mechanics, Computer Methods in Applied Mechanics and Engineering 193 pp 3523– (2004) · Zbl 1068.74076 · doi:10.1016/j.cma.2003.12.041 [23] Iarve, Mesh independent modeling of cracks by using higher order shape functions, International Journal for Numerical Methods in Engineering 56 pp 869– (2003) · Zbl 1078.74658 · doi:10.1002/nme.596 [24] Patzak, Process zone resolution by extended finite elements, Engineering Fracture Mechanics 70 pp 957– (2003) · doi:10.1016/S0013-7944(02)00160-1 [25] Benvenuti, A regularized x-FEM model for the transition from continuous to discontinuous displacements, International Journal for Numerical Methods in Engineering 74 pp 911– (2008) · Zbl 1158.74479 · doi:10.1002/nme.2196 [26] Benvenuti, A regularized x-FEM framework for embedded cohesive interfaces, Computer Methods in Applied Mechanics and Engineering 197 pp 4367– (2008) · Zbl 1194.74364 · doi:10.1016/j.cma.2008.05.012 [27] Oliver, A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM, Computer Methods in Applied Mechanics and Engineering 195 pp 4732– (2006) · Zbl 1144.74043 · doi:10.1016/j.cma.2005.09.020 [28] Dávila, Failure criteria for FRP laminates, Journal of Composite Materials 39 (4) pp 323– (2005) · doi:10.1177/0021998305046452 [29] Mollenhauer, Examination of ply cracking in composite laminates with open-holes: a Moiré Interferometric and Numerical Study, Composites Part A 37 pp 282– (2006) · doi:10.1016/j.compositesa.2005.06.004 [30] Whitney, Structural Analysis of Laminated Anisotropic Plates pp 339– (1987) [31] König, Composite Materials: Testing and Design, ASTM STP 1242 13 pp 60– (1997) [32] Liu, Composite Materials: Fatigue and Fracture, 4, ASTM STP 1156 (1993) [33] Gurvich, Strength size effect for anisotropic brittle materials under random stress state, Computer Science and Technology 59 (11) pp 1701– (1999) · doi:10.1016/S0266-3538(99)00030-5 [34] Iarve EV Mollenhauer D Kim R Delamination onset prediction in joints by using critical Weibull failure volume method [35] Crossman, Damage in Composite Materials pp 118– (1982) [36] Johnson, Characterization of matrix crack-induced laminate failure-part I: experiments, Journal of Composite Materials 35 (22) pp 2009– (2001)
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