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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 |

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\textit{E. V. Iarve} et al., Int. J. Numer. Methods Eng. 88, No. 8, 749--773 (2011; Zbl 1242.74126)

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