A new multi-layer approach for progressive damage simulation in composite laminates based on isogeometric analysis and Kirchhoff-Love shells. I: Basic theory and modeling of delamination and transverse shear.

*(English)*Zbl 1446.74163Summary: In this two-part paper we introduce a new formulation for modeling progressive damage in laminated composite structures. We adopt a multi-layer modeling approach, based on Isogeometric Analysis (IGA), where each ply or lamina is represented by a spline surface, and modeled as a Kirchhoff-Love thin shell. Continuum Damage Mechanics is used to model intralaminar damage, and a new zero-thickness cohesive-interface formulation is introduced to model delamination as well as permitting laminate-level transverse shear compliance. In Part I of this series we focus on the presentation of the modeling framework, validation of the framework using standard Mode I and Mode II delamination tests, and assessment of its suitability for modeling thick laminates. In Part II of this series we focus on the application of the proposed framework to modeling and simulation of damage in composite laminates resulting from impact. The proposed approach has significant accuracy and efficiency advantages over existing methods for modeling impact damage. These stem from the use of IGA-based Kirchhoff-Love shells to represent the individual plies of the composite laminate, while the compliant cohesive interfaces enable transverse shear deformation of the laminate. Kirchhoff-Love shells give a faithful representation of the ply deformation behavior, and, unlike solids or traditional shear-deformable shells, do not suffer from transverse-shear locking in the limit of vanishing thickness. This, in combination with higher-order accurate and smooth representation of the shell midsurface displacement field, allows us to adopt relatively coarse in-plane discretizations without sacrificing solution accuracy. Furthermore, the thin-shell formulation employed does not use rotational degrees of freedom, which gives additional efficiency benefits relative to more standard shell formulations.

For Part II, see [the authors, ibid. 62, No. 3, 587-601 (2018; Zbl 1448.74067)].

For Part II, see [the authors, ibid. 62, No. 3, 587-601 (2018; Zbl 1448.74067)].

##### MSC:

74K25 | Shells |

74A40 | Random materials and composite materials |

74A45 | Theories of fracture and damage |

74S22 | Isogeometric methods applied to problems in solid mechanics |

74-10 | Mathematical modeling or simulation for problems pertaining to mechanics of deformable solids |

##### Keywords:

composite laminates; Kirchhoff-Love shells; isogeometric analysis (IGA); NURBS; cohesive interface; impact damage
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\textit{Y. Bazilevs} et al., Comput. Mech. 62, No. 3, 563--585 (2018; Zbl 1446.74163)

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