Computational Mechanics

, Volume 62, Issue 3, pp 563–585 | Cite as

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

  • Y. BazilevsEmail author
  • M. S. Pigazzini
  • A. Ellison
  • H. Kim
Original Paper


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.


Composite laminates Kirchhoff–Love shells Isogeometric analysis (IGA) NURBS Cohesive interface Impact damage 



This work was supported by NASA Advanced Composites Project No. 15-ACP1-0021. We thank F. Leone, C, Rose, and C. Davila from NASA Langley Research Center for their valuable comments and suggestions.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Y. Bazilevs
    • 1
    Email author
  • M. S. Pigazzini
    • 1
  • A. Ellison
    • 1
  • H. Kim
    • 1
  1. 1.Department of Structural EngineeringUniversity of California, San DiegoLa JollaUSA

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