Non-local damage modeling for composite laminates: application to isogeometric analysis for impact simulations

High-fidelity progressive damage simulations of composite materials are important for advancements in damage tolerant design. We recently proposed a novel modeling approach for damage analysis of composite laminates, in which multi-layer structures are represented as individual plies connected through zero-Thickness cohesive interfaces. The model is developed in the framework of Isogeometric Analysis (IGA). By using Non-Uniform Rational B-Spline (NURBS) basis functions for representing geometries and discretizing the displacement field, IGA allows for a more direct connection between numerical simulation and CAD software. In addition, compared to traditional polynomial basis functions, NURBS functions allow for better representation of geometries and higher order inter-element continuity properties. The computational efficiency of the proposed modeling approach stems from the adoption of Kirchhoff-Love shell elements for the modeling of individual lamina. Intralaminar damage is introduced in the framework of continuum damage mechanics, in which a strain-softening damage model drives the degradation of material elastic properties. However, the use of local strain measures, in combination with strainsoftening degradation models, may lead to damage localization problems. These cause the governing equations to become ill-posed and their approximate solution to be highly mesh-sensitive. Our work aims to re-establish the objectivity with respect to the adopted discretization. We extend our analysis framework by introducing a smoothed strain field to re-place the local strain measures used in the damage model. Our approach builds on the Gradient-Enhanced Damage (GED) model and is specialized for the Kirchhoff-Love shell structural model. The smoothed strain field is obtained by solving an additional set of partial differential equations on each ply of the composite laminate. The GED model can be applied to smooth tensor-valued quantities, such as strains, on generic-shaped geometries in the three-dimensional space, including complex and curved aerospace structures modeled by means of shell elements. In this work, we propose numerical examples in order to illustrate the validity of the GED model.