Overcoming the cohesive zone limit in the modelling of composites delamination with TUBA cohesive elements

TL;DR

The paper tackles the mesh-density bottleneck in cohesive-zone modelling of composite delamination, especially for Mode I, by introducing a $C^1$-continuous triangular plate element (TUBA3) and a compatible cohesive element (TUBA3-CE) implemented as Abaqus user elements. The approach leverages Kirchhoff plate theory continuity and sub-triangle support to enable coarse meshes while preserving global delamination behavior, and it provides analytical and sub-domain integration strategies to accelerate computations. Validation on a DCB benchmark shows that elements up to $11\times$ CZL yield critical-load predictions within a few percent of a reference model, with CPU-time reductions of about 94% compared to standard cohesive elements. Local stress and damage fields near the cohesive zone are less accurate due to the plate-only kinematics, indicating a trade-off between global accuracy and computational efficiency, and motivating future work toward Kirchhoff plate formulations without curvature DOFs for improved local field predictions.

Abstract

The wide adoption of composite structures in the aerospace industry requires reliable numerical methods to account for the effects of various damage mechanisms, including delamination. Cohesive elements are a versatile and physically representative way of modelling delamination. However, using their standard form which conforms to solid substrate elements, multiple elements are required in the narrow cohesive zone, thereby requiring an excessively fine mesh and hindering the applicability in practical scenarios. The present work focuses on the implementation and testing of triangular thin plate substrate elements and compatible cohesive elements, which satisfy C1-continuity in the domain. The improved regularity meets the continuity requirement coming from the Kirchhoff Plate Theory and the triangular shape allows for conformity to complex geometries. The overall model is validated for mode I delamination, the case with the smallest cohesive zone. Very accurate predictions of the limit load and crack propagation phase are achieved, using elements as large as 11 times the cohesive zone.

Figures (25)

• Figure 1: Stress and damage profiles near the crack tip of a 2D DCB specimen, obtained with Abaqus cohesive contact analysis. The element length is 0.0125 mm in the propagation region.
• Figure 2: DCB load-displacement curves obtained with structural CEs RussoChen2019Jarticle. Standard CE results, analytical solution and experimental data are also reported for comparison.
• Figure 3: Area coordinates of a point in the generic triangle.
• Figure 4: Argyris triangle (TUBA6).
• Figure 5: Bell triangle (TUBA3).