Composite laminates, consisting of bonded layers of different materials, find extensive applications in various industries, including aerospace, automobiles, and shipbuilding sectors due to their exceptional strength-to-body-weight ratio and tailored mechanical properties. Due to different strengths and properties resulting from different fiber directions, the design analysis and optimization of composite laminates requires repetitive numerical simulations to explore various layer materials and stacking sequences.

For such simulations, researchers typically use the renowned finite-element (FE) analysis based on three-dimensional (3D) elasticity theory. However, the large degrees of freedom (DOF) of composite laminates make 3D FE analysis resource-heavy, time-intensive, and impractical for repetitive simulations. Therefore, a numerical technique that is as accurate as FE analysis while being faster and more flexible, is needed.

Addressing these issues, Professor Kyunghoon Lee and Shinseong Kang from the Department of Aerospace Engineering at Pusan National University developed an innovative Lego-like construction and analysis method for composite laminates.

"Inspired by substructuring and reduced order modeling (ROM) techniques, we developed a two-stage, offline-online framework that leverages component-based ROM. Like Lego bricks, our technique allows us to readily change layer materials including fiber angles, the number of layers, and their stacking sequence to build a composite laminate on the fly, enabling rapid yet accurate simulations," explains Prof. Lee.

Their study was published in the International Journal of Mechanical Sciences on June 21, 2024.

In component-based ROM, complex systems are broken down into simpler subsystems that are individually analyzed using ROM. This ROM technique involves developing reduced models with lower DOFs. To achieve this goal, the researchers utilized static condensation (SC) combined with port reduction (PR) and reduced basis element (RBE) methods, leading to PR-SC and PR-SCRBE analysis methods.

The SC method allows the stacking of any number of layers in any sequence as needed, by treating each layer of the composite laminate as a component. Next, the PR method reduces the DOFs of the connected boundaries of layers, accelerating the solution process. Lastly, the RBE method allows rapid and accurate evaluation of intradomain solutions of layers for the changes in layer materials.

This technique operates in two stages: the offline stage and the online stage. In the offline stage, a library of composite layers, parametrically representing various layer materials and fiber angles, is compiled. In the online stage, a composite laminate is constructed on demand by setting up the layer materials, fiber angles, and stacking sequence. This constructed laminate is then analyzed using the PR-SC method, or the PR-SCRBE method if more computational efficiency is required than accuracy.

The researchers demonstrated the technique in a three-point bending test and a tensile test, assessing the accuracy and efficiency of the PR-SC and PR-SCRBE methods. For each example, they used three different composite laminates with different layers.

Results revealed that the PR-SC analysis had negligible accuracy loss compared to the FE analysis while improving speed. On the other hand, PR-SCRBE showed moderate accuracy loss with a much larger improvement in speed. The researchers suggest employing PR-SC for accuracy and PR-SCRBE for efficiency as required.

"By utilizing the proposed technique for virtual testing of composites, we can identify optimal designs while minimizing time and material costs. This technique offers significant potential benefits across various fields. For example, better composites can lead to lighter and stronger airplanes and automobiles with improved fuel economy and reduced pollution.

"Additionally, energy industries can utilize this technique to develop digital twins of assets, enabling real-time monitoring and significantly reducing maintenance costs," remarks a hopeful Prof. Lee, emphasizing the potential applications of this technique.

In conclusion, this innovative technique offers a viable alternative to the cumbersome 3D FE analysis technique for repetitive analysis of composite laminates.

More information: Shinseong Kang et al, Lego-like composite laminate construction and analysis on the fly, International Journal of Mechanical Sciences (2024). DOI: 10.1016/j.ijmecsci.2024.109458