Simulation and optimization of composite materials and products
Composites imitate nature’s design to achieve outstanding properties as a result of a complex structural hierarchy. However, this complexity presents the engineer with a huge design and optimization challenge. How can such a complex, multi-disciplinary problem be tackled in an efficient and effective manner?
There are many stages in the simulation and design process of a composite based product, involving models of the composite materials and micro-mechanics, ply and laminate structures. The success of property optimization requires that the underlying models are of good quality, and that the inherent complexity of composite systems is managed and ideally reduced, focusing on the most important parameters. Hence we can identify the following key steps:
- Reducing model complexity by identifying key parameters with correlation and sensitivity analysis.
- Fitting the model to experimental data by “reverse engineering”.
- Optimizing composite and product properties.
In reality, these steps are closely linked, and run to some extent in parallel as shown in the figure below.
Reducing complexity: correlation and sensitivity analysis
Composite models typically involve a very large number of parameters that could be varied. The aim is to focus on parameters with the strongest influence on the response functions of interest. For example, the case of CFRP composites model calibration involves 23 input and 9 different response goals, requiring an extensive range of experimental test data. An exploration of this large space with a Design of Experiment procedure showed up correlations between some of the response goals, and identified the least significant input variables, enabling very significant reduction in complexity. Moreover this meant a reduction in the experimental tests needed to characterize the material model from four to just two.
Similarly, a model for the impact resistance of laminate composite plate could be reduced in complexity following a sensitivity analysis. Specifically, the shear stress parameter in the material model was found to have basically no influence on the ability of the model to reproduce impact damage.
In the reverse (or inverse) engineering step, the remaining input parameters are fit to test data representing the un-correlated response functions identified in the correlation analysis. In the case of virtual prototyping for impact resistance applications such as crash helmets, the composite laminate model parameters were determined by matching experimental and numerical response curves. The latter example demonstrates that a good match across Maximum Energy and Adsorbed Energy targets could be achieved with a multi-objective optimisation approach, whereas a trial-and-error procedure failed to achieve both targets simultaneously.
In order to enable detailed computational studies of composite wing structures, a reliable 3D structural model needs to be identified. In particular, the models should be validated in both structural and aero-elastic responses. The challenge of missing parameters is overcome by reverse engineering based on a multi-objective optimization method driving the FEM solver. It allows the parameter values for in this case the thickness of the honeycomb and fibreglass layers to be determined so as to minimise the deviations of the different response functions from experiment.
Once models of good quality and manageable complexity are in place, the material and product properties can be optimised. For example, strength improvement to composite T-joints under bending was possible by focussing on the bio-inspired objective of a uniform stress distribution. The resulting optimised ply stacking pattern improved the strength and failure displacement of the T-joint without significantly affecting the global stiffness properties. As this example indicates, in most cases a trade-off between different desired properties needs to be made. Consider the optimization of a blade composite structure, aiming to minimize weight as well as the risk of failure. Integrating the structure and analysis modeling tools into an overarching optimization framework provided decision support data that show the effect of structure variations such as fibre orientation and number of layers on different design objectives, hence supporting rational trade-off decisions. A similar optimzsation loop can be carried out on the microstructural level itself, as was demonstrated in a recent case example for glass fibre/glass bead composites.
A rational design workflow for composite optimization is enabled by integrating simulation with statistical analysis tools, applying a strategy of continuous complexity reduction, reverse engineering and optimisation is applied throughout. Powerful integration and optimization software is essential to realise such rational composite design in an efficient and effective manner.