Predicting the Flexural Strength of Bio-Based Composites

How can we accelerate the development of bio-based composites on base of three ingredients without experimentally testing every formulation? 

Bio-based composites offer a promising and sustainable alternative to conventional engineering materials, with the potential to reduce environmental impact while maintaining high mechanical performance. However, manufacturing and testing are resource-intensive, making it impractical to experimentally explore all-natural filler–fibre-resin combinations and ratios. Predictive modelling is therefore essential, although natural materials present challenges due to batch-to-batch variability, heterogeneous chemical compositions, complex morphologies, and matrix–filler–fibre interactions. Micromechanical models provide a physically interpretable link between constituent properties, microstructure, and composite behaviour, but simplified assumptions can limit their accuracy. Data-driven models can capture complex relationships and variability represented in their training data, yet often require substantial datasets. Combining these approaches in a grey-box framework can improve predictive accuracy and data efficiency while retaining physical interpretability, reducing the experimental effort required for material optimisation. To explore the foundations of such a framework, Alex Pravin, a Materials Science & Engineering master's student at TU Delft, investigated two independent modelling routes for predicting the flexural strength of these composites. This research is part of the CBE-Ssuchy-Next project. This project has received funding from the Circular Bio-based Europe Joint Undertaking (CBE JU) . The JU receives support from the European Union Horizon Europe research and innovation programme and the Bio Based Industries Consortium.

Route 1: Classical micromechanics

The first route evaluated classical micromechanical models (Rule of Mixtures, Halpin-Tsai, Mori-Tanaka, and Lewis-Nielsen) against experimental flexural data. However, these models proved unreliable predictors when constrained to independently measured filler properties: an inverse Lewis-Nielsen fitting procedure showed that the filler stiffness required to match composite behaviour differs substantially from the intrinsic filler modulus measured via nanoindentation. This route mapped out the physical boundaries and limitations of classical micromechanics for highly filled morphology-rich bio-based systems. These findings highlight the limitations of the models tested for highly filled bio-based systems with complex filler morphologies, while leaving open the need to identify and evaluate alternative micromechanical approaches better suited to these materials.

Route 2: Interpretable data-driven modelling

The second route developed Sparse Symbolic Regression (SISSO) models which is a symbolic regression method that identifies compact mathematical equations from a large set of candidate combinations of input features. It produces interpretable models linking material descriptors like filler volume fraction, porosity, density, and particle size to target properties, such as flexural strength. The model was initially used for two different fillers independently. A weighted similarity framework was then introduced to adapt the equations to new fillers, with Bayesian optimisation used to determine the similarity weights; the resulting blended predictions were validated. The main aim is to see the accuracy of the model prediction if it is given a totally new filler with known material descriptors.

The results show that simple, physically meaningful descriptors yield stable, interpretable SISSO equations. The similarity-weighted blending of these equations gives reasonable first-order predictions for new fillers, though performance remains moderate. This motivates extending the framework to a three-way formulation, in which the new filler is treated as an independent reference filler rather than an interpolated point between well known fillers, an extension outlined as future work but not implemented or validated in this project.

What comes next?

The next step is to expand the dataset with more formulations, additional natural fillers, fibres, and different resin systems. Combining this broader experimental evidence with relevant material and processing descriptors could help the models capture a wider range of composite behaviour. Validation on unseen formulations will be essential to establish whether this translates into more reliable predictions and more efficient material screening. Furthermore, identifying and validating micromechanical models that can supplement the experimental datasets with physics-based predictions and descriptors and integrating this in the SISSO could improve data efficiency and predictions. The outcome will be an interpretable, data-efficient hybrid micromechanical-SISSO-based prediction engine capable of accelerating material screening for sustainable composite development, reducing experimental cost, and supporting industrial adoption of bio-based fillers.