Towards identification of material parameters of fibre-reinforced polymers through digital volume correlation and micro-mechanical simulations with FEniCSx.
Fibre-reinforced polymers (FRP) have a good balance between strength, toughness, weight, corrosion resistance, formability and price. They are used in vehicles, wind turbines, buildings and other applications¹. Currently, their weight-saving advantage is partly mitigated by a lack of confidence in the prediction of their mechanical behaviour². This can be improved with the use of virtual testing frameworks, which would facilitate simulations of hierarchical FRP architectures at different scale-lengths. However, such frameworks rely on the understanding of the materials’ micromechanics³. Thus, the goal here is to improve the accuracy of the models by advancing characterisation.
The required identification of constitutive parameters in this process⁴ is frequently based on inverse simulations using experimental results to construct an objective function. The progress in image analysis now allows such a function to be linked to full fields of deformation from digital volume correlation (DVC) of micro- and nano X-ray tomography. This information can then be used to adjust the parameters of micro-mechanical models by computer-based simulations⁵,⁶. Ultimately, a full field of deformation from DVC and finite element analysis would be compared to determine in-situ parameters of micro-mechanical models of FRP.
To study the feasibility of the approach, optimisation based on genetic algorithms and gradient-descent is applied on synthetic FRP microstructures to find the parameters of a softening model⁸ for the polymer matrix. The in-house modelling of the constitutive behaviour is based on the NewFrac, dolfinx_materials and fenics-constitutive projects⁸–¹⁰. FEniCSx 0.8.x¹¹–¹³ is used to generate the target deformation, and SciPy provides the optimisation framework that drives FEniCSx simulations to seek for the optimal parameters. The results show that the combination of full-field DVC and simulations provides a mean for parameter identification of in-situ properties of FRP.
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