Machine learning based multiscale calibration of mesoscopic constitutive models for composite materials: application to brain white matter

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A modular pipeline for improving the constitutive modelling of composite materials is proposed.The method is leveraged here for the development of subject-specific spatially-varying brain white matter mechanical properties. For this application, white matter microstructural information is extracted from diffusion magnetic resonance imaging (dMRI) scans, and used to generate hundreds of representative volume elements (RVEs) with randomly distributed fibre properties. By automatically running finite element analyses on these RVEs, stress-strain curves corresponding to multiple RVE-specific loading cases are produced. A mesoscopic constitutive model homogenising the RVEs’ behaviour is then calibrated for each RVE, producing a library of calibrated parameters against each set of RVE microstructural characteristics. Finally, a machine learning layer is implemented to predict the constitutive model parameters directly from any new microstructure. The results show that the methodology can predict calibrated mesoscopic material properties with high accuracy. More generally, the overall framework allows for the efficient simulation of the spatially-varying mechanical behaviour of composite materials when experimentally measured location-specific fibre geometrical characteristics are provided.