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.
The Monte Carlo method has been widely used for the estimation of uncertainties in mechanical engineering design. However, while extremely flexible, this method remains impractical in terms of computational time and scalability. To bypass these limitations, other more efficient approaches such as the spectral stochastic finite element method (SSFEM) or the collocation method have been proposed. SSFEM, pioneered by Spanos and Ghanem [1], provides accurate statistics of the output, has the advantage of being samplingindependent and can be modular in terms of operations, albeit code intrusive. While linear elasticity has been extensively covered in the literature, the application of SSFEM to nonlinear mechanical behaviour remains relatively unexplored [2]. Our preliminary work focusses on a seamless and efficient modular framework avoiding the need to know a priori the material law. In particular, we i) benchmark our proposed framework with an optimised house-code and ii) make use of a hybrid formulation to capture discontinuous behaviours. The method is finally illustrated with a few applications.
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