Abstract
Multiscale computational modelling is challenging due to the high computational cost of direct numerical simulation by finite elements. To address this issue, concurrent multiscale methods use the solution of cheaper macroscale surrogates as boundary conditions to microscale sliding windows. The microscale problems remain a numerically challenging operation both in terms of implementation and cost. In this work we propose to replace the local microscale solution by an Encoder-Decoder Convolutional Neural Network that will generate fine-scale stress corrections to coarse predictions around unresolved microscale features, without prior parametrisation of local microscale problems. We deploy a Bayesian approach providing credible intervals to evaluate the uncertainty of the predictions, which is then used to investigate the merits of a selective learning framework. We will demonstrate the capability of the approach to predict equivalent stress fields in porous structures using linearised and finite strain elasticity theories.
Highlights
Multi-scale structural analyses are prominent in mechanical and bio-mechanical engineering
Full finite element analysis (FEA) for stress prediction is usually prohibitively expensive for those structures, as the finite element mesh needs to be very dense to capture the effect of the fine scale features
Multiscale computational modelling can be approached in two ways. Homogenisation, be it through the principles of micromechanics [59] or asymptotic expansions [48], performs all microscale computations over a representative volume element (RVE), assuming that the macroscale displacement gradients do not vary over the material sample
Summary
Multi-scale structural analyses are prominent in mechanical and bio-mechanical engineering (e.g. composite materials such as carbon-reinforced polymers or concrete, porous materials such as bones). Multiscale computational modelling can be approached in two ways Homogenisation, be it through the principles of micromechanics [59] or asymptotic expansions [48], performs all microscale computations over a representative volume element (RVE), assuming that the macroscale displacement gradients do not vary over the material sample. The results of homogenisation are applied to the boundary of regions of interest for concurrent microscale corrections to be performed [15,24,39,40,42] These approaches are computationally more expensive and practically more intrusive than methods based on RVEs. These approaches are computationally more expensive and practically more intrusive than methods based on RVEs Their deployment is necessary when predicting the microscale response to fast macroscale gradients, for instance due to sharp macroscale geometrical features. The proposed method belongs to this latter class of methods
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