A Bayesian multiscale CNN framework to predict local stress fields in structures with microscale features

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.

Deep learning prediction of stress fields in additively manufactured metals with intricate defect networks

“…Indeed, we found that the U-Net made erroneous stress predictions near the image boundary when trained on smaller images, or on large images without padding. Similar errors appear in related work such as [30], where the receptive field of 104 × 104 𝑝𝑥 was larger than the image size of 32 × 32 𝑝𝑥 and images were not appropriately padded; indeed, nonphysical stress predictions were visible near the image boundary in figures included in [31]. Other related work has shown that inappropriate image padding can worsen predictions of mechanical response [42].…”

“…Their StressNet model applied a series of convolutional filters to images of the beam geometry, and predicted the Von Mises stress for each pixel of the image; these values were compared to the stress on the same model computed by FE. This architecture has recently been extended to predict the mechanical response of fiber-reinforced composites at the microscale [29] and mesoscale [30], and also to predict stress concentrations around microscale pores in a multiscale FE model [31]. Alternative CNN architectures such as generative adversarial network [32] or image colorization networks [33] used to predict stress from microstructural images with varying levels of success.…”

A Graph-based probabilistic geometric deep learning framework with online physics-based corrections to predict the criticality of defects in porous materials

“…The multiscale framework that we use here is a direct extension of our previous work [Krokos et al, 2021]. As mentioned in section [2.2], the examples that we show in this work are dedicated to linear elasticity for porous media made of a homogeneous matrix with a random distribution of microscale features that are modelled as spherical voids.…”

“…Our paper addresses these two points by extending our previous work [Krokos et al, 2021], while adding two novel algorithmic elements. First, we manage to tackle 3D problems by using geometric learning where instead of voxelised images we learn directly from the mesh that is used to perform the FE simulations.…”

“…If that assumption does not hold, for instance due to fast macroscale gradients induced by sharp macroscale features, then concurrent scale coupling methods are employed that are usually more expensive and intrusive compared to RVE based methods. In these techniques the results of homogenisation are applied to the boundary of regions of interest for concurrent microscale corrections to be performed [Raghavan and Ghosh, 2004;Oden et al, 2006;Kerfriden et al, 2009;Hesthaven et al, 2015;Paladim et al, 2016;Krokos et al, 2021] which may be performed in a purely downward approach [Oden et al, 1999], or with 2-way coupling [Gendre et al, 2009] In this work we propose a Neural Network (NN) based concurrent scale coupling method to tackle 3D multiscale problems and specifically we focus on porous media with no separation of scales. Neural Networks (NNs) have been successfully employed in solving engineering problems by reproducing the output of simulation codes in a variety of fields like fluid dynamics [Lye et al, 2020;Raissi et al, 2020], solid mechanics [Nie et al, 2019;Jiang et al, 2020;Deshpande et al, 2021] and computational biology [Senior et al, 2019[Senior et al, , 2020.…”