Stochastic Interaction-Based Deep Material Networks for composites

As a data-driven surrogate of heterogenous material responses, a Deep Material Network (DMN) is built by combining analytical homogenisation solutions and material constitutive relations into a neural network architecture [1]. DMN was reformulated from the interaction view-point as the Interaction-Based DMN (IB-DMN) [2], in order to improve its training performance. In this approach, the interaction learnable parameters characterize the micro-structure organization of the heterogeneous material, while the phase constitutive behaviors are explicitly modelled at some material nodes of the IB-DMN.
After having decoupled the phase volume fraction of composite materials from the topological parameters representing the fiber distribution [3], a stochastic IB-DMN could be developed in which the fiber distribution variability is reflected in the IB-DMN topological parameters. In order to explicitly define the IB-DMN learnable parameters from a micro-structure realization, these topological parameters are predicted from a combination of an encoder and neural network, with a micro-structure image serving as input data. The encoder part of a trained Convolution Neural Network encoder-decoder extracts the feature vectors of the heterogeneous material from the image, and these feature vectors are in turns used as input of a trained feed-forward neural network predicting the topological parameters of the IB-DMN, yielding a “Image to IB-DMN” framework.
The methodology is applied in the context of Unidirectional (UD) composites, for which Stochastic Volumes Elements (SVEs) serve as images of micro-structure realizations.
This project has received funding from the European Union’s Horizon Europe Framework Programme under grant agreement No. 101056682 for the project ‘‘DIgital DEsign strategies to certify and mAnufacture Robust cOmposite sTructures (DIDEAROT)’’. The contents of this publication are the sole responsibility of ULiege and do not necessarily reflect the opinion of the European Union. Neither the European Union nor the granting authority can be held responsible for them.