Interaction-Based Deep Material Networks for stochastic and damaging composite materials

As a surrogate model of the meso-scale homogenised response for non-linear multi-scale simulations, the Deep Material Network (DMN) incorporates analytical homogenisation solutions and material constitutive relations into a neural network model yielding mechanistic building blocks [1]. In order to improve its training efficiency, the DMN was reformulated in [2] from the interaction view-point [2]. Since it is thermodynamically consistent, the IB-DMN can extrapolate the response to different micro-scale material behaviours and loading histories, limiting the size of the data set that is needed for its training. In most of the cases, only the elastic meso-scale homogenised response is required for the training.
In the present work, the IB-DMN parameters are first redefined by decoupling the phase volume fraction from the topological interaction parameters, leading to a IB-DMN that can handle arbitrary phase volume fraction. Then, the architecture of the interactions is modified in order to study its effect on the accuracy of the IB-DMN predictions when the phases exhibit a damage process. Besides, a training strategy relying on a non-linear response exhibiting softening is considered in order to improve its accuracy.

[1] Liu Z., Wu C., Koishi M. A deep material network for multiscale topology learning and accelerated nonlinear modelling of heterogeneous materials, Computer Methods in Applied Mechanics and Engineering, Vol. 345, pp. 1138–1168, 2019.
[2] Nguyen V.D., Noels L. Interaction-based material network: A general framework for (porous) microstructured materials, Computer Methods in Applied Mechanics and Engineering, Vol. 389, pp. 114300, 2022.