Orientation-aware interaction-based deep material network in polycrystalline materials modeling

TL;DR

This work proposes the orientation-aware interaction-based deep material network (ODMN), which incorporates an orientation-aware mechanism and an interaction mechanism grounded in the Hill-Mandel principle that accurately predicts both mechanical responses and texture evolution under complex plastic deformation.

Abstract

Multiscale simulations are indispensable for connecting microstructural features to the macroscopic behavior of polycrystalline materials, but their high computational demands limit their practicality. Deep material networks (DMNs) have been proposed as efficient surrogate models, yet they fall short of capturing texture evolution. To address this limitation, we propose the orientation-aware interaction-based deep material network (ODMN), which incorporates an orientation-aware mechanism and an interaction mechanism grounded in the Hill-Mandel principle. The orientation-aware mechanism learns the crystallographic textures, while the interaction mechanism captures stress-equilibrium directions among representative volume element (RVE) subregions, offering insight into internal microstructural mechanics. Notably, ODMN requires only linear elastic data for training yet generalizes effectively to complex nonlinear and anisotropic responses. Our results show that ODMN accurately predicts both mechanical responses and texture evolution under complex plastic deformation, thus expanding the applicability of DMNs to polycrystalline materials. By balancing computational efficiency with predictive fidelity, ODMN provides a robust framework for multiscale simulations of polycrystalline materials.

Figures (20)

• Figure 1: Schematic of the ODMN architecture. The material network is structured as a binary tree of depth $N$. The green area represents the $2^N$ material nodes $\mathcal{M}^{i}$, each responsible for learning the phase volume fractions and crystallographic orientation distributions. The purple circles denote the interaction mechanisms that enforce the stress-equilibrium directions $\vec{\mathbf{N}}^{l}_{p}$ between material nodes. Here, $l$ and $p$ indicate the depth and position of a tree node within the material network, respectively.
• Figure 2: Schematic of the ODMN homogenization process. For a two-phase RVE, each material node $\mathcal{M}^{i}$ is assigned a stiffness matrix $\mathbb{C}^{i}$ corresponding to its constituent phase ($\mathbb{C}^{p1}$ or $\mathbb{C}^{p2}$). These stiffness matrices are rotated to account for crystallographic orientations, yielding $\mathbb{C}_{R}^{i}$. The rotated matrices are then recursively aggregated to compute the homogenized stiffness matrix ($\bar{\mathbb{C}}^{\text{ODMN}}$).
• Figure 3: Schematic of the ODMN online prediction process, including downscaling the macroscopic deformation gradient $\bar{\mathbf{F}}$, evaluating local material law, resolving the nonlinear system, and upscaling to compute the homogenized stress $\bar{\mathbf{P}}$ and tangent stiffness $\bar{\mathbb{L}}$.
• Figure 4: Schematic of (a) crystallographic orientation initialization at $t=0$ and (b) texture evolution during deformation ($t>0$) with updates via polar decomposition and ODF reconstruction.
• Figure 5: The geometry of the single-phase polycrystalline RVE used in simulations. (a) RVE with random crystallographic texture. (b) RVE with preferred orientation.