Deep Material Network (DMN) has recently emerged as a data-driven surrogate model for heterogeneous materials. Given a particular microstructural morphology, the effective linear and nonlinear behaviors can be successfully approximated by such physics-based neural-network like architecture. In this work, a novel micromechanics-informed parametric DMN (MIpDMN) architecture is proposed for multiscale materials with a varying microstructure characterized by several parameters. A single-layer feedforward neural network is used to account for the dependence of DMN fitting parameters on the microstructural ones. Micromechanical constraints are prescribed both on the architecture and the outputs of this new neural network. The proposed MIpDMN is also recast in a multiple physics setting, where physical properties other than the mechanical ones can also be predicted. In the numerical simulations conducted on three parameterized microstructures, MIpDMN demonstrates satisfying generalization capabilities when morphology varies. The effective behaviors of such parametric multiscale materials can thus be predicted and encoded by MIpDMN with high accuracy and efficiency.

翻译：深度材料网络（DMN）近期作为一种数据驱动的异质材料替代模型崭露头角。针对特定微观结构形态，这种基于物理的类神经网络架构可成功逼近等效线性和非线性行为。本文提出一种新型的基于微观力学的参数化DMN（MIpDMN）架构，适用于由多个参数表征的微观结构变化的跨尺度材料。采用单层前馈神经网络来刻画DMN拟合参数对微观结构参数的依赖性。该新型神经网络的结构与输出均受到微观力学约束的限定。所提出的MIpDMN还可重构为多物理场模式，除力学性能外，亦可预测其他物理属性。在三种参数化微观结构的数值模拟中，MIpDMN在形态变化时展现出令人满意的泛化能力。此类参数化跨尺度材料的等效行为可通过MIpDMN实现高精度、高效率的预测与编码。