This work proposes a physics-informed deep learning (PIDL)-based constitutive
model for investigating the viscoelastic-viscoplastic behavior of short
fiber-reinforced nanoparticle-filled epoxies under various ambient conditions.
The deep-learning model is trained to enforce thermodynamic principles, leading
to a thermodynamically consistent constitutive model. To accomplish this, a
long short-term memory network is combined with a feed-forward neural network
to predict internal variables required for characterizing the internal
dissipation of the nanocomposite materials. In addition, another feed-forward
neural network is used to indicate the free-energy function, which enables
defining the thermodynamic state of the entire system. The PIDL model is
initially developed for the three-dimensional case by generating synthetic data
from a classical constitutive model. The model is then trained by extracting
the data directly from cyclic loading-unloading experimental tests. Numerical
examples show that the PIDL model can accurately predict the mechanical
behavior of epoxy-based nanocomposites for different volume fractions of fibers
and nanoparticles under various hygrothermal conditions.

本文提出了一种基于物理约束的深度学习（PIDL）的本构模型，用于研究不同环境条件下短纤维增强纳米填充环氧的粘弹性 - 粘塑性行为。深度学习模型通过强制施加热力学原理来训练，从而得到一个热力学一致的本构模型。通过将长短期记忆网络与前馈神经网络相结合，预测用于表征纳米复合材料内耗的内部变量。此外，还使用了另一个前馈神经网络来指示自由能函数，从而定义整个系统的热力学状态。PIDL 模型首先针对三维情况进行开发，通过从经典本构模型生成合成数据来训练模型，然后通过从循环加载 - 卸载实验测试中直接提取数据进行训练。数值实例表明，PIDL 模型可以准确预测不同纤维和纳米颗粒体积分数下基于环氧树脂的纳米复合材料在各种湿热条件下的力学行为。