A Mechanics-Informed Neural Network Framework for Data-Driven Nonlinear Viscoelasticity

A mechanics-informed, data-driven framework for learning the constitutive law of a complex viscoelastic material from strain-stress data is proposed. It features a robust and accurate method for training a regression-based surrogate model capable of capturing a highly nonlinear and time-dependent material behavior while preserving principles that are important to solid mechanics. The proposed framework forces desirable mathematical properties on the ANN architecture, to guarantee the strong satisfaction of the laws of mechanics and thermodynamics. It extends a previous mechanics-informed framework, developed for the nonlinear elastic setting, to account for dependence of the stress on the entire strain history in general. An internal-variable three potential approach to viscoelasticity is considered, and it is adapted to an ANN framework in which the ANNs are taught to satisfy the second law of thermodynamics, stability conditions, consistency (preservation of rigid body modes), and the recovery of elastic limits. Finally, the performance of the proposed framework for data-driven modeling is illustrated on the computational homogenization of a viscoelastic woven fabric material.