  In this work, a hybrid physics-based data-driven surrogate model for the
microscale analysis of heterogeneous material is investigated. The proposed
model benefits from the physics-based knowledge contained in the constitutive
models used in the full-order micromodel by embedding them in a neural network.
Following previous developments, this paper extends the applicability of the
physically recurrent neural network (PRNN) by introducing an architecture
suitable for rate-dependent materials in a finite strain framework. In this
model, the homogenized deformation gradient of the micromodel is encoded into a
set of deformation gradients serving as input to the embedded constitutive
models. These constitutive models compute stresses, which are combined in a
decoder to predict the homogenized stress, such that the internal variables of
the history-dependent constitutive models naturally provide physics-based
memory for the network. To demonstrate the capabilities of the surrogate model,
we consider a unidirectional composite micromodel with transversely isotropic
elastic fibers and elasto-viscoplastic matrix material. The extrapolation
properties of the surrogate model trained to replace such micromodel are tested
on loading scenarios unseen during training, ranging from different
strain-rates to cyclic loading and relaxation. Speed-ups of three orders of
magnitude with respect to the runtime of the original micromodel are obtained.
