  The constitutive behavior of polymeric materials is often modeled by finite
linear viscoelastic (FLV) or quasi-linear viscoelastic (QLV) models. These
popular models are simplifications that typically cannot accurately capture the
nonlinear viscoelastic behavior of materials. For example, the success of
attempts to capture strain rate-dependent behavior has been limited so far. To
overcome this problem, we introduce viscoelastic Constitutive Artificial Neural
Networks (vCANNs), a novel physics-informed machine learning framework for
anisotropic nonlinear viscoelasticity at finite strains. vCANNs rely on the
concept of generalized Maxwell models enhanced with nonlinear strain
(rate)-dependent properties represented by neural networks. The flexibility of
vCANNs enables them to automatically identify accurate and sparse constitutive
models of a broad range of materials. To test vCANNs, we trained them on
stress-strain data from Polyvinyl Butyral, the electro-active polymers VHB 4910
and 4905, and a biological tissue, the rectus abdominis muscle. Different
loading conditions were considered, including relaxation tests, cyclic
tension-compression tests, and blast loads. We demonstrate that vCANNs can
learn to capture the behavior of all these materials accurately and
computationally efficiently without human guidance.
