Viscoelastic Constitutive Artificial Neural Networks (vCANNs) $-$ a framework for data-driven anisotropic nonlinear finite viscoelasticity
This work addresses the challenge of predicting complex material behavior for applications in engineering and biomechanics, though it appears incremental as it builds on generalized Maxwell models with neural network enhancements.
The authors tackled the problem of accurately modeling nonlinear viscoelastic behavior in materials like polymers and biological tissues, which existing models fail to capture, and demonstrated that their vCANNs framework can learn and represent this behavior accurately and efficiently across multiple materials and loading conditions.
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.