Theory and implementation of inelastic Constitutive Artificial Neural Networks

Abstract

Nature has always been our inspiration in the research, design and development of materials and has driven us to gain a deep understanding of the mechanisms that characterize anisotropy and inelastic behavior. All this knowledge has been accumulated in the principles of thermodynamics. Deduced from these principles, the multiplicative decomposition combined with pseudo potentials are powerful and universal concepts. Simultaneously, the tremendous increase in computational performance enabled us to investigate and rethink our history-dependent material models to make the most of our predictions. Today, we have reached a point where materials and their models are becoming increasingly sophisticated. This raises the question: How do we find the best model that includes all inelastic effects to explain our complex data? Constitutive Artificial Neural Networks (CANN) may answer this question. Here, we extend the CANNs to inelastic materials (iCANN). Rigorous considerations of objectivity, rigid motion of the reference configuration, multiplicative decomposition and its inherent non-uniqueness, restrictions of energy and pseudo potential, and consistent evolution guide us towards the architecture of the iCANN satisfying thermodynamics per design. We combine feed-forward networks of the free energy and pseudo potential with a recurrent neural network approach to take time dependencies into account. We demonstrate that the iCANN is capable of autonomously discovering models for artificially generated data, the response of polymers for cyclic loading and the relaxation behavior of muscle data. As the design of the network is not limited to visco-elasticity, our vision is that the iCANN will reveal to us new ways to find the various inelastic phenomena hidden in the data and to understand their interaction. Our source code, data, and examples are available at doi.org/10.5281/zenodo.10066805

54 pages, 14 figures, 14 tables

References in corpus (7)

• A new family of Constitutive Artificial Neural Networks towards automated model discovery
• Automated discovery of generalized standard material models with EUCLID
• Discovering plasticity models without stress data
• Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domains
• Evolution TANN and the identification of internal variables and evolution equations in solid mechanics
• Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations
• On sparse regression, Lp-regularization, and automated model discovery

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