Polyconvex inelastic constitutive artificial neural networks

PAMM, vol. 24

Abstract

Abstract The characterization of the material behavior of inelastic materials requires a high degree of expert knowledge to identify and constitutively describe the material response. In addition, specific models are usually pre‐selected in the course of characterization and only the best parameters for these specific models are determined, but therefore not necessarily the best models. Unfortunately, a more general description of these pre‐selected models results in an increased effort during characterization, which is barely practicable by hand. This is where machine learning algorithms may help us. To get the best of both worlds, powerful machine learning and sound thermodynamic considerations, inelastic Constitutive Artificial Neural Networks (iCANNs) discover generic formulations of the Helmholtz free energy and pseudo potential. Constitutive relations guide us towards thermodynamically consistent descriptions of stresses and inelastic strains; a concept that is applicable to a wide range of inelastic phenomena from viscoelasticity, elastoplasticity, phase transformations to growth and remodeling of living tissues. Here, we equip the original iCANN framework to guarantee polyconvexity a priori, which ensures at least one minimizing deformation. We investigate the ability of our iCANN to identify the material behavior of a viscoelastic polymer at different stretch levels and strain rates. We made our source code, data, and example accessible to the public at https://doi.org/10.5281/zenodo.11084354 .

Authors 5

1. Hagen Holthusen corresponding Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Aachen Germany

2. Lukas Lamm Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Aachen Germany

3. Tim Brepols Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Aachen Germany

4. Stefanie Reese Aachen Institute of Applied Mechanics

   University of Siegen · RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Aachen Germany

   University of Siegen Siegen Germany

5. Ellen Kuhl

   Stanford University

   Affiliation as printed

   Department of Mechanical Engineering Stanford University Stanford California USA