Isotropic and anisotropic viscoelasticity at finite deformations: Modeling with neural networks and calibration using experimental data

• Applicant: Dr.-Ing. Karl Alexander Kalina
• Subject Area: Mechanics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 571269372

Many polymers and biological tissues exhibit pronounced rate-dependent behavior and deform strongly under load. In addition, biomaterials or 3D-printed polymers are characterized by anisotropic behavior. These materials therefore require precise models to describe (an)isotropic viscoelasticity at finite deformations. Since the formulation and calibration of the material equations using experimental data for complex material behavior is often a major challenge, there are increasing efforts to apply data-based methods. Approaches that are integrated into a strict physical framework have proven to be particularly promising. In addition, access to an extensive experimental database for training the models represents a considerable challenge. The overarching goal of this project is therefore to develop a consistent data-driven framework for continuum mechanical modeling of the (an)isotropic viscoelastic behavior of soft materials at finite deformations. The focus is on a Physics-Augmented Neural Network (PANN) that combines data-based methods with physical and thermodynamic principles. The model should be applicable for both compressible and incompressible viscoelastic materials. The explicit integration of constitutive conditions into the architecture of the network ensures a physically consistent material description. A particular focus is on the use of experimental data, which can be obtained on flat samples with full-field displacement measurement via Digital Image Correlation (DIC). In combination with the Virtual Fields Method (VFM), this makes it possible to calibrate the PANN with an extensive database that is experimentally accessible and goes beyond standard experiments such as uniaxial tensile tests. The PANN will be calibrated using unsupervised learning so that no stress data is required. The framework is first developed for the isotropic case and then extended to anistotropy. Since areas with incomplete DIC measurements are to be expected in real experiments, an extension of the VFM is to be developed to compensate for these missing data. In addition, an automatic selection of the number of internal variables as well as an identification of anisotropy class and preferred directions will be integrated into the training process to further reduce the manual modeling effort. The methodology will initially be developed and validated over the course of the project using synthetically generated data before being transferred to real experimental data for polymers. In the long term, the framework will enable flexible, physically based and partially automated material modeling.

• DFG Programme: Research Grants