Discrete data-adaptive approximation of hyperelastic energy functions

Wiesheier S, Mergheim J, Steinmann P (2023)

Publication Type: Journal article

Publication year: 2023


Book Volume: 416

Article Number: 116366

DOI: 10.1016/j.cma.2023.116366


Phenomenological constitutive modeling is prone to uncertainty and results in loss of information as data coming from experiments are not used directly in calculations. Data-driven approaches are a promising alternative to constitutive modeling. We present a new data-adaptive approach to model hyperelastic rubber-like materials at finite strains. Our proposed modeling procedure combines the advantages of phenomenological hyperelasticity with the data-driven paradigm of directly including experimental data in calculations. We suggest formulating a finite-element-like approximation of the strain energy function as a sum of basis functions expanded over a set of invariants multiplied by unknown parameters. The parameters are determined by an optimization algorithm to match measured experimental data (full-field displacements and global reaction forces) in a least-squares sense. We verify our approach and show that computation times are similar compared to those of phenomenological models. By numerical examples, we demonstrate the ability of our approach to re-identify O(10) parameters.

Authors with CRIS profile

How to cite


Wiesheier, S., Mergheim, J., & Steinmann, P. (2023). Discrete data-adaptive approximation of hyperelastic energy functions. Computer Methods in Applied Mechanics and Engineering, 416. https://doi.org/10.1016/j.cma.2023.116366


Wiesheier, Simon, Julia Mergheim, and Paul Steinmann. "Discrete data-adaptive approximation of hyperelastic energy functions." Computer Methods in Applied Mechanics and Engineering 416 (2023).

BibTeX: Download