On sparse regression, Lp‐regularization, and automated model discovery

JA McCulloch, SR St. Pierre, K Linka… - International Journal for …, 2024 - Wiley Online Library
Sparse regression and feature extraction are the cornerstones of knowledge discovery from
massive data. Their goal is to discover interpretable and predictive models that provide …

[HTML][HTML] Theory and implementation of inelastic constitutive artificial neural networks

H Holthusen, L Lamm, T Brepols, S Reese… - Computer Methods in …, 2024 - Elsevier
The two fundamental concepts of materials theory, pseudo potentials and the assumption of
a multiplicative decomposition, allow a general description of inelastic material behavior …

[HTML][HTML] I too I2: A new class of hyperelastic isotropic incompressible models based solely on the second invariant

E Kuhl, A Goriely - Journal of the Mechanics and Physics of Solids, 2024 - Elsevier
In contemporary elasticity theory, the strain–energy function predominantly relies on the first
invariant I 1 of the deformation tensor; a practice that has been influenced by models derived …

[HTML][HTML] Neural integration for constitutive equations using small data

F Masi, I Einav - Computer Methods in Applied Mechanics and …, 2024 - Elsevier
Data-driven models based on deep learning algorithms intend to overcome the limitations of
traditional constitutive modelling by directly learning from data. However, the need for …

[HTML][HTML] Automated model discovery for human cardiac tissue: Discovering the best model and parameters

D Martonová, M Peirlinck, K Linka, GA Holzapfel… - Computer Methods in …, 2024 - Elsevier
For more than half a century, scientists have developed mathematical models to understand
the behavior of the human heart. Today, we have dozens of heart tissue models to choose …

Nonlinear consolidation finite element analysis of a layered soft soil foundation under multistage loading based on the continuous drainage boundary

K Ma, Z Gao, J Wang, Y Zhang, M Zong, W Wu… - Computers and …, 2024 - Elsevier
To comprehensively consider the impacts of stratification, residual pore water pressure, soil
nonlinearity, and boundary permeability on consolidation settlement of soft soil foundations …

[HTML][HTML] Best-in-class modeling: A novel strategy to discover constitutive models for soft matter systems

K Linka, E Kuhl - Extreme Mechanics Letters, 2024 - Elsevier
The ability to automatically discover interpretable mathematical models from data could
forever change how we model soft matter systems. For convex discovery problems with a …

[HTML][HTML] Filled Elastomers: Mechanistic and Physics-Driven Modeling and Applications as Smart Materials

W Xian, YS Zhan, A Maiti, AP Saab, Y Li - Polymers, 2024 - mdpi.com
Elastomers are made of chain-like molecules to form networks that can sustain large
deformation. Rubbers are thermosetting elastomers that are obtained from irreversible …

Internal resonance induced nonlinear vibration and acoustic radiation of a hyperelastic cantilever structure immersed in fluid

G Wang, Y Li, Y Qu, F Xie, H Gao - International Journal of Non-Linear …, 2024 - Elsevier
Hyperelastic structures can exhibit peculiar nonlinear vibration and acoustic behavior due to
the existence of geometric and material nonlinearities. In order to comprehend the nonlinear …

Democratizing biomedical simulation through automated model discovery and a universal material subroutine

M Peirlinck, K Linka, JA Hurtado, GA Holzapfel, E Kuhl - bioRxiv, 2023 - biorxiv.org
Personalized computational simulations have emerged as a vital tool to understand the
biomechanical factors of a disease, predict disease progression, and design personalized …