Journal article 186 views 63 downloads
Stretch-based hyperelastic electromechanical constitutive metamodels via gradient enhanced Gaussian predictors using hierarchical structure discovery
,
Jesús Martínez-Frutos ,
Roman Poya ,
Johann Sienz ,
Antonio Gil
Computer Methods in Applied Mechanics and Engineering, Volume: 448, Issue: Part A, Start page: 118349
Swansea University Authors:
Nathan Ellmer, Johann Sienz , Antonio Gil
-
PDF | Version of Record
© 2025 The Author(s). This is an open access article distributed under the terms of the Creative Commons CC-BY license.
Download (13.98MB)
DOI (Published version): 10.1016/j.cma.2025.118349
Abstract
This paper introduces a new approach to developing electromechanical constitutive metamodels via the use of Gradient Enhanced Gaussian Predictors (Kriging). The formulation uses principal stretches for the isotropic mechanics, invariants for the electrostatics and coupling terms, and accounts for an...
| Published in: | Computer Methods in Applied Mechanics and Engineering |
|---|---|
| ISSN: | 0045-7825 1879-2138 |
| Published: |
Elsevier BV
2026
|
| Online Access: |
Check full text
|
| URI: | https://cronfa.swan.ac.uk/Record/cronfa70361 |
| Abstract: |
This paper introduces a new approach to developing electromechanical constitutive metamodels via the use of Gradient Enhanced Gaussian Predictors (Kriging). The formulation uses principal stretches for the isotropic mechanics, invariants for the electrostatics and coupling terms, and accounts for anisotropy through the relevant inclusion of anisotropic invariants associated with a respective symmetry integrity basis. Three novelties are presented in this paper. The first is the use of orthogonal projections to identify the most appropriate set of inputs - related to material anisotropy - for use in the metamodel. By projecting the stress and electric field data into several derivative bases - defined for each anisotropic class - and then reconstructing the quantities, the errors in reconstruction can be assessed thus inferring the most appropriate class of anisotropy. Furthermore, the procedure forms a pre-processing stage and is particularly useful when an underlying model is completely unknown as seen when modelling Relative Volume Elements. The second novelty arises from the use of a hybrid formulation, namely the principal stretches for isotropic mechanics and the electromechanical anisotropic invariants. This is beneficial during the projection procedure in reducing the cases where the projection matrix becomes singular but requires careful development of the correlation function to maintain physical symmetry conditions. Thirdly, the electromechanical metamodels are calibrated upon the concentric styled data before being integrated within a Finite Element framework and tested upon a range of challenging simulations including bending actuators with induced torsion, frilling due to bending with selected electrode placement, as well as buckling plates tested with three rank-one laminate materials with increasing levels of anisotropy due to physical contrasts. The successful calibration and implementation of the metamodels can be witnessed amongst the wide range of presented numerical examples. |
|---|---|
| Keywords: |
Gradient Kriging; Constitutive modelling; Principal stretches; Electromechanics; Anisotropy |
| College: |
Faculty of Science and Engineering |
| Funders: |
N. Ellmer and A. J. Gil wish to acknowledge the financial support provided by the Defence, science and technology laboratory (Dstl). Additionally, A. J. Gil acknowledges the support of The Luverhulme Trust through a Leverhulme Fellowship. R. Ortigosa and J. Martínez-Frutos acknowledge the support of grant PID2022-141957OA-C22 funded by MICIU/AEI/10.13039/501100011033 and by “RDF A way of making Europe”. |
| Issue: |
Part A |
| Start Page: |
118349 |