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2026
 Barillas, Max;  Ortigosa, Rogelio;  Martínez-Frutos, Jesús;  Hernández, Joaquín A.;  Parga, S. Ares;  Bonet, Javier;  García-González, Alberto
Hyper-reduced order modeling for nonlinear electromechanics using multi-field POD and ECM for dielectric elastomer actuators Journal Article 
In: Computers & Structures, vol. 330, pp. 108366, 2026, ISSN: 0045-7949.
Abstract | BibTeX | Tags: Electromechanical modeling, Empirical cubature method (ECM), Hyperreduction, Model order reduction (MOR), Multiphysics simulation, PID2022-141957OA-C22, Proper orthogonal decomposition (POD) | Links: 
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@article{BARILLAS2026108366,

title = {Hyper-reduced order modeling for nonlinear electromechanics using multi-field POD and ECM for dielectric elastomer actuators},

author = {Max Barillas and Rogelio Ortigosa and Jesús Martínez-Frutos and Joaquín A. Hernández and S. Ares Parga and Javier Bonet and Alberto García-González},

url = {https://www.sciencedirect.com/science/article/pii/S0045794926002701},

doi = {https://doi.org/10.1016/j.compstruc.2026.108366},

issn = {0045-7949},

year  = {2026},

date = {2026-01-01},

urldate = {2026-01-01},

journal = {Computers & Structures},

volume = {330},

pages = {108366},

abstract = {This paper introduces a projection-based hyper-reduction methodology within the context of nonlinear electromechanics, specifically tailored for the simulation of dielectric elastomer actuators (DEAs). While high-fidelity finite element (FE) models are robust in capturing complex coupled multiphysics responses (in this case, coupling the quasi-static electric and hyperelastic mechanics responses), their high computational cost often renders them impractical for multi-query engineering problems such as material selection or optimal control. To overcome this limitation, we present a framework that combines a multi-field Proper Orthogonal Decomposition (POD) with the Empirical Cubature Method (ECM). This integration constitutes theone of the first applications of hyper-reduced order modeling (HROM) to handle the high-dimensional nonlinearities inherent in large-deformation electrical-mechanical coupling. A key advantage of this methodology is its ability to preserve the underlying mathematical structure of the high-fidelity FE framework. By treating the assembly of the reduced residual as a quadrature problem, our hyper-reduction scheme ensures that the variational consistency of the original problem is maintained. This guarantees that crucial properties of the tangent stiffness matrix, such as positive or negative definiteness, are inherited by the HROM, which is fundamental to robust and stable Newton–Raphson iterations for strongly nonlinear electromechanical problems. We validate the methodology through complex benchmarks, including a plate beam and a circular membrane geometry. For the most complex cases, the proposed HROM achieved a 35-fold speedup on a standard commercial CPU compared to the full-order model while maintaining a relative error below 1%. This was realized by solving in a reduced space with less than 0.05% of the original dimensionality and evaluating nonlinear operators on a reduced mesh containing less than 20% of the original elements. Finally, the framework is leveraged to perform an exhaustive parametric exploration of material properties for the Ecoflex polymer family under gravitational effects, demonstrating its utility for the accelerated design optimization and material selection in soft robotics.},

keywords = {Electromechanical modeling, Empirical cubature method (ECM), Hyperreduction, Model order reduction (MOR), Multiphysics simulation, PID2022-141957OA-C22, Proper orthogonal decomposition (POD)},

pubstate = {published},

tppubtype = {article}

}

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This paper introduces a projection-based hyper-reduction methodology within the context of nonlinear electromechanics, specifically tailored for the simulation of dielectric elastomer actuators (DEAs). While high-fidelity finite element (FE) models are robust in capturing complex coupled multiphysics responses (in this case, coupling the quasi-static electric and hyperelastic mechanics responses), their high computational cost often renders them impractical for multi-query engineering problems such as material selection or optimal control. To overcome this limitation, we present a framework that combines a multi-field Proper Orthogonal Decomposition (POD) with the Empirical Cubature Method (ECM). This integration constitutes theone of the first applications of hyper-reduced order modeling (HROM) to handle the high-dimensional nonlinearities inherent in large-deformation electrical-mechanical coupling. A key advantage of this methodology is its ability to preserve the underlying mathematical structure of the high-fidelity FE framework. By treating the assembly of the reduced residual as a quadrature problem, our hyper-reduction scheme ensures that the variational consistency of the original problem is maintained. This guarantees that crucial properties of the tangent stiffness matrix, such as positive or negative definiteness, are inherited by the HROM, which is fundamental to robust and stable Newton–Raphson iterations for strongly nonlinear electromechanical problems. We validate the methodology through complex benchmarks, including a plate beam and a circular membrane geometry. For the most complex cases, the proposed HROM achieved a 35-fold speedup on a standard commercial CPU compared to the full-order model while maintaining a relative error below 1%. This was realized by solving in a reduced space with less than 0.05% of the original dimensionality and evaluating nonlinear operators on a reduced mesh containing less than 20% of the original elements. Finally, the framework is leveraged to perform an exhaustive parametric exploration of material properties for the Ecoflex polymer family under gravitational effects, demonstrating its utility for the accelerated design optimization and material selection in soft robotics.
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