Benchmarking physics-informed frameworks for data-driven hyperelasticity

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dc.catalogadorgjm
dc.contributor.authorTaç, Vahidullah
dc.contributor.authorLinka, Kevin
dc.contributor.authorSahli Costabal, Francisco
dc.contributor.authorKuhl, Ellen
dc.contributor.authorTepole, Adrian Buganza
dc.date.accessioned2024-05-30T16:23:24Z
dc.date.available2024-05-30T16:23:24Z
dc.date.issued2023
dc.description.abstractData-driven methods have changed the way we understand and model materials. However, while providing unmatched flexibility, these methods have limitations such as reduced capacity to extrapolate, overfitting, and violation of physics constraints. Recently, frameworks that automatically satisfy these requirements have been proposed. Here we review, extend, and compare three promising data-driven methods: Constitutive Artificial Neural Networks (CANN), Input Convex Neural Networks (ICNN), and Neural Ordinary Differential Equations (NODE). Our formulation expands the strain energy potentials in terms of sums of convex non-decreasing functions of invariants and linear combinations of these. The expansion of the energy is shared across all three methods and guarantees the automatic satisfaction of objectivity, material symmetries, and polyconvexity, essential within the context of hyperelasticity. To benchmark the methods, we train them against rubber and skin stress–strain data. All three approaches capture the data almost perfectly, without overfitting, and have some capacity to extrapolate. This is in contrast to unconstrained neural networks which fail to make physically meaningful predictions outside the training range. Interestingly, the methods find different energy functions even though the prediction on the stress data is nearly identical. The most notable differences are observed in the second derivatives, which could impact performance of numerical solvers. On the rich data used in these benchmarks, the models show the anticipated trade-off between number of parameters and accuracy. Overall, CANN, ICNN and NODE retain the flexibility and accuracy of other data-driven methods without compromising on the physics. These methods are ideal options to model arbitrary hyperelastic material behavior.
dc.fuente.origenORCID
dc.identifier.doi10.1007/s00466-023-02355-2
dc.identifier.urihttps://doi.org/10.1007/s00466-023-02355-2
dc.identifier.urihttp://www.scopus.com/inward/record.url?eid=2-s2.0-85160813588&partnerID=MN8TOARS
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/86069
dc.identifier.wosidWOS:000998752700001
dc.information.autorucEscuela de Ingeniería; Sahli Costabal, Francisco; S/I; 154857
dc.language.isoen
dc.nota.accesocontenido parcial
dc.pagina.final65
dc.pagina.inicio49
dc.revistaComputational Mechanics
dc.rightsacceso restringido
dc.subjectPhysics-informed machine learning
dc.subjectPolyconvexity
dc.subjectNonlinear mechanics
dc.subjectNeural networks
dc.subjectConstitutive models
dc.subject.ddc600
dc.subject.deweyTecnologíaes_ES
dc.titleBenchmarking physics-informed frameworks for data-driven hyperelasticity
dc.typeartículo
dc.volumen73
sipa.codpersvinculados154857
sipa.trazabilidadORCID;2024-05-27
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