Next Article in Journal
The Complex Rayleigh Waves in a Functionally Graded Piezoelectric Half-Space: An Improvement of the Laguerre Polynomial Approach
Next Article in Special Issue
Nonlinear Regression Operating on Microstructures Described from Topological Data Analysis for the Real-Time Prediction of Effective Properties
Previous Article in Journal
Towards Deterministic Computation of Internal Stresses in Additively Manufactured Materials under Fatigue Loading: Part I
Previous Article in Special Issue
Data-Oriented Constitutive Modeling of Plasticity in Metals
Open AccessArticle

A Data-Driven Learning Method for Constitutive Modeling: Application to Vascular Hyperelastic Soft Tissues

1
Aragon Institute of Engineering Research, Universidad de Zaragoza, 50018 Zaragoza, Spain
2
Laboratori de Càlcul Numèric, E.T.S. de Ingeniería de Caminos, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
3
ESI Group Chair, Processes and Engineering in Mechanics and Materials (PIMM) Laboratory, Arts et Metiers Institute of Technology, 75013 Paris, France
*
Author to whom correspondence should be addressed.
Materials 2020, 13(10), 2319; https://doi.org/10.3390/ma13102319
Received: 21 April 2020 / Revised: 7 May 2020 / Accepted: 15 May 2020 / Published: 18 May 2020
(This article belongs to the Special Issue Empowering Materials Processing and Performance from Data and AI)
We address the problem of machine learning of constitutive laws when large experimental deviations are present. This is particularly important in soft living tissue modeling, for instance, where large patient-dependent data is found. We focus on two aspects that complicate the problem, namely, the presence of an important dispersion in the experimental results and the need for a rigorous compliance to thermodynamic settings. To address these difficulties, we propose to use, respectively, Topological Data Analysis techniques and a regression over the so-called General Equation for the Nonequilibrium Reversible-Irreversible Coupling (GENERIC) formalism (M. Grmela and H. Ch. Oettinger, Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E 56, 6620, 1997). This allows us, on one hand, to unveil the true “shape” of the data and, on the other, to guarantee the fulfillment of basic principles such as the conservation of energy and the production of entropy as a consequence of viscous dissipation. Examples are provided over pseudo-experimental and experimental data that demonstrate the feasibility of the proposed approach. View Full-Text
Keywords: machine learning; manifold learning; topological data analysis; GENERIC; soft living tissues; hyperelasticity; computational modeling machine learning; manifold learning; topological data analysis; GENERIC; soft living tissues; hyperelasticity; computational modeling
Show Figures

Figure 1

MDPI and ACS Style

González, D.; García-González, A.; Chinesta, F.; Cueto, E. A Data-Driven Learning Method for Constitutive Modeling: Application to Vascular Hyperelastic Soft Tissues. Materials 2020, 13, 2319.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop