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

David González,Francisco Chinesta,Elías Cueto,Alberto García-González

doi:10.3390/ma13102319

Abstract

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.

Highlights

Computationalmechanics is not absent of the data “fever”
Basic equations—those with a higher epistemic value, such as equilibrium or compatibility—are kept, while those which are frequently phenomenological in nature—constitutive equations—are substituted by experimental data, and the name of this family of methods
The so-called equation-free approach substitutes the constitutive law of a material not by experimental data, but by a pseudo-experimental result coming from microscale, first-principle computations [10]

Summary

Introduction

Even if the so-called data-driven computational mechanics discipline presents distinctive features over what is commonly known as “big data”, the possibility of employing raw experimental data to perform simulations has attracted the attention of many researchers recently [1,2,3,4,5,6,7,8,9] In these approaches, basic equations—those with a higher epistemic value, such as equilibrium or compatibility—are kept, while those which are frequently phenomenological in nature—constitutive equations—are substituted by experimental data, and the name of this family of methods.

Methods

Results

Conclusion