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The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
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A Data-Driven Learning Method for Constitutive Modeling: Application to Vascular Hyperelastic Soft Tissues.

David González1, Alberto García-González2, Francisco Chinesta3

  • 1Aragon Institute of Engineering Research, Universidad de Zaragoza, 50018 Zaragoza, Spain.

Materials (Basel, Switzerland)
|May 24, 2020
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Summary
This summary is machine-generated.

This study introduces a novel machine learning approach for constitutive laws, effectively handling experimental data variability and ensuring thermodynamic consistency. The method combines Topological Data Analysis and the GENERIC formalism for robust modeling of complex materials like soft tissues.

Keywords:
GENERICcomputational modelinghyperelasticitymachine learningmanifold learningsoft living tissuestopological data analysis

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Area of Science:

  • Computational Mechanics
  • Materials Science
  • Machine Learning

Background:

  • Machine learning of constitutive laws is challenged by significant experimental data dispersion, especially in soft living tissues.
  • Ensuring thermodynamic compliance (energy conservation, entropy production) is crucial for accurate material modeling.

Purpose of the Study:

  • To develop a robust machine learning framework for constitutive laws capable of handling experimental variability.
  • To integrate thermodynamic principles into the machine learning process for physically consistent models.

Main Methods:

  • Utilizing Topological Data Analysis (TDA) to uncover underlying data structures and mitigate dispersion.
  • Employing regression over the General Equation for the Nonequilibrium Reversible-Irreversible Coupling (GENERIC) formalism for thermodynamic adherence.

Main Results:

  • The proposed approach successfully unveils the true data 'shape' despite experimental scatter.
  • Demonstrated rigorous compliance with thermodynamic laws, including energy conservation and entropy production.
  • Validated feasibility using both pseudo-experimental and real experimental data.

Conclusions:

  • The combined TDA and GENERIC formalism offers a powerful method for machine learning constitutive laws with dispersed experimental data.
  • This approach enhances the reliability and physical realism of material models, particularly for complex systems like biological tissues.