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For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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Strain energy quantifies the energy stored within a material due to deformation under loading conditions, a fundamental concept in materials science and engineering. The strain energy can be modeled when a material is subjected to axial loading with uniformly distributed stress. In this scenario, the stress experienced by the material is the internal force divided by the cross-sectional area, and the strain induced is directly proportional to this stress through the modulus of elasticity.
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Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations.

Vahidullah Taç1, Manuel Rausch2, Francisco Sahli Costabal3

  • 1Department of Mechanical Engineering, Purdue University, West Lafayette, IN, USA.

Computer Methods in Applied Mechanics and Engineering
|July 10, 2023
PubMed
Summary

We developed a data-driven model for anisotropic finite viscoelasticity using neural ordinary differential equations. This flexible approach accurately models complex material behaviors, outperforming traditional methods.

Keywords:
Data-driven mechanicsNeural ordinary differential equationsNonlinear mechanicsPhysics-informed machine learningTissue mechanicsViscoelasticity

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Area of Science:

  • Computational mechanics
  • Materials science
  • Applied mathematics

Background:

  • Viscoelasticity describes materials exhibiting time-dependent strain.
  • Traditional models often struggle with complex, anisotropic behaviors and large deformations.
  • Physics-based constraints like objectivity and thermodynamics are crucial for accurate modeling.

Purpose of the Study:

  • To develop a fully data-driven model for anisotropic finite viscoelasticity.
  • To incorporate physics-based constraints into data-driven potentials.
  • To enable accurate modeling of viscoelastic materials under arbitrary conditions.

Main Methods:

  • Utilizing neural ordinary differential equations (NODEs) as core components.
  • Replacing traditional Helmholtz free energy and dissipation potentials with data-driven functions.
  • Training the model on stress-strain data from diverse biological and synthetic materials.

Main Results:

  • The data-driven model successfully captures anisotropic finite viscoelasticity.
  • The approach adheres to objectivity and the second law of thermodynamics.
  • The model demonstrates superior performance compared to traditional closed-form viscoelasticity models.

Conclusions:

  • Data-driven potentials offer enhanced flexibility for modeling diverse viscoelastic materials.
  • The NODEs-based framework provides a robust method for complex material behavior prediction.
  • This approach advances the accurate simulation of materials like brain tissue and myocardium.