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A Numerical Scheme for Anisotropic Reactive Nonlinear Viscoelasticity.

Gerard A Ateshian1, Courtney A Petersen1, Steve A Maas2

  • 1Department of Mechanical Engineering, Columbia University, New York, NY 10027.

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This study enhances reactive viscoelasticity, a model for material behavior, by introducing an efficient computational method for stress calculations and ensuring frame indifference for anisotropic materials. This improves the modeling of nonlinear viscoelastic responses.

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Area of Science:

  • Materials Science
  • Continuum Mechanics
  • Chemical Engineering

Background:

  • Reactive viscoelasticity models solids as mixtures of strong and weak bonds.
  • Weak bonds break and reform under stress, analogous to chemical reactions.
  • Existing models face computational challenges with weak bond generation summation.

Purpose of the Study:

  • To develop an effective numerical scheme for calculating stress tensors in reactive viscoelastic materials.
  • To establish conditions for frame indifference in anisotropic nonlinear viscoelasticity.
  • To validate the updated framework with computational and experimental data.

Main Methods:

  • Formulated an efficient numerical scheme for strain energy density and stress tensor evaluation.
  • Derived conditions for frame indifference, applicable to fiber-reinforced materials.
  • Performed code verification and model validation against experimental results.

Main Results:

  • An effective computational method for reactive nonlinear viscoelasticity was successfully implemented.
  • Frame indifference conditions were established for anisotropic materials.
  • The updated formulation demonstrated accuracy through validation.

Conclusions:

  • The study presents a computationally efficient and theoretically sound advancement in reactive nonlinear viscoelasticity.
  • The findings facilitate more accurate modeling and simulation of complex material behaviors.
  • This work provides a robust framework for analyzing anisotropic viscoelastic materials.