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This study introduces a new method for identifying viscoelastic material properties using internal measurements. The approach effectively reconstructs material behavior even with incomplete or noisy data.

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Computational Engineering

Background:

  • Viscoelastic materials exhibit time-dependent mechanical properties.
  • Accurate material parameter identification is crucial for predicting material behavior.
  • Inverse problems in viscoelasticity are often ill-posed and challenging.

Purpose of the Study:

  • To develop a robust methodology for inverse identification of linearly viscoelastic material parameters.
  • To address challenges posed by steady-state dynamics and limited interior measurement data.
  • To enable viscoelasticity imaging under partially or completely underspecified boundary conditions.

Main Methods:

  • Solving the inverse problem of viscoelasticity imaging by minimizing a modified error in constitutive equation (MECE) functional.
  • Incorporating the conservation of linear momentum as a constraint.
  • Utilizing a quadratic penalty term for measurement data within the MECE functional.
  • Applying regularization through a penalty parameter and Morozov's discrepancy principle.

Main Results:

  • The methodology demonstrates robust performance in identifying viscoelastic material parameters.
  • Successful application even with incomplete and noisy interior measurement data.
  • Effective handling of scenarios with underspecified boundary conditions.

Conclusions:

  • The proposed MECE functional approach provides a reliable method for viscoelastic material identification.
  • The technique is resilient to data imperfections, offering practical applicability.
  • This work advances the field of viscoelasticity imaging and material characterization.