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Finite Element Model Updating Combined with Multi-Response Optimization for Hyper-Elastic Materials Characterization.

Saúl Íñiguez-Macedo1, Rubén Lostado-Lorza2, Rubén Escribano-García3

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Summary

This study introduces a new, cost-effective method using multi-response surface (MRS) and desirability functions to determine elastomer material constants (Cᵢ). The approach simplifies modeling complex material behaviors, offering a more economical alternative for researchers.

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finite element methodhyperelastic materialsmodel updatingmulti-response optimization

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Area of Science:

  • Materials Science
  • Mechanical Engineering
  • Computational Mechanics

Background:

  • Standardized tests for elastomer behavior yield complex stress-strain curves requiring expensive equipment.
  • Current model updating methods for determining material constants (Cᵢ) are computationally intensive.
  • Simpler force-displacement curves are preferred but require robust parameterization.

Purpose of the Study:

  • To develop an automated, economical methodology for determining elastomer material constants (Cᵢ).
  • To combine model updating with multi-response surface (MRS) methods and desirability functions.
  • To reduce the computational cost associated with elastomer behavior modeling.

Main Methods:

  • Utilized standardized tensile, compression, and shear tests.
  • Employed parameterized finite element (FE) models with experimental force-displacement data.
  • Integrated multi-response surface (MRS) and desirability functions for automated Cᵢ constant determination.
  • Generated quadratic regression models for error functions (ER) between experimental and FE curves.

Main Results:

  • The proposed methodology successfully determined Cᵢ constants for NBR, EVA, SBR, and PUR elastomers.
  • The Mooney-Rivlin hyper-elastic model demonstrated the least error across studied materials.
  • Achieved low error in Cᵢ constant adjustment (e.g., MAEnorm = 0.054 for NBR).

Conclusions:

  • The combined MRS and desirability function approach offers a simpler, more economical alternative for obtaining optimal Cᵢ constants.
  • This methodology can be applied to any elastomer type, reducing computational expense.
  • Validated the effectiveness of the proposed method for accurate elastomer behavior modeling.