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Numerical approximation for algorithmic tangent moduli for nonlinear viscoelastic model with CSDA method.

Xinggui Fan1, Jinsheng Xu2, Xiong Chen1

  • 1Nanjing University of Science and Technology, Xiaolingwei 200#, Xuanwu District, Nanjing, Jiangsu, China.

Scientific Reports
|August 7, 2024
PubMed
Summary

The complex step derivative approximation (CSDA) offers a computationally efficient and robust method for numerical differentiation in viscoelastic material models. This technique accurately evaluates algorithmic tangent moduli, outperforming other numerical methods.

Keywords:
Algorithmic tangent moduliCSDAFinite element methodViscoelastic model

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Area of Science:

  • Computational mechanics
  • Materials science
  • Numerical analysis

Background:

  • Viscoelastic materials exhibit time-dependent mechanical properties.
  • Accurate numerical evaluation of constitutive models is crucial for simulating material behavior.
  • Traditional numerical differentiation methods can suffer from accuracy and efficiency issues.

Purpose of the Study:

  • To revisit and apply the complex step derivative approximation (CSDA) to nonlinear viscoelastic constitutive models.
  • To evaluate the effectiveness and computational efficiency of CSDA for determining algorithmic tangent moduli.
  • To compare CSDA performance against analytical methods and other numerical differentiation techniques.

Main Methods:

  • Implementation of the complex step derivative approximation (CSDA) for numerical differentiation.
  • Application of CSDA to a class of nonlinear viscoelastic constitutive models.
  • Numerical evaluation of algorithmic tangent moduli using CSDA.
  • Validation through three distinct numerical tests and comparison with analytical solutions.

Main Results:

  • The CSDA scheme demonstrates high computational efficiency and robustness for numerical differentiation.
  • CSDA accurately determines the algorithmic tangent moduli of viscoelastic constitutive models.
  • Performance of CSDA is superior to other numerical differentiation techniques, irrespective of the finite difference interval size.

Conclusions:

  • The complex step derivative approximation (CSDA) is a highly effective and efficient method for numerical differentiation in the context of viscoelastic materials.
  • CSDA provides a robust approach for evaluating algorithmic tangent moduli, enhancing the accuracy of constitutive model simulations.
  • This study validates CSDA as a superior numerical technique for complex material modeling.