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Inverse analysis for heterogeneous materials and its application to viscoelastic curing polymers

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Abstract

This contribution aims at achieving two important goals: First, it outlines a numerical inverse homogenization strategy able to recover material parameters of the microstructure by using results of macroscopic tests. Second, it considers parameter identification for viscoelastic heterogeneous materials, which is a step providing the basis for the further extension toward the general treatment of dissipative processes. The approach proposed couples the Levenberg–Marquardt method with the multiscale finite element method. In this combination, the former is a gradient-based optimization strategy used to minimize a merit function while the latter is a numerical homogenization technique needed to solve the direct problem. The specific example studied in the paper deals with the investigation of a composite consisting of a viscoelastic curing polymer and a nonlinear elastic material. It proposes a three-step procedure for the evaluation of its material parameters and discusses the accuracy and the uniqueness of the solution.

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Acknowledgments

The second author acknowledges funding by the ERC-Advanced Grant MOCOPOLY.

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Authors and Affiliations

  1. TU Dortmund, 44227, Dortmund, Germany

    Sandra Klinge

  2. University of Erlangen-Nuremberg, 91058, Erlangen, Germany

    Paul Steinmann

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  1. Sandra Klinge
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  2. Paul Steinmann
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Correspondence to Sandra Klinge.

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Klinge, S., Steinmann, P. Inverse analysis for heterogeneous materials and its application to viscoelastic curing polymers. Comput Mech 55, 603–615 (2015). https://doi.org/10.1007/s00466-015-1126-5

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