## Inverse identification of viscoelastic material properties using an error in constitutive equations approach

This work presents a methodology based on the concept of error in constitutive equations for the inverse reconstruction of viscoelastic properties using steady-state dynamics. The ECE algorithm presented herein consists of two main steps. In the first step, kinematically admissible strains and dynamically admissible stresses are generated through two auxiliary forward problems. In the second step, a new update of the complex shear and bulk moduli as functions of frequency are obtained by minimizing an ECE functional that measures the discrepancy between the kinematically admissible strains and the dynamically admissible stresses. The feasibility of the methodology is demonstrated through two numerical experiments. It was found that the magnitude and phase of the complex shear modulus can be accurately reconstructed in the presence of noise, while the magnitude of the bulk modulus is more sensitive to noise and can be reconstructed with less accuracy, in general, than the shear modulus. Furthermore, the phase of the bulk modulus, which is related to energy dissipation, can be accurately reconstructed.

### Duke Scholars

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*Proceedings of the 8th International Conference on Structural Dynamics, EURODYN 2011*(pp. 2564–2568).

*Proceedings of the 8th International Conference on Structural Dynamics, EURODYN 2011*, 2564–68, 2011.

*Proceedings of the 8th International Conference on Structural Dynamics, EURODYN 2011*, 2011, pp. 2564–68.