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Efficient formulations of the material identification problem using full-field measurements

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Abstract

The material identification problem addressed consists of determining the constitutive parameters distribution of a linear elastic solid using displacement measurements. This problem has been considered in important applications such as the design of methodologies for breast cancer diagnosis. Since the resolution of real life problems involves high computational costs, there is great interest in the development of efficient methods. In this paper two new efficient formulations of the problem are presented. The first formulation leads to a second-order cone optimization problem, and the second one leads to a quadratic optimization problem, both allowing the resolution of the problem with high efficiency and precision. Numerical examples are solved using synthetic input data with error. A regularization technique is applied using the Morozov criterion along with an automatic selection strategy of the regularization parameter. The proposed formulations present great advantages in terms of efficiency, when compared to other formulations that require the application of general nonlinear optimization algorithms.

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Acknowledgments

This research was financially supported by the Uruguayan National Research and Innovation Agency (ANII: project codes FMV-3-2011-1-6125 and POS-2011-1-3570) and the “Comisión Sectorial de Investigación Científica (CSIC)”.

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  1. Facultad de Ingeniería, Instituto de Estructuras y Transporte, Universidad de la República, Montevideo, Uruguay

    Jorge M. Pérez Zerpa & Alfredo Canelas

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  1. Jorge M. Pérez Zerpa
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  2. Alfredo Canelas
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Correspondence to Jorge M. Pérez Zerpa.

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Pérez Zerpa, J.M., Canelas, A. Efficient formulations of the material identification problem using full-field measurements. Comput Mech 58, 235–255 (2016). https://doi.org/10.1007/s00466-016-1291-1

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