Abstract
Characterizing nonhomogeneous elastic property distribution of solids is of great significance in various engineering fields. In this paper, we observe that the solution to the inverse problem utilizing the standard optimization-based inverse approach is sensitive to the sizes of inclusions. The standard optimization-based inverse approach minimizes a cost function, containing the absolute error between the measured and computed displacements in L2 norm. To address this issue, we propose a novel inverse scheme to characterize nonhomogeneous shear modulus distribution of solids. In this novel method, the cost function is modified, and is dependent on the size of the inclusions. A number of simulated experiments are performed, and demonstrate that the proposed approach is capable of improving the shear modulus contrast in inclusions and reducing the size sensitivity. Furthermore, a theoretical analysis is conducted to validate what we have observed in simulated experiments. This theoretical analysis reveals that what we have observed in the simulated experiments is not induced by the numerical issues Instead, the size sensitivity issue is induced by regularization. The findings of this work encourage us to propose new cost functions for the optimization-based inverse approach to improve the quality of the shear modulus reconstruction.
Highlights
IntroductionMakes it possible for us to measure full-field displacement fields with high accuracy [1,2,3]
The advancement of high-resolution imaging modalities like digital imaging correlation (DIC)makes it possible for us to measure full-field displacement fields with high accuracy [1,2,3]
In the optimization-based inverse approach, the inverse problem in elasticity is posed to be a constrained minimization problem, where a cost function accounting for the discrepancy between measured and computed displacements is usually defined in the L2 norm and minimized iteratively
Summary
Makes it possible for us to measure full-field displacement fields with high accuracy [1,2,3]. The measured full-fields displacement fields can be utilized to identify the nonhomogeneous elastic distribution of solids. Mapping the nonhomogeneous elastic distribution usually requires solving an inverse problem in elasticity. There are many inverse approaches that have been developed to solve the inverse problem, including virtual fields methods [4,5,6], optimization-based approaches [7,8], etc. In the optimization-based inverse approach, the inverse problem in elasticity is posed to be a constrained minimization problem, where a cost function accounting for the discrepancy between measured and computed displacements is usually defined in the L2 norm and minimized iteratively
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