Error in Constitutive Equation based Approach for Isotropic Material Parameter Estimation in Frequency-Domain Elastodynamics

Abstract

A new version of error in constitutive equation (ECE)-based material parameter identification technique for linear elastic structure in frequency-domain elastodynamics has been proposed in this article. The inverse identification problem is solved by minimizing the ECE cost functional. The ECE functional measures the error in constitutive equation due to two incompatible stress and strain fields. This incompatibility is produced due to the generation of these two fields following dissimilar constraints. The stress field is dynamically admissible and the strain field is kinematically admissible with the measured displacement data. First, the strain field is generated by using a simple penalization technique with weak incorporation of full or partial noisy measured displacement data. This penalization technique also acts as a regularization to tackle the ill-posedness of the inverse problem. Then the stress field is generated by solving a linear system of equations. Thus, in the proposed methodology, the generation of incompatible stress and strain field is uncoupled in nature which reduces the numerical computational cost in contrast to standard modified error in constitutive equation (MECE)-based method. Afterward, explicit linear update formulas are formed for isotropic material model. In numerical examples, identification of heterogeneous isotropic material parameters is performed for 3D structures. The numerical experimentation shows that the proposed method can effectively identify the elastic material parameter distribution in a few number of iterations. The present method can be utilized in large-scale elastic parameter estimation problem because of its low computational cost.