Material Parameter Identification in Transient Dynamics by Error in Constitutive Equation Approach

A study on material parameter identification of linearly elastic structures is presented in this work by minimizing the norm of the error in constitutive equation (ECE) from partial and corrupted measurements in transient dynamics. The identification problem is formulated as an optimization problem where the objective function measures the constitutive discrepancy due to the incompatible pair of stress and strain fields. These two fields are generated by solving two different forward problems related to linear elasticity. In the inverse algorithm, we used an effective penalty based approach to weakly satisfy the measured partial strain or displacement data. This technique not only allows us to incorporate the measurement field but helps to regularize the ill-posedness of the inverse problem. Here, we have proposed explicit material parameter update formulas for linear elastic materials. Eventually numerical examples of reconstruction of Young's modulus for 1D bar and beam are given here to present application of the proposed algorithm.