An optimization approach to algebraic Rf/ϕ strain analysis

Abstract

In algebraic R_f/ϕ strain analysis, there is a lack of the uncertainty of strain caused by, as common in measured post-strain objects, the violation of the assumption of the independence between the major-axis directions and axial ratios of pre-strain objects. A new R_f/ϕ strain method is developed to reduce this uncertainty. The method minimizes the sum of the K-th power of the negative determinant of the tensor difference between each post-strain object and the unknown strain. The method for $K=1$ yields an analytical solution of strain, equivalent to existing algebraic estimators of strain. Both synthetic datasets and real examples are used to validate the method for varying K values of 1–10. The strain results illustrate that the method decreases in standard error and tends to increase in accuracy with an increasing K. The variation of the estimated strain with K is helpful to appraise the violation of the independence assumption.