Least squares computation of the prestrain and work hardening parameters of sheet metal

For most metals the load-extension and stress-strain graphs are too complicated for easy mathematical analysis, and empirical equations must be formed. One such equation, which is especially useful when large strains are experienced, is Swift's equation σ = A( B + ∊) ⁿ where ∊ and σ represent logarithmic strain and true stress, respectively. The prestrain and work hardening coefficient are represented by B and n respectively, and A is a constant for the metal being used. Non-linear least squares optimization methods are more accurate than elementary methods for computing A. B. and n from discrete data pairs (∊ _i ,σ _i )i= 1,2,…, N (N≥3) determined experimentally, and a model is developed which adapts the Gauss-Newton and Levenberg-Marquardt algorithms for this purpose. Numerical results for a number of specimen sheets are reported, and comparisons of the reliability and efficiency of the two algorithms are made.