Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#355572] of Wilkins Aquino

Papers Published

  1. Chen, MJ; Aquino, W; Walsh, TF; Reu, PL; Johnson, KL; Rouse, JW; Jared, BH; Bishop, JE, A Generalized Stress Inversion Approach with Application to Residual Stress Estimation, Journal of Applied Mechanics, vol. 87 no. 11 (November, 2020) [doi]
    (last updated on 2021/05/15)

    We develop a generalized stress inversion technique (or the generalized inversion method) capable of recovering stresses in linear elastic bodies subjected to arbitrary cuts. Specifically, given a set of displacement measurements found experimentally from digital image correlation (DIC), we formulate a stress estimation inverse problem as a partial differential equation-constrained optimization problem. We use gradient-based optimization methods, and we accordingly derive the necessary gradient and Hessian information in a matrix-free form to allow for parallel, large-scale operations. By using a combination of finite elements, DIC, and a matrix-free optimization framework, the generalized inversion method can be used on any arbitrary geometry, provided that the DIC camera can view a sufficient part of the surface. We present numerical simulations and experiments, and we demonstrate that the generalized inversion method can be applied to estimate residual stress.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320