Extracting residual stresses from experiments through inverse methods

Journal article

Residual stresses are stresses present in a body in the absence of loads. They are found universally in biological systems and play a key role in many industrial applications as they alter a body’s effective material properties. Typically, in biomechanics, they are the result of growth, remodeling, or other active processes. In industry, they are the consequence of manufacturing processes such as welding, cooling, or quenching. To study the response of materials with residual stresses, their initial values must be known, and neglecting their contribution may lead to wrong predictions, even at the qualitative level. It is therefore crucial to estimate them. Residual stresses can be obtained by simulating the underlying physics using numerical methods, or using experimental setups. The former approach is limited by the amount of constitutive models and associated phenomenological parameters needed in the simulation. In the latter approach, residual stress quantification is restricted to a certain region and its accuracy is affected by noisy measurements. In this paper we propose an inverse approach to reconstruct residual stress fields using domain displacements as an input. This displacement field is measured during the motion of the sample when it is sectioned (divided) into different regions through cutting experiments that partially relieve stresses. We demonstrate through various examples that residual stress recovery is possible both for linear and nonlinear solids while the formulation is independent of the physics of the residual stress source. Our findings show accurate reconstructions of residual stress when sufficiently many cuts have been performed, with errors below 10% and 20% for the linear and nonlinear examples, respectively, even for high input errors in the strain field (O(40%)). This unique mixed numerical-experimental approach is also valid to improve the quantification of residual stress fields in existing experimental methods.

Authors: Sanz-Herrera, JA; Goriely, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: International Journal of Mechanical Sciences
• Volume: 309
• Article number: 111002
• Publication date: 2025-11-10
• Acceptance date: 2025-11-08
• DOI: 10.1016/j.ijmecsci.2025.111002
• EISSN: 1879-2162
• ISSN: 0020-7403
• Language: English
• Keywords: nonlinear mechanics; biomechanics; finite element method; residual stress; inverse methods; experimental stress analysis