Concordia 3D framework: notch stress about 6x faster

Ayhan Ince, a professor in the Department of Mechanical, Industrial and Aerospace Engineering at Concordia University's Gina Cody School of Engineering and Computer Science, has developed a three-dimensional modelling framework for metal parts under repeated loading. According to a release published on EurekAlert on 4 November 2026, the framework calculates how the metal deforms in the volume around holes, grooves and other geometric transitions. In a computer-based comparison on a relatively simple notched steel bar, it finished in 4.5 minutes, against 28 minutes for a more detailed nonlinear simulation that accounts for permanent deformation. That makes it approximately six times faster. eurekalert.org

Why the region beneath the surface matters

Small features such as a hole in a vehicle axle can become high-stress points under repeated forces, and fatigue damage and cracks develop there. A part may be pulled, compressed, bent and twisted, sometimes at the same time. eurekalert.org

Simplified methods developed over decades efficiently calculate the material response at such critical points, but they predict only what happens at the surface. Detailed nonlinear simulations show the surrounding material, but they require considerable computing power, especially for many load histories, materials or design variations. Ince combined several mechanics models into one framework that calculates how forces are distributed and how the metal deforms throughout the three-dimensional region near the critical area. It works when several types of loading act together and change over time. eurekalert.org

Daniel Kujawski of Western Michigan University, who was not involved in the study, called it an "important contribution to advanced notch analysis". He said the method "provides a potential bridge" between point-based calculations and assessments of damage in the surrounding material. eurekalert.org

Scope of the test and next steps

The authors compared the framework with detailed nonlinear simulations for one steel material and one notched bar under three loading patterns. Because full nonlinear simulations grow more demanding with model size and loading complexity, Ince expects a larger efficiency gain for big components. This expectation has not yet been tested. eurekalert.org

The team plans to examine other materials and geometries and to validate the predictions in physical experiments. Those tests will show how widely the method applies to real components. The work was published in Theoretical and Applied Fracture Mechanics (DOI 10.1016/j.tafmec.2026.105851). eurekalert.org

Concordia 3D framework predicts stress near notches about 6 times faster than nonlinear simulation

Why the region beneath the surface matters

Scope of the test and next steps

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