Volume 57, Number 3, May-June 2023
|1195 - 1223
|08 May 2023
Analysis of a method to compute mixed-mode stress intensity factors for non-planar cracks in three-dimensions
Department of Mechanical Engineering, Stanford University, Stanford, CA 94035, USA
2 School of Engineering, Brown University, Providence, RI 02912, USA
3 Department of Mathematics, University of Pavia, Via A. Ferrata 1, 27100 Pavia, Italy
* Corresponding author: firstname.lastname@example.org
Accepted: 28 December 2022
In this work, we present and prove results underlying a method which uses functionals derived from the interaction integral to approximate the stress intensity factors along a three-dimensional crack front. We first prove that the functionals possess a pair of important properties. The functionals are well-defined and continuous for square-integrable tensor fields, such as the gradient of a finite element solution. Furthermore, the stress intensity factors are representatives of such functionals in a space of functions over the crack front. Our second result is an error estimate for the numerical stress intensity factors computed via our method. The latter property of the functionals provides a recipe for numerical stress intensity factors; we apply the functionals to the gradient of a finite element approximation for a specific set of crack front variations, and we calculate the stress intensity factors by inverting the mass matrix for those variations.
Mathematics Subject Classification: 46N40 / 70G75 / 74G15 / 74R10
Key words: Fracture mechanics / singularities / stress intensity factors
© The authors. Published by EDP Sciences, SMAI 2023
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