Journal: Engineering with Computers

Article Title: Bridging experiments and defects’ mechanics: a data-driven toolbox for configurational force analysis

doi: 10.1007/s00366-025-02262-5

Figure Lengend Snippet: a Experimental setup for in-plane displacement field measurement using digital image correlation on a compact tension specimen with a surface speckle. b Representation of the strain field ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\varepsilon}_{22}$$\end{document} ) overlaid with the crack path and the equivalent domain integration (EDI) scheme. The domain incrementally expands outward from the crack tip, enabling the numerical evaluation of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{J}_{k}$$\end{document} -integral and mode-decomposed SIFs. Each domain contour corresponds to a discrete area increment ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:dA$$\end{document} ) mapped to a regularised measurement grid. The direction of crack extension or virtual crack extension (VCE) vector is assumed along the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{x}_{1}$$\end{document} -axis

Article Snippet: In addition to the analytical benchmark, we validated the decomposition against a finite element displacement field generated in Abaqus.

Techniques: Plasmid Preparation

Journal: Engineering with Computers

Article Title: Bridging experiments and defects’ mechanics: a data-driven toolbox for configurational force analysis

doi: 10.1007/s00366-025-02262-5

Figure Lengend Snippet: Workflow of the computational toolbox for extracting configurational forces and stress intensity factors. Flowchart illustrating the key modules of the MATLAB-based toolbox, including data input, preprocessing, invariant integral calculations ( J - and M -integrals), mode decomposition, and post-processing. Solid arrows represent the core computational pipeline, while dashed lines indicate optional or user-controlled functionalities. The workflow accommodates both 2D and 3D displacement, or displacement/deformation gradient data and supports materials with isotropic, anisotropic, or elastoplastic behaviour

Article Snippet: In addition to the analytical benchmark, we validated the decomposition against a finite element displacement field generated in Abaqus.

Techniques:

Journal: Engineering with Computers

Article Title: Bridging experiments and defects’ mechanics: a data-driven toolbox for configurational force analysis

doi: 10.1007/s00366-025-02262-5

Figure Lengend Snippet: Validation of the toolbox using synthetic displacement fields for a stationary mixed-mode crack: a Synthetic displacement field generated using Westergaard’s solution for a stationary crack under mixed-mode loading: (mode I: 3 MPa m 0.5 , mode II: 1 MPa m 0.5 , and mode III: 2 MPa m 0.5 ), assuming plane stress conditions. The field of view spans 200 × 200 mm² with a crack tip at the centre. b Calculated J -integral and decomposed SIFs for modes I–III as a function of domain expansion using the EDI method. Convergence trends are shown as the domain extends away from the crack tip, demonstrating accurate recovery of input values. c The sensitivity of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{J}_{k}$$\end{document} -integral and SIF components to the direction of the VCE, varied from − 90° to + 90° in 5° increments. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{J}_{1}$$\end{document} directly calculated from the field, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{J}_{1}^{I+I+III}$$\end{document} calculated from summing the mode-specific \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{J}_{1}$$\end{document} overlap

Article Snippet: In addition to the analytical benchmark, we validated the decomposition against a finite element displacement field generated in Abaqus.

Techniques: Biomarker Discovery, Generated

Journal: Engineering with Computers

Article Title: Bridging experiments and defects’ mechanics: a data-driven toolbox for configurational force analysis

doi: 10.1007/s00366-025-02262-5

Figure Lengend Snippet: Analysis of a 3D displacement field from a fatigue crack using the computational toolbox. a Optical image of a compact tension specimen showing the notch and a fully developed fatigue crack. b The three-dimensional displacement field (U z ), aligned with the loading direction, was measured via DVC after 230,000 loading cycles (P min = 450 N, P max = 4500 N). Displacement field extracted with a 96 × 96 × 96 voxel subset and 75% overlap. c Illustration of the radial slicing of the crack front used for virtual crack extension (VCE) analysis, with layers sampled from 0° to 90° along the crack edge at 1° intervals. d \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{J}_{1}^{I,III,III}$$\end{document} integral and SIFs convergence for the crack front at 33°, showing stable convergence, using the equivalent domain integral method, 1 mm away from the crack tip. e Mode I–III and the J -integral across the crack front, revealing dominant mode I

Article Snippet: In addition to the analytical benchmark, we validated the decomposition against a finite element displacement field generated in Abaqus.

Techniques: