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This study aims to generalize the M-integral for analyzing mixed-mode fracture energies in finite structures.

June 27, 2026Applied SciencesOpen Access

Three-Dimensional Mixed-Mode Fracture Analysis in Finite Structures Using a Generalized Domain Integral: Crack Front Energy Partition and Thickness Effects

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Randomized trial evaluates mixed-mode fracture energy in finite structures, indicating significant thickness effects.

This study aims to generalize the M-integral for analyzing mixed-mode fracture energies in finite structures.
Developed a three-dimensional Mθ3D integral based on bilinear strain energy density.
Implemented in Cast3M finite element code using a toroidal integration domain.
Numerical validations conducted on the Mixed-Mode Crack Growth (MMCG) specimen.
Achieved practical domain independence for all three fracture modes.
Showed significant deviations from plane-strain assumptions, particularly in thicker specimens.
Revealed a notable mode III component even under mode I + II loading due to Poisson effects.

Kabir et al. (2026) studied this question.

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