Crack-Tip Opening as a Probe for Length-Scale Separation in Geometrically Nonlinear Solids
Abstract
Soft elastic solids are highly deformable materials where fracture is driven by the complex coupling of geometric and material nonlinearities. While geometric nonlinearity (GNL) arises kinematically from the intrinsic capacity of solids to undergo large deformations, material nonlinearity stems from the constitutive behavior unique to each class of materials. Because GNL is a universal feature of all highly deformable solids, establishing its standalone impact is a prerequisite for understanding nonlinear fracture. Here, we focus on brittle soft solids to study the role of GNL alone on the near-tip fields of a static crack under mode I plane-strain conditions, providing a canonical baseline for integrating material nonlinearities in future investigations. By utilizing a compressible St. Venant-Kirchhoff material model, we analyze crack behavior under large deformations in the absence of material nonlinearity. We propose a robust postprocessing methodology based on the crack-tip opening displacement (CTOD) profile and derive asymptotic analytical solutions. Our results reveal a distinct near-tip region where the CTOD departs from classical linear elastic predictions, transitioning into a nonlinear regime dictated by Poisson's ratio. Using a matched-asymptotics approach, we define a physical nonlinear length scale λnl that bounds this region and scales quadratically with the far-field stress intensity factor KI. We show that GNL acts as an intrinsic strain-stiffening mechanism sufficient to trigger energy partitioning, effectively shielding the crack tip and imparting an apparent toughening. Ultimately, we conclude that the geometrically nonlinear material model serves as a foundational framework for the broader study of nonlinear elastic fracture mechanics.
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BibTeX
@misc{lazomolina2026cracktip,
title = {{Crack-Tip Opening as a Probe for Length-Scale Separation in Geometrically Nonlinear Solids}},
author = {Raúl Lazo-Molina and Mokhtar Adda-Bedia and Mohit Pundir and Rodrigo Arias and David S. Kammer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.25771},
eprint = {2607.25771},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.25771},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Crack-Tip Opening as a Probe for Length-Scale Separation in Geometrically Nonlinear Solids
AU - Raúl Lazo-Molina
AU - Mokhtar Adda-Bedia
AU - Mohit Pundir
AU - Rodrigo Arias
AU - David S. Kammer
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2607.25771
UR - https://arxiv.org/abs/2607.25771
AB - Soft elastic solids are highly deformable materials where fracture is driven by the complex coupling of geometric and material nonlinearities. While geometric nonlinearity (GNL) arises kinematically from the intrinsic capacity of solids to undergo large deformations, material nonlinearity stems from the constitutive behavior unique to each class of materials. Because GNL is a universal feature of all highly deformable solids, establishing its standalone impact is a prerequisite for understanding nonlinear fracture. Here, we focus on brittle soft solids to study the role of GNL alone on the near-tip fields of a static crack under mode I plane-strain conditions, providing a canonical baseline for integrating material nonlinearities in future investigations. By utilizing a compressible St. Venant-Kirchhoff material model, we analyze crack behavior under large deformations in the absence of material nonlinearity. We propose a robust postprocessing methodology based on the crack-tip opening displacement (CTOD) profile and derive asymptotic analytical solutions. Our results reveal a distinct near-tip region where the CTOD departs from classical linear elastic predictions, transitioning into a nonlinear regime dictated by Poisson's ratio. Using a matched-asymptotics approach, we define a physical nonlinear length scale λ_nl that bounds this region and scales quadratically with the far-field stress intensity factor K_I. We show that GNL acts as an intrinsic strain-stiffening mechanism sufficient to trigger energy partitioning, effectively shielding the crack tip and imparting an apparent toughening. Ultimately, we conclude that the geometrically nonlinear material model serves as a foundational framework for the broader study of nonlinear elastic fracture mechanics.
ER -