A discrete crack-tip theory for nonlinear lattice networks
Abstract
Crack-tip fields govern deformation localization and failure initiation. Classical continuum fracture mechanics describes these fields through theories such as the Hutchinson-Rice-Rosengren (HRR) field for nonlinear power-law solids. However, continuum descriptions break down near cracks in soft and architected materials, where load is transmitted through discrete chains, fibers, or struts. Here, we develop a discrete crack-tip theory for lattice networks with nonlinear chains. The theory has two central components. First, at large deformation, the strain of a representative chain in layer i depends approximately linearly on the applied macroscopic strain, εi≈ ki(λ−1), defining a layer-dependent strain-amplification factor ki. Second, along topology-selected chain directions, termed discrete HRR lines, the layer-to-layer ratios of ki follow a two-regime scaling law. Together, for a power-law chain force-strain relation with exponent p, the inner discrete regime predicts εi∼ i−1/p and fi∼ i−1, which differs from the classical continuum HRR prediction. The theory also explains why the intrinsic fracture energy approaches a size-independent limit as the network size increases. Photoelastic hydrogel experiments further validate our theory. These results reveal a two-regime crack-tip scaling law in nonlinear lattice networks and provide a framework for predicting chain deformation and intrinsic fracture energy.
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BibTeX
@misc{liu2026discrete,
title = {{A discrete crack-tip theory for nonlinear lattice networks}},
author = {Jiabin Liu and Shaoting Lin and Juntao Huang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04568},
eprint = {2609.04568},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04568},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A discrete crack-tip theory for nonlinear lattice networks
AU - Jiabin Liu
AU - Shaoting Lin
AU - Juntao Huang
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04568
UR - https://arxiv.org/abs/2609.04568
AB - Crack-tip fields govern deformation localization and failure initiation. Classical continuum fracture mechanics describes these fields through theories such as the Hutchinson-Rice-Rosengren (HRR) field for nonlinear power-law solids. However, continuum descriptions break down near cracks in soft and architected materials, where load is transmitted through discrete chains, fibers, or struts. Here, we develop a discrete crack-tip theory for lattice networks with nonlinear chains. The theory has two central components. First, at large deformation, the strain of a representative chain in layer i depends approximately linearly on the applied macroscopic strain, ε_i≈ k_i(λ−1), defining a layer-dependent strain-amplification factor k_i. Second, along topology-selected chain directions, termed discrete HRR lines, the layer-to-layer ratios of k_i follow a two-regime scaling law. Together, for a power-law chain force-strain relation with exponent p, the inner discrete regime predicts ε_i∼ i^−1/p and f_i∼ i^−1, which differs from the classical continuum HRR prediction. The theory also explains why the intrinsic fracture energy approaches a size-independent limit as the network size increases. Photoelastic hydrogel experiments further validate our theory. These results reveal a two-regime crack-tip scaling law in nonlinear lattice networks and provide a framework for predicting chain deformation and intrinsic fracture energy.
ER -