# Localized Necking Model for Punching Fracture Simulation in Unstiffened and Stiffened Panels
###### Abstract  
The ductile fracture of thin-shell structures was studied here using a localized necking model. The punching experiments for unstiffened and stiffened panels were compared with numerical predictions using a combined ductile fracture and localized necking model using shell elements. The plasticity and fracture model parameters of JIS G3131 SPHC steel were identified by performing calibration experiments on standard flat bars, notched tension, central hole tension, plane strain tension, and shear specimens. The plasticity beyond the onset of necking was modeled using the Swift hardening law. The damage indicator framework with a combined Hosford-Coulomb fracture model and the domain of shell-to-solid equivalence (DSSE) were adopted to characterize the fracture initiation. The model parameters were calibrated based on the loading paths to fracture initiation, which were extracted from a non-linear finite element (FE) analysis. The presented HC-DSSE model was validated using punch tests and was able to predict fracture initiation with good accuracy. ductile fracture; localized necking; punch tests; fracture simulation; domain of shell-to-solid equivalence; Hosford-Coulomb model; shell element +
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Footnote †: 2021: 11, 3774. [[https://doi.org/10.3390/app11093774](https://doi.org/10.3390/app11093774)]([https://doi.org/10.3390/app11093774](https://doi.org/10.3390/app11093774))  
Footnote †: 2021: 11, 3774. [[https://doi.org/10.3390/app1109374](https://doi.org/10.3390/app1109374)]([https://doi.org/10.3390/app1109374](https://doi.org/10.3390/app1109374))  
Footnote †: 2021: 11, 3774. [[https://doi.org/10.3390/app11093774](https://doi.org/10.3390/app11093774)]([https://doi.org/10.3390/app11093774](https://doi.org/10.3390/app11093774))  
Footnote †: 2021: 111, 3774. [[https://doi.org/10.3390/app11093774](https://doi.org/10.3390/app11093774)]([https://doi.org/10.3390/app11093774](https://doi.org/10.3390/app11093774))  
Footnote †: 2021: 11, 3774. [[https://doi.org/10.3390/app11093774](https://doi.org/10.3390/app11093774)]([https://doi.org/10.3390/app11093774](https://doi.org/10.3390/app11093774))  
Footnote †: 2021: 11, 3774. [[https://doi.org/10.3390/app1109374](https://doi.org/10.3390/app1109374)]([https://doi.org/10.3390/app1109374](https://doi.org/10.3390/app1109374))
models show a similar fracture locus. The MMC and HC models have been widely used and validated in ductile fracture experiments and simulations with solid elements [3; 7; 8; 9; 10; 11; 12]. [PERSON] and [PERSON] [13] developed a combined HC model with localized necking, which is termed as the domain of shell-to-solid equivalence (DSSE). [PERSON] et al. [14] proposed the Bressan-Williams-Hill (BWH) criterion to predict fracture ignition with shell elements based on [PERSON]'s localized necking criterion, which is a stress-based FLC. [PERSON] et al. [15] derived an extended strain-based version that considers non-proportional loading from the original BWH. Recently, fracture models with shell elements were applied to the simulation of thin-walled structures [7; 13; 16; 17; 18]. The HC-DSSE model consists of fewer material constants than those of other models, which are frequently used because of the low number of experiments required to calibrate the material constants.