### Abstract

The paper analyzes the vertical penetration of a small object through a floating sea ice plate. The analysis takes into account the fact that the bending cracks reach only through part of the ice plate thickness and have a variable depth profile. The cracks are modeled according to the Rice-Levy nonlinear softening line spring model. The plate-crack interaction is characterized in terms of the compliance functions for the bending moments and normal forces in the crack plane, which are computed by an energy-based variational finite-difference method. The radial crack is divided into vertical strips, and a numerical algorithm with step-by-step loading is developed to calculate the vertical growth of the crack in each strip for a prescribed radial crack length increment. The initiation of crack strips from the surface of the plate is decided on the basis of a yield strength criterion with a fracture based flow rule. Systems of up to 300 nonlinear equations are solved by the Levenberg-Marquardt optimization algorithm. The maximum load is reached when the circumferential cracks begin to form. Numerical calculations, comparison of the results with test data, and a study of scaling laws are relegated to the companion paper, which follows in this issue. Numerical calculations show a typical quasi brittle size effect such that the plot of log σ_{N} versus log h (where σ_{N} = nominal stress at maximum load and h = plate thickness) is a descending curve whose slope is negligible only for h < 0.2 m and then gets gradually steeper, asymptotically approaching -1/2. The calculated size effect agrees with the existing test data, and contradicts previous plasticity solutions.

Original language | English |
---|---|

Pages (from-to) | 1310-1315 |

Number of pages | 6 |

Journal | Journal of Engineering Mechanics |

Volume | 124 |

Issue number | 12 |

DOIs | |

Publication status | Published - 1998 Dec |

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### All Science Journal Classification (ASJC) codes

- Mechanics of Materials
- Mechanical Engineering

### Cite this

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*Journal of Engineering Mechanics*, vol. 124, no. 12, pp. 1310-1315. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:12(1310)

**Size effect in penetration of sea ice plate with part-through cracks. I : Theory.** / Bažant, Zdeněk P.; Kim, Jang Jay H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Size effect in penetration of sea ice plate with part-through cracks. I

T2 - Theory

AU - Bažant, Zdeněk P.

AU - Kim, Jang Jay H.

PY - 1998/12

Y1 - 1998/12

N2 - The paper analyzes the vertical penetration of a small object through a floating sea ice plate. The analysis takes into account the fact that the bending cracks reach only through part of the ice plate thickness and have a variable depth profile. The cracks are modeled according to the Rice-Levy nonlinear softening line spring model. The plate-crack interaction is characterized in terms of the compliance functions for the bending moments and normal forces in the crack plane, which are computed by an energy-based variational finite-difference method. The radial crack is divided into vertical strips, and a numerical algorithm with step-by-step loading is developed to calculate the vertical growth of the crack in each strip for a prescribed radial crack length increment. The initiation of crack strips from the surface of the plate is decided on the basis of a yield strength criterion with a fracture based flow rule. Systems of up to 300 nonlinear equations are solved by the Levenberg-Marquardt optimization algorithm. The maximum load is reached when the circumferential cracks begin to form. Numerical calculations, comparison of the results with test data, and a study of scaling laws are relegated to the companion paper, which follows in this issue. Numerical calculations show a typical quasi brittle size effect such that the plot of log σN versus log h (where σN = nominal stress at maximum load and h = plate thickness) is a descending curve whose slope is negligible only for h < 0.2 m and then gets gradually steeper, asymptotically approaching -1/2. The calculated size effect agrees with the existing test data, and contradicts previous plasticity solutions.

AB - The paper analyzes the vertical penetration of a small object through a floating sea ice plate. The analysis takes into account the fact that the bending cracks reach only through part of the ice plate thickness and have a variable depth profile. The cracks are modeled according to the Rice-Levy nonlinear softening line spring model. The plate-crack interaction is characterized in terms of the compliance functions for the bending moments and normal forces in the crack plane, which are computed by an energy-based variational finite-difference method. The radial crack is divided into vertical strips, and a numerical algorithm with step-by-step loading is developed to calculate the vertical growth of the crack in each strip for a prescribed radial crack length increment. The initiation of crack strips from the surface of the plate is decided on the basis of a yield strength criterion with a fracture based flow rule. Systems of up to 300 nonlinear equations are solved by the Levenberg-Marquardt optimization algorithm. The maximum load is reached when the circumferential cracks begin to form. Numerical calculations, comparison of the results with test data, and a study of scaling laws are relegated to the companion paper, which follows in this issue. Numerical calculations show a typical quasi brittle size effect such that the plot of log σN versus log h (where σN = nominal stress at maximum load and h = plate thickness) is a descending curve whose slope is negligible only for h < 0.2 m and then gets gradually steeper, asymptotically approaching -1/2. The calculated size effect agrees with the existing test data, and contradicts previous plasticity solutions.

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U2 - 10.1061/(ASCE)0733-9399(1998)124:12(1310)

DO - 10.1061/(ASCE)0733-9399(1998)124:12(1310)

M3 - Article

AN - SCOPUS:0032454982

VL - 124

SP - 1310

EP - 1315

JO - Journal of Engineering Mechanics - ASCE

JF - Journal of Engineering Mechanics - ASCE

SN - 0733-9399

IS - 12

ER -