# Size effect in penetration of sea ice plate with part-through cracks. II: Results

Zdeněk P. Bažant, Jang Jay H. Kim

Research output: Contribution to journalArticle

13 Citations (Scopus)

### Abstract

After development of the theory in the part I paper, systems of up to 300 nonlinear equations are solved in this paper by the Levenberg-Marquardt optimization algorithm. The maximum load is reached when the circumferential cracks begin to form. Numerical calculations show a typical quasi brittle size effect such that the plot of log σN versus log h (where αN = 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 1316-1324 9 Journal of Engineering Mechanics 124 12 https://doi.org/10.1061/(ASCE)0733-9399(1998)124:12(1316) Published - 1998 Jan 1

### Fingerprint

Sea ice
Nonlinear equations
Plasticity
Cracks

### All Science Journal Classification (ASJC) codes

• Mechanics of Materials
• Mechanical Engineering

### Cite this

title = "Size effect in penetration of sea ice plate with part-through cracks. II: Results",
abstract = "After development of the theory in the part I paper, systems of up to 300 nonlinear equations are solved in this paper by the Levenberg-Marquardt optimization algorithm. The maximum load is reached when the circumferential cracks begin to form. Numerical calculations show a typical quasi brittle size effect such that the plot of log σN versus log h (where αN = 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.",
author = "Bažant, {Zdeněk P.} and Kim, {Jang Jay H.}",
year = "1998",
month = "1",
day = "1",
doi = "10.1061/(ASCE)0733-9399(1998)124:12(1316)",
language = "English",
volume = "124",
pages = "1316--1324",
journal = "Journal of Engineering Mechanics - ASCE",
issn = "0733-9399",
publisher = "American Society of Civil Engineers (ASCE)",
number = "12",

}

In: Journal of Engineering Mechanics, Vol. 124, No. 12, 01.01.1998, p. 1316-1324.

Research output: Contribution to journalArticle

TY - JOUR

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

T2 - Results

AU - Bažant, Zdeněk P.

AU - Kim, Jang Jay H.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - After development of the theory in the part I paper, systems of up to 300 nonlinear equations are solved in this paper by the Levenberg-Marquardt optimization algorithm. The maximum load is reached when the circumferential cracks begin to form. Numerical calculations show a typical quasi brittle size effect such that the plot of log σN versus log h (where αN = 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 - After development of the theory in the part I paper, systems of up to 300 nonlinear equations are solved in this paper by the Levenberg-Marquardt optimization algorithm. The maximum load is reached when the circumferential cracks begin to form. Numerical calculations show a typical quasi brittle size effect such that the plot of log σN versus log h (where αN = 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.

UR - http://www.scopus.com/inward/record.url?scp=0032467568&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032467568&partnerID=8YFLogxK

U2 - 10.1061/(ASCE)0733-9399(1998)124:12(1316)

DO - 10.1061/(ASCE)0733-9399(1998)124:12(1316)

M3 - Article

AN - SCOPUS:0032467568

VL - 124

SP - 1316

EP - 1324

JO - Journal of Engineering Mechanics - ASCE

JF - Journal of Engineering Mechanics - ASCE

SN - 0733-9399

IS - 12

ER -