### Abstract

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

Place of Publication | Espoo |

Publisher | VTT Technical Research Centre of Finland |

Number of pages | 50 |

ISBN (Print) | 951-38-4650-4 |

Publication status | Published - 1994 |

MoE publication type | Not Eligible |

### Publication series

Series | VTT Publications |
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Number | 212 |

ISSN | 1235-0621 |

### Fingerprint

### Keywords

- transport theorem
- fracture mechanics
- thermomechanics
- crack
- crack growth
- moving coordinates
- cracking (fracturing)
- crack propagation
- mathematical models

### Cite this

*Transport theorem and material derivatives in the description of crack growth process by thermomechanics*. Espoo: VTT Technical Research Centre of Finland. VTT Publications, No. 212

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*Transport theorem and material derivatives in the description of crack growth process by thermomechanics*. VTT Publications, no. 212, VTT Technical Research Centre of Finland, Espoo.

**Transport theorem and material derivatives in the description of crack growth process by thermomechanics.** / Santaoja, Kari.

Research output: Book/Report › Report

TY - BOOK

T1 - Transport theorem and material derivatives in the description of crack growth process by thermomechanics

AU - Santaoja, Kari

N1 - Project code: VAL37051

PY - 1994

Y1 - 1994

N2 - This publication derives mathematical expressions for two particular purposes in the theory of fracture mechanics. The first goal lies in the traditional fracture mechanics (i.e. Griffith & Rice). For this subject an expression that can be used in the derivation of a relationship between the derivative of the potential energy with respect to the crack length is derived. Second goal is the formulation of mathematical preliminaries for an extended theory that can be used in the simulation of the (curved) crack growth process in two-dimensional materials in general. Both investigations utilize the approach in which two coordinate systems are introduced: one is a fixed frame and the other is attached to the crack tip and therefore it translates and rotates with the growing crack. The obtained equations are formulated also for the finite deformation analyses.

AB - This publication derives mathematical expressions for two particular purposes in the theory of fracture mechanics. The first goal lies in the traditional fracture mechanics (i.e. Griffith & Rice). For this subject an expression that can be used in the derivation of a relationship between the derivative of the potential energy with respect to the crack length is derived. Second goal is the formulation of mathematical preliminaries for an extended theory that can be used in the simulation of the (curved) crack growth process in two-dimensional materials in general. Both investigations utilize the approach in which two coordinate systems are introduced: one is a fixed frame and the other is attached to the crack tip and therefore it translates and rotates with the growing crack. The obtained equations are formulated also for the finite deformation analyses.

KW - transport theorem

KW - fracture mechanics

KW - thermomechanics

KW - crack

KW - crack growth

KW - moving coordinates

KW - cracking (fracturing)

KW - crack propagation

KW - mathematical models

M3 - Report

SN - 951-38-4650-4

T3 - VTT Publications

BT - Transport theorem and material derivatives in the description of crack growth process by thermomechanics

PB - VTT Technical Research Centre of Finland

CY - Espoo

ER -