### Abstract

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.

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

Number | 212 |

ISSN | 1235-0621 |

### Keywords

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

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## Cite this

Santaoja, K. (1994).

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