2. Benchmark solution#

2.1. Calculation method#

At each propagation step, the following two quantities will be calculated:

  • the number of pieces that make up the bottom of the crack,

  • the position of the crack.

Since the advance of the crack is the same for all points at the bottom of the crack, the expected value of these quantities can be calculated manually (figure).

_images/10000000000002D200000259B35436DCE18A8075.png

Figure 2.1-a : position of the bottom of the crack after each propagation step. The pieces that make up each background are also visible.

2.2. Reference quantities and results#

The number of pieces that make up each crack bottom is as follows (figure):

No spread

Crack

Number of pieces

0

\({\mathit{FISS}}_{0}\)

1

1

\({\mathit{FISS}}_{1}\)

4

2

\({\mathit{FISS}}_{2}\)

1

The position of the crack at each propagation step is as follows (figure):

No spread

Crack

Length

0

\({\mathit{FISS}}_{0}\)

4.0

1

\({\mathit{FISS}}_{1}\)

16.0

2

\({\mathit{FISS}}_{2}\)

28.0