Snapshot 1: model A with high

Snapshot 2: model B at low displacement rate (

)

Snapshot 3: model B at high displacement rate (

)

Snapshot 4: model C with

Snapshot 5: model C with

The definition of a fracture (shear pin) element is: if

, then

, else

, where

is the fracture force. In an in-series array with a spring having a constant

(model A), the array's constitutive definition is: if

, then

, else

.

If the fracture element is in-series with a three-element viscoelastic solid model (model B), the array's definition is: if

, then

, else

, where

and

are the springs' constants,

is the dashpot's viscosity, and

is the displacement rate. According to this model, therefore, the fracture's occurrence is determined by both the elements' constants and the displacement rate.

If two springs

and

) with two fracture elements (

and

) in series are combined in a parallel array (model C), this array's definition is

(if

, then

, else 0) + (if

, then

, else 0). Thus, according to this model, the details of the serrated force-displacement depend on the absolute and relative magnitudes of the four elements' constants.

[1] B. Drake, "A Quasi-Rheological Model Element for Fracture,"

*Journal of Texture Studies*,

**2**, 1971 pp. 265–372.

[2] R. I. Tanner, F. Qi, and S-C. Dai, "Bread Dough Rheology and Recoil,"

*Journal of Non-Newtonian Fluid Mechanics*,

**148**, 2008 pp. 33–40.