PSI - Issue 28

Juan Du et al. / Procedia Structural Integrity 28 (2020) 577–583 J. Du et al./ Structural Integrity Procedia 00 (2019) 000–000

579

3

mechanical signal. The bone adaptive activities were divided into three stages with respect to the magnitude of mechanical stimuli, representing resorption (low mechanical stimuli) and formation (high mechanical stimuli) along with a ‘quiescent zone’, where formation and resorption processes were in balance (hence moderate stimuli) [14][15][16]. It was also proposed that strain could also contribute towards mechanical stimuli, therefore, affecting the remodelling process [17].

Table 1: Model specification Volume size Number of material sets

5.04 mm×5.64 mm×5.04 mm

21

Element type Element size

C3D8R 60 µm 663264

Total number of elements

Figure 1: Loading schematic for microscale bone sample. Orange arrows (top) represent location of applied load; encastre constraint (fixed both translational and rotational degrees of freedom) was applied on the bottom.

Within a loading cycle, non-static loading conditions can result in varying mechanical signals. The model describes the effect of changing mechanical stimuli (signals) in elements on the shift of adaptation response and density change in bone by allocating the signals to stages with defined boundaries. More specifically, the mechanical signal calculated at element i , S i , can cause three different responses of bone to the activity, Λ i , defined by the relative value of the signal compared with the apposition and resorption limits of the homeostatic interval, S ref : S R and S F , respectively. The value of Λ i was a dimensionless quantity and can be expressed as the following set of equations:

    

    

i

S S 

1,

Resorption



R

i

i

0,

'

'

S S S  

Lazy

 

,

(2)

R

F

1,

Formation

i

S S 

F

where the value of S R and S F are set to 3000 με and 5000 με [12] (Table 2).