PSI - Issue 40

Vladlen Nazarov et al. / Procedia Structural Integrity 40 (2022) 341–347 Vladlen Nazarov / Structural Integrity Procedia 00 (2022) 000 – 000

343

3

Fig. 1. Cross section of the cylindrical tube at undeformed (left) and deformed (right) states.

As a mechanical characteristic of micropores, let us consider porosity, which characterizes the relative change in the cross sectional area of tube   s ds   sec (1) b b u  is an initial boundary radii (here is the hypothesis that one of the boundary radii is the same for an incompressible material and a material with micropores), a a u  for incompressible material and  a a u  for material with micropores. Difference between displacements for porous tube and incompressible tube at the same arbitrary radius

r r u u    

(2)

We define porosity as the relative change in the area of an elementary ring

     du u r r

u

du

u

du

 dr r d 

  d

 dr r d  



   

  r

 

r

r

r

r







(3)

r

dr

r

dr

dr

r

dr

At u r r  and

r  

dr d 

(4)

 

Cauchy strains

u

du

r

r

(5)

,





r 





r

dr

0   incompressibility condition

0   and

At

u

du

u

du

r

  r

r

r

(6)

0        

r

r





r

dr

r

dr