Crack Paths 2012

numerical analyses on different S F R Cstructural elements, able to account for both

material non-linearity and fibre resistant contribution in the post-cracking stage.

At each loading increment (or iteration within a fixed increment) and for each single

element in which the structure is subdivided, the total strain vector {8} calculated from

the adopted FE code is passed to the user-material subroutine. Following the above

described procedure, these strain values are used for the evaluation of the proper

material stiffness matrix depending on the current cracking stage and, knownit, for the

determination of corresponding stresses, which are then passed back to the FE code for

the execution of external convergence checks. O n this point, it should be reminded that

the proposed model is based on a strain decomposition scheme in the cracked stage; as a

consequence, it is also necessary to check the convergence on total strain through an

internal iterative procedure, like the one summarizedin the fl o wchart reported Fig. 3.

for the k-th external iteration andthe j-th internal one

{scij : {Sop-1’ {scrlij : {sik' {grail-4

%

u

I

{at —> [0.11 {as = {elk —> 11x11

4 [D11 : ( (113,104+ (113M104 )‘1 ( [I] + (113.101 [13.11)

{ 8 c r l }_j )W l j :V1‘i — >[])crl]‘i

l1 {6s}j : lDslj {elk {6P : lDlj {$}k—> { iscij =_ {6P I’ isslj

I’ {EJJ ([Dcl Jil. isclj

I

{6W1}J : {6}]

_’ {SHIP =([Dcr1]J)_1 {6M1}J

{ 8 P: {8c}j+ { S u l p

l

{e}j I {Elk

N O

e11 Eras“ ; isms" Ewe?"

[1 YES

[D] k I [D]

{gik I {6}J

Figure 3. Flow chart of the internal iterative procedure to obtain strain decomposition.

C O M P A R I SWO IN TS EH X P E R I M E NRTEASLU L T S

S F R Cbeamsin bending

In order to verify the effectiveness of the proposed procedure, an experimental program

carried out on S F R Cbeams in bending has been first considered [8]. More in details,

655