PSI - Issue 1

Behzad V. Farahani et al. / Procedia Structural Integrity 1 (2016) 226–233 Behzad V. Farahani et al./ Structural Integrity Procedia 00 (2016) 000 – 000

232

7

1.0

1.000

0.8

800

0.6

600

Load P [N]

0.4

400

Non-local Damage

0.2

200

Experimental Test RPIM, Local Damage Model

0.0

0

0.0000

0.0005

0.0010

0.0015

0.0020

0.0

0.1

0.2

0.3

0.4

0.5

Load Point A Deflection [mm]

Effective Strain

(a) (b) Fig. 3- (a) Response of load P -deflection on point A obtained for local and non-local damage models compared to the experimental solution Malvar and Warren (1988) and (b) Variation of non-local damage in terms of effective strain at the crack tip First, the numerical analysis initiates with the local damage model to obtain the response of the load P in terms of the deflection on point A , then it continues to the analysis of the non-local damage model, which will permit to acquire the final result and the variation of damage versus effective strain. The total displacement enforcement is 0.5( ) v mm  (divided in 20 incremental steps). Furthermore, in the case of non-local damage analysis a 2 nd order weight function is considered, while = 0.2 and h and RGP parameters are accordingly computed as ℎ = 0.0164 ( ) and = 0.0033 ( ) . The preliminary results are compared to the experimental solution reported by Malvar and Warren (1988). Fig. 3-a shows the obtained response of load P versus deflection on point A . The variation of damage-effective strain at the crack tip is presented in Fig. 3-b. Additionally, to assess the performance of the proposed damage algorithm, it is interesting to present the total von-mises equivalent stress profile over the beam (see Fig. 4). The obtained results of load-deflection agree well with the experimental solution. Moreover, it is visible that RPIM is capable to produce the smooth stress field.

Fig. 4- Profile of equivalent von-Mises stress over the half beam obtained from non-local damage model

4. Conclusions The RPIM meshless method, as an advanced discretization technique, has the potential to analyse the damage models in concrete structures using a rate-independent constitutive law. Due to the non-linear damage solution, the Newton-Raphson non-linear algorithm was employed, creating a pseudo-time stepping scheme capable to enforce displacement increments. Moreover, the return-mapping algorithm has the potential to link the local damage model to non-local one in an elegant way, producing results very close to the experimental test. In addition, the proposed damage algorithm is applicable to the other concrete structures with regard to tensile and compressive loading stages.