Crack Paths 2009

applied load P in Fig. 2e, together with some results taken from the literature [12, 13].

As can be observed, the load vs C M S Dresults are in satisfactory agreement with the

literature results even if some differences can be appreciated in the decreasing branch of

the numerical curves. In Fig. 2e the elastic-plastic case is also shown: the Drucker

Prager plasticity criterion is assumed for the uncracked material with tension

σ

(compression) yield stress equal to

) ( , =

8.2

)28(

M P a

, respectively and hardening

c t Y

equal to

H = 0 (perfect plasticity).

As can be observed, the plastic behaviour slightly

modifies the load-CMSDcurve which has a lower peak with respect to the elastic cases.

In Fig. 2b, d, expected crack paths are reproduced by the numerical simulations for the

two meshes.

200

200

180

220

2 0

1 0 0

220

180

(b)

400

(a)

2 0

1 0 0

(c)

220

1 8 0

12345E+004

Experimental (Alfaiate et al. [14])

(d)

d

3-nodedmesh(Alfaiate etal. [14])

Pres.study G f = 1 0N0/ m (mesha) f = 10 c

(f)

Pres.study G f = 1 0N0/m, el-pl (mesh a)

0E+000

0E+000 1E-005 2E-005 3E-005 4E-005 5E-005

(e)

relative displacement, d(m)

Figure 2. Single-edge notched beamunder four point shear: (a) discretisation with 301 4-noded

bilinear elements and 343 nodes; (c) discretisation with 660 triangular elements and 378 nodes.

(b) Crack path for mesh (a); (d) crack path for mesh (c). Load P vs vertical relative crack

displacement (e) and detail of relative crack displacement measurement (f).

C O N C L U S I O N S

A new continuous finite elements (FE) formulation to simulate strong discontinuity

problems, such as the fracture process in brittle or quasi-brittle solids, is herein

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