1. Reference problem#

1.1. Geometry#

To validate the cohesive law CZM_EXP_MIX, which is more specific to almost fragile materials, we model a notched concrete beam subjected to 3-point bending, based on the experimental data from the thesis of P.-E. Peterson [bib1]. This test is in fact one of the most frequent experimental references for validating models of surface or volume damage of concrete.

A beam of length \(2m\), height \(200\mathit{mm}\) and thickness \(50\mathit{mm}\), notched in the middle on \(100\mathit{mm}\) (half the height of the beam) is simply supported on its two ends.

_images/10000201000002C1000000F1E180B6898A12F132.png

Interface elements (60 QUAD4)

Figure 1: Representation of the 3-point bending beam. The thickness is \(50\mathit{mm}\)

1.2. Material properties#

1.2.1. The law used is law CZM_EXP_MIX.#

Material parameters are defined under the keywords RUPT_FRAG or RUPT_FRAG_FO

Young’s module: \(E=30\mathit{GPa}\)

Poisson’s ratio \(\nu =0.2\)

Critical surface energy density \({G}_{c}\):

GC= 137 N/m

critical stress \({\sigma }_{c}\):

SIGM_C = 3.3 MPa

Penalization of the Lagrangian

PENA_LAGR =300

Slip stiffness

RIGI_GLIS =10 (by default)

1.3. Boundary conditions and loads#

Embed: The movements imposed following Oy are zero at the 2 support points (GROUP_NO: CL1 and CL2). We block the next 0x movement on one of the two supports.

Displacement: An imposed displacement following Oy is applied above the crack (GROUP_NO: Dpl).