1. Reference problem#

1.1. Geometry#

_images/Shape1.gif

The structure studied is a \(375\mathrm{mm}\) long bar. Since the problem is purely \(\mathrm{1D}\), his section has no influence.

1.2. Material properties#

In modeling A, the material obeys a law of fragile elastic behavior (ENDO_SCALAIRE) with a damage gradient (modeling *_ GRAD_VARI).

ELAS

ENDO_SCALAIRE

NON_LOCAL

E= \(30000\mathrm{MPa}\) NAKED = \(0\)

SY= \(3\mathrm{MPa}\) GAMMA = \(4\)

C_ GRAD_VARI = \(1.875N\) PENA_LAGR = \(1.5\)

In modeling B, the material obeys a law ENDO_FISS_EXP for which the following parameters are entered: E = 30,000 Mpa, NU = 0, ft = 3 MPa, fc=30 MPa (without affecting the 1D result), Gf=0.1 N/mm, p=1.5, D=50 mm (without affecting the 1D result), Gf=0.1 N/mm, p=1.5, D=50 mm.

1.3. Loading conditions#

The left part of the bar (\(125\mathrm{mm}\) long) is forced to remain rigid (blocking the degrees of freedom of movement). As for the right part of the bar, it is subject to a uniform axial deformation \({\varepsilon }_{0}\), that is to say to an imposed displacement whose spatial distribution is linear. A single parameter therefore controls the intensity of the load: the level of deformation imposed \({\varepsilon }_{0}\).

In the directions perpendicular to the axis of the bar, the movements are blocked: the problem is purely \(\mathrm{1D}\). Furthermore, as the Poisson’s ratio is zero, no clamping stress develops in these directions.