1. Reference problem

1.1. Geometry

The geometry is chosen deliberately simple, to translate a state of homogeneous stresses and deformations, as is the case in uniaxial traction. This is a volume element represented by a square with side \(\mathrm{0.01mm}\). The modeling is axisymmetric, and the traction takes place with imposed deformation.

1.2. Material properties

The characteristics are as follows:

Keyword ELAS:

YOUNG = \(143006.0\mathrm{MPa}\)

NU= \(0.33\)

Keyword CIN2_CHAB:

R0= \(0.01893467592\mathrm{MPa}\)

B= \(0.2709891156\)

R_I= \(0.04392231516\mathrm{MPa}\)

K= \(2.751852265\)

W= \(-1.157794066\)

G1_0= \(211.5567568\)

G2_0= \(0.9105873193\)

C1_I= \(3946.594428\)

C2_I= \(49.33873423\)

A_I= \(10.60515818\)

Keyword LEMAITRE

EXP_N = \(14.97577311\)

ETA = \(278.5754646\)

UN_SUR_K = \(1/278.5754646\)

UN_SUR_M = \(0.0\)

1.3. Boundary conditions and loads

\(\mathrm{DY}=0\) on the bottom

\(\mathrm{DX}=0\) on the left side

\(\mathrm{DY}\) imposed on the top, such as:

\(\mathrm{DY}(t)=({\mathrm{EPS}}_{\mathrm{final}}\ast H)/\mathrm{tmax}\ast t\)

With \({\mathrm{EPS}}_{\mathrm{final}}=0.01\)

\(H=0.01\mathrm{mm}\)

\(\mathrm{Tmax}=\mathrm{10000s}\)

This corresponds to an imposed deformation rate of \(0.01/10000=1.E–6/s\)

1.4. Initial conditions

Zero stresses and deformations.