1. Reference problem#

1.1. Geometry#

_images/1000097C000069D5000031320E42FBA4DB364EED.svg

Bar length

: \(1m\)

Bar section

: \(5{\mathrm{cm}}^{2}\)

1.2. Material properties#

1.2.1. Isotropic hardening and linear kinematics#

_images/10000A0A000069BB00003A9A478AF30F2329E070.svg

Young’s module:

\(E=2.{10}^{11}\mathrm{Pa}\)

Work hardening slope:

\({E}_{t}={2.10}^{9}\mathrm{Pa}\)

Elastic limit:

\(\sigma ={2.10}^{8}\mathrm{Pa}\)

Poisson’s ratio:

\(\nu =\mathrm{0,3}\)

Coefficient of thermal expansion:

\(\alpha ={1.10}^{-5}{K}^{-1}\)

1.2.2. Pinto-Menegotto model#

_images/10001994000069BB0000437D9A4C85602318F7A0.svg

1.3. Boundary conditions and loading#

Boundary conditions:

The bar is recessed. Travel is therefore blocked in all three directions.

In \(\mathrm{N1}\) and \(\mathrm{N2}\): \(\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=0\)

Charging:

The loading path is described by the evolution of the temperature, which is uniform across the bar:

\(t\)

0

1

2

2

2

3

4

5

6

7

\(T(°C)\)

50

—50

—50

—300

—300

—100

—150

—350

—200

The reference temperature is \(0°C\).

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