Linear elasticity

The material properties of a linear elastic material are defined by four quantities:

Young’s modulus $E~[\text{Pa}]$,
the mean coefficient of thermal expansion $\alpha~[1/\text{K}]$,
Poisson’s ratio $\nu~[1]$,
the density $\rho~[\text{kg}/\text{m}^3]$.

In the name.i2 file, all materials used are first defined using MP sets:

MP set number T 1 V $E$ $\alpha$ $\nu$ $\rho$

Material properties must be assigned in the first load case and apply to all load cases. First, one of the defined sets (the default set) is assigned to the entire body:

AS 1 /M set number /$\dots$

If some elements have material properties different from those described by the default set, additional sets are assigned to them:

AS 1 /M set number$_1$ /M set number$_2$ E element number list$_2$ /M set number$_3$ E element number list$_3$/$\dots$

Note
More than one assignment of material properties to a single element may occur within an AS batch. In that case, the material properties are overwritten. Only the last assigned set therefore applies.

Note
In linear problems, material properties can depend on the global coordinates $x$, $y$, $z$ and the temperature $T$, using any of the available functional dependencies, see the Reference Manual.

Example

Let us consider two materials with constant properties $E_1=2\cdot10^5~\text{MPa}$, $E_2=1.8\cdot10^4~\text{MPa}$, and $\nu_1=\nu_2=0.3$. The modulus of elasticity $E_1$ applies to the entire body, $E_2$ to elements 11 through 25. Let us assume that the coefficient of thermal expansion $\alpha$ and the density $\rho$ are not needed for solving the problem.

The name.i2 file will contain:

⋮
MP 1 T 1 V 2.0e11 0 0.3 0
MP 2 T 1 V 1.8e10 0 0.3 0
⋮
AS 1 /M 1/M 2 E 11:25/…
⋮

Example

Let us consider a material with constant properties $\alpha=1\cdot10^{-5}~1/\text{K}$, $\nu=0.3$, $\rho=7850~\text{kg}/\text{m}^3$, and with a modulus of elasticity that depends on temperature:

$T~[^\circ\text{C}]$	$20$	$100$	$200$
$E~[\text{MPa}]$	$2.10\cdot10^5$	$2.05\cdot10^5$	$1.90\cdot10^5$

The dependence is described using a table (see the Reference Manual), where the temperature has identification number 5 (see the Reference Manual).

The name.i2 file will contain:

⋮
IV 1 T 5 V 20 100 200
MP 1 T 1 I 1 V 2.10e11 2.05e11 1.90e11
             V 3*1.e-5 V 3*0.3 V 3*7850
⋮