Orthotropic, linear elastic material model. The model parameters are summarized
in Tab. 2.
Local coordinate system, which determines axes of material orthotrophy
can by specified using lcs array. This array contains six numbers,
where the first three numbers represent directional vector of a local x-axis,
and next three numbers represent directional vector of a local y-axis.
The local z-axis is determined using the vector product.
The right-hand coordinate system is assumed.
Orthotropic linear elastic material - OrthoLE
Local coordinate system
can also be specified using scs parameter. Then local coordinate
system is specified in so called ``shell''
coordinate system, which is defined locally on each particular element
and its definition is as follows: principal z-axis is perpendicular to
shell mid-section, x-axis is perpendicular to z-axis and normal to
user specified vector (so x-axis is parallel to plane, with being
normal to this plane) and y-axis is perpendicular both to x and z
axes. This definition of coordinate system can be used only with plates
and shells elements.
When vector is parallel to z-axis an error occurs. The scs array contain three numbers
defining direction vector . If no local coordinate system is
specified, by default a global coordinate system is used.
For 3D case the material compliance matrix has the following form
By inversion, the material stiffness matrix has the form
is Young's modulus in the -th direction, is the shear modulus in plane, is the major Poisson ratio, and is the minor Poisson ratio. Assuming that
etc., then is referred to as the major Poisson ratio, while is referred as the minor Poisson ratio.
Note that there are only nine independent material parameters,
because of symmetry conditions. The symmetry condition yields
The model description and parameters are summarized
in Tab. 2.
Orthotropic, linear elastic material - summary.
||Orthotropic, linear elastic material
||OrthoLE num(in) #
d(rn) # Ex(rn) # Ey(rn) #
Ez(rn) # NYyz(rn) # NYxz(rn) # NYxy(rn) #
Gyz(rn) # Gxz(rn) # Gxy(rn) #
tAlphax(rn) # tAlphay(rn) #
tAlphaz(rn) # [ lcs(ra) #] [ scs(ra) #]
||- num material model number
||- d material density
||- Ex, Ey, Ez Young moduli for x,y, and z directions
||- NYyz, NYxz, NYxy major Poisson's ratio
||- Gyz, Gxz, Gxy shear moduli
||- tAlphax, tAlphay, tAlphaz thermal
dilatation coefficients in x,y,z directions
||- lcs Array defining local material x and y axes of orthotrophy
||- scs Array defining a normal vector n. The local x axis is
parallel to plane with n being plane normal. The material local z-axis
is perpendicular to shell mid-section.
||3dMat, PlaneStress, PlaneStrain, 1dMat,
2dPlateLayer, 2dBeamLayer, 3dShellLayer, 2dPlate, 2dBeam, 3dShell,