Experiments show that axial elongation is always accompanied by lateral contraction of the bar. The ratio for a linear-elastic material is:
This is known as Poisson’s ratio. Similarly, the shear modulus (modulus of rigidity) is defined as:
It can be shown that for an isotropic material
The shear modulus can be easily calculated if the modulus of elasticity and Poisson’s ratiohare known.
Most linear elastic materials are assumed to be isotropic (their elastic properties are the same in all directions).
Anisotropic material exhibits different elastic properties in different directions. The significant directions of the material are labeled as preferred directions, and it is easiest to express the material behavior with respect to these directions.
The stress-strain relationship for an isotropic linear elastic method is expressed as
Where is the Lame constant and (the shear modulus) is expressed as
and
A Poisson’s ratio of 0.5, which would be appropriate for an incompressible material, can be used for the following elements: plane stress, shell, truss, or beam. A Poisson’s ratio which is close (but not equal) to 0.5 can be used for constant dilation elements and reduced integration elements in situations which do not include other severe kinematic constraints. Using a Poisson’s ratio close to 0.5 for all other elements usually leads to behavior that is too stiff.
Anisotropic materials are best expressed through compliance tensor S
which for an orthotropic material can be expressed through the “engineering constants”: the three moduli , and Poisson’s ratios , and and the shear moduli , and associated with the material directions.
In general, is not equal to but they are related by
Material stability requires the following conditions for orthotropic elastic constants:
When the left-hand side of the last inequality approaches zero, the material exhibits incompressible behavior.
CivilFEM allows the definition of an orthotropic generic material, giving the user control over all orthotropic parameters. If the orientation box is left unchecked, the material properties are oriented to the Global Cartesian axes. The user can define a new coordinate system and assing it to the material as shown in the figure below. This option grants total control over the material orientation, as a general new coordinate system can be created.
is the Lame constant and 
(the shear modulus) is expressed as
, 
and 
Poisson’s ratios 
, 
and 
and the shear moduli 
, 
and 
associated with the material directions.
is not equal to 
but they are related by 
