Saturday, July 19, 2014

Intrinsic Anisotropic Poisson Effect that exists in the basic Applied Element Formulation

In my previous article, I had discussed about the AEM program for linear 2D materials that I had written in Python. Although, poisson's ratio was not considered in that program, I found that when elements are compressed (or stretched) diagonally, an intrinsic poisson effect is induced. However, such poisson effect is non existent when elements are compressed (or stretched) orthogonally. This is mainly because when the elements are compressed diagonally, the diagonal displacement induces extra force on the two lateral elements as shown in figure 1.

Note: Element properties used in all of the simulations presented here are: 
Young's Modulus (E) = 207 GPa
Shear Modulus (G) = 79.1 GPa
Element Dimension (a by b) = 0.1 m by 0.1 m
Element Thickness (T) = 0.15 m
Load (L) = 1000 kN [each red arrows]
Also in all of the figures presented here, green squares represent undeformed elements and blue squares represent deformed elements. Displacements are magnified 500 times.
Figure 1: Lateral displacements induced (represented by black arrows) when force (represented by red arrows) is applied in a direction diagonal to the element edges. This is the intrinsic anisotropic poisson effect induced in the basic applied element formulation.