# How to properly validate transverse isotropic elasticity Finite Element Code

I have written a piece of code solving the linear elasticity problem on transversely isotropic materials (before that, the code only supported isotropic materials).

I would like to validate it before using it for other applications, have you got any idea how to do it ? I would like to be sure that the 5 independents coefficients : E1, E3, nu12, nu13, G are well integrated in the code.

• Find some well documented examples and see if it produces comparable results... Don’t use it to calculate a new structure like a bridge yet... Mar 26, 2018 at 7:59

# Definitions

Before we can answer your question, let us look at two standard definitions of terms (from ASME Guide for Verification and Validation in Computational Solid Mechanics) :

1) Verification: The process of determining that a computational model accurately represents the underlying mathematical model and its solution.

2) Validation: The process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model.

You probably mean "verification" rather than "validation" in your question.

# Verification of anisotropic elasticity

Assuming you want to verify your code for three-dimensional problems, there is a sequence of steps that's needed.

1) Frame indifference: Rotate your elements and confirm that stresses are not developed due to pure rotation.

2) Exact solutions: Search for exact solutions for 3D anisotropic elasticity in the literature and confirm that your code can reproduce those. (see, e.g., http://www-personal.umich.edu/~jbarber/Ting.pdf)

3) Manufactured solutions: Create exact manufactured solutions and verify that your code can match those. (see, e.g., www.eng.utah.edu/~banerjee/Notes/MMS.pdf)

If you can pass these tests for a wide range of loading paths, you can be reasonable sure that your implementation is OK. However, I don't think one can prove correctness of an implementation in a mathematical sense.