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.