# Double dot product in Cylindrical Polar coordinates

1. Jul 31, 2014

### jemme

Hello,

I'm working with a problem in linear elasticity, and I have to calculate the strain energy function as follows:

2W = σijεij

Where σ and ε are symmetric rank 2 tensors.

For cartesian coordinates it is really easy because the metric is just the identity matrix, hence:

2W = σxxεxx + σyyεyy + σzzεzz + 2 σxyεxy + 2 σxzεxz + 2 σzyεzy

My question is how the expression should be for cylindrical polar coordinates (r,θ,z)

Thanks!

2. Jul 31, 2014

### Staff: Mentor

Since cylindrical polar coordinates are likewise orthogonal, it's going to be pretty much analogous.

Chet