Could anyone tell me in tensor notation how to obtain the component of a strain rate normal to a surface and then calculate the components of that strain rate in the local coordinate flame so that I can subtract the normal strain rate from say, S11, and get the Tangental strain rate component acting on the surface.

Any book/website where this is actually done would also be useful.

Thanks.

Component of a tensor normal to a surface is (normal vector)*(tensor) where * is the inner product. The resulting vector is in whatever coordinate frame the normal and tensor components are in - to convert to another frame is simply a coordinate transformation.