How to determine elastic constants of transversely isotropic material by tension experiment?

Hello. I am working to design an experiment to  determine elastic constants of transversely isotropic material (also plastic-like material). There are five independent coefficients, and with experiment methods described in this paper doi:10.1016/j.ijrmms.2011.12.004, I need to carry out at least 3 tensile experiments. In the experiments, I need to measure not only the tensile strain-stress curve, but also at least one transverse strain to determine the poisson's ratio in the plane of transverse isotropy to a stress acting parallelly to it.

My question is, how to determine all elastic constants of transversely isotropic material by tension experiment, without measuring the transverse strain? Is it possible?

I want to discuss this, because that compared with axial strain, transverse strain is hard to measure in the experiment. Any comments are welcome.

Best,

Yang