You need Tension and compression static test data in longitudinal and transverse direction. DIC will give you displacements and strain but not stress. Stress needs to be obtained through load/gauge area from experiments. Plot stress-DIC stain then...
Then slope of longitudinal tension will give E1 while slope of transverse will give E2. Assume transverse isotropy and take E2=E3 (valid assumption).
obtain any one Poisson's ratio by nu12=transverse strain(e22)/ longitudinal strain(e11). From DIC data. nu13 will be obtained though reciprocal relations given in any standard text book of composite. nu23=nu13.
Now shear modulus, G12=E1/2(1+nu12), similarly G23 and G13.
apart from this you also require to predict damage. Take Hashin damage available in abaqus. It has 6 parameters
max stress of longitudinal tension stress stain will give Xt1
max stress of transverse tension stress stain will give Xt2
max stress of longitudinal compression stress stain will give XC1
max stress of transverse compression stress stain will give XC2
Shear strength can be obtained through expression given in Christian failure criteria. S12=0.5 SQRT(Xt1*XC1)...similarly for S23
Further damage evolution will also be required to further degrade the strength during load drop due to failure. for this you require energies in tension and compression. These are obtained through area under the load displacement curve in tension and compression data for both longitudinal and transverse direction that you have.