A machine learning based surrogate constitutive model is presented for the elasto-damage response of transversely isotropic materials, such as fiber reinforced composites and wood. In the context of continuum damage mechanics, the nonlinear constitutive response of such materials is formulated by means of damage variables that correspond to various damage mechanisms. These damage variables, in combination with the initial (undamaged) elasticity tensor, are used to evaluate the nonlinear relation between stress and strain tensors. Instead of analytically expressing the relation between damage variables and strain state, an artificial neural network is employed. The training data is generated by performing single-element analyses for plane stress states using the Finite Element Program ABAQUS/Standard 2024 (Dassault Systèmes Simulia Corp., Johnston, Rhode Island, USA). Radial strain loading paths are prescribed, and the built-in Hashin elasto-damage material model for fiber reinforced composites is employed. The simulation output is the evolution of the stress tensor and the damage variables as a function of the strain tensor input. The neural network is trained by minimizing the error between the damage variables predicted by the network and the Finite Element Method computations. The trained network is then implemented as a constitutive material law into ABAQUS/Explicit via the VUMAT interface. Structural simulations are carried out to predict the nonlinear response of composite components.