We propose a general machine learning framework called Generalized Standard Material Networks: a framework based on convex neural networks for learning the mechanical behavior of generalized standard materials. The theory of generalized standard materials postulates the existence of two thermodynamic potentials; the Helmholtz potential and the dissipation rate potential. We parameterize the two potentials with two artificial neural networks, which alone define the constitutive material response. Due to a specifically designed network architecture, the potentials are convex by definition. This guarantees a non-negative dissipation rate and thus thermodynamic consistency. A stress-free state without internal variable evolution in the reference configuration is achieved by constraining the networks derivatives to be zero at the origin. Formulating the machine learning approach in the theory of generalized standard materials has the advantage that a multitude of different material characteristics can be described within one overarching framework. Among others, this general framework is capable of learning elastic, viscoelastic, plastic, and viscoplastic material responses with hardening. Plastic material responses are implicitly covered by the theory of generalized standard materials, which means that the existence of the yield surface and the plastic evolution law with the Karush-Kuhn-Tucker conditions do not have to be assumed explicitly. By testing the proposed framework numerically on five benchmark material models, we show satisfactory prediction accuracy to unseen data, and we show that the framework exhibits a high robustness to noise, which can be explained by the physical constraints imposed on the material behavior. Finally, we unveil the meaning of internal variables in the proposed framework, and we show that a carefully chosen number of internal variables strikes a balance between fitting accuracy and model complexity.