Current machine learning (ML)-based constitutive models can effectively surrogate classical models; yet, finite element simulations remain computationally expensive, particularly for history-dependent materials. This work introduces FE material patches—arbitrarily-shaped discretized subdomains—into the implicit solution of quasi-static mechanical boundary value problems. We propose a data-driven framework leveraging the message-passing in graph neural networks (GNNs) to replace explicit constitutive models, numerical integration, and expensive matrix operations. FE material patches are represented as graphs where the mesh connectivity is encoded by undirected edge features, while boundary displacements and reaction forces serve as nodal features. By carefully adjusting the architectures that perform the feature update to the material behavior, a direct mapping from displacements to forces is made during the solution procedure of the FE solver. This allows, in turn, for the explicit computation of the consistent spatial tangents via automatic differentiation, enabling seamless integration into existing implicit FE solvers. Furthermore, custom layers are integrated to enforce force and momentum equilibria, preventing rigid body motion. The models are evaluated on both homogeneous and nonuniform patches under isotropic elasticity and history-dependent behaviors. We show that the framework approximately preserves conventional FE convergence behavior and speeds up the solution procedure. Ultimately, this contribution generalizes surrogate modeling, embedding the material behavior into the underlying numerical solver structures, aiming to provide a scalable alternative to expensive FE methods, suitable for arbitrary geometries.