  The development of accurate constitutive models for materials that undergo
path-dependent processes continues to be a complex challenge in computational
solid mechanics. Challenges arise both in considering the appropriate model
assumptions and from the viewpoint of data availability, verification, and
validation. Recently, data-driven modeling approaches have been proposed that
aim to establish stress-evolution laws that avoid user-chosen functional forms
by relying on machine learning representations and algorithms. However, these
approaches not only require a significant amount of data but also need data
that probes the full stress space with a variety of complex loading paths.
Furthermore, they rarely enforce all necessary thermodynamic principles as hard
constraints. Hence, they are in particular not suitable for low-data or
limited-data regimes, where the first arises from the cost of obtaining the
data and the latter from the experimental limitations of obtaining labeled
data, which is commonly the case in engineering applications. In this work, we
discuss a hybrid framework that can work on a variable amount of data by
relying on the modularity of the elastoplasticity formulation where each
component of the model can be chosen to be either a classical phenomenological
or a data-driven model depending on the amount of available information and the
complexity of the response. The method is tested on synthetic uniaxial data
coming from simulations as well as cyclic experimental data for structural
materials. The discovered material models are found to not only interpolate
well but also allow for accurate extrapolation in a thermodynamically
consistent manner far outside the domain of the training data. Training aspects
and details of the implementation of these models into Finite Element
simulations are discussed and analyzed.
