A data-driven approach for plasticity using history surrogates: Theory and application in the context of truss structures

Data-driven methods and algorithms show immense potential for future advancements in the modeling and simulation of complex mechanical systems. However, in order to actually exploit this potential, the methods must be extended to consider inelastic and path-dependent material behavior—a step that appears more complex than in conventional material modeling, where this can be achieved with the help of additional, mostly internal, history variables. The effect of such history variables must thereby be transferred to the data-driven framework. This is achieved in the present paper by defining an appropriate history surrogate as well as a so-called propagator. The history surrogate contains tangible quantities that represent the backward path–uniquely in the ideal case–and enrich the conventional database entries of matching pairs of stresses and strains. The propagator defines the update of the history surrogate from one discrete time step to another. As a major advantage, the newly developed method retains the structures of the data-driven algorithm for elastic material behavior and therefore allows a rather straightforward extension of preexisting program codes. Thus, for instance, heterogeneous problems in which purely elastic and elastoplastic materials are present can be solved without further significant coding effort. Furthermore, several material classes covering different inelastic phenomena such as plasticity with isotropic and kinematic hardening as well as phase transformations in shape memory alloys can be considered in our framework.