Validation Criteria for Data-driven Models of History-dependent Materials
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This paper addresses the validation of identified data-driven material models for history-dependent materials, which today are often represented using neural networks. Our validation criteria, however, apply to any identified material model, including traditional parameterized models used in materials science. The work focuses on a fundamental question in Computational Mechanics: Is a computed solution—obtained using such an identified data-driven material model—actually valid? Surprisingly, this question remains largely unexplored in current research. To investigate it, we revisit our previously proposed data-driven computational framework for history-dependent stable materials. This framework is rooted in the thermodynamics of irreversible processes with internal variables, a well-established and central methodology in materials science. We assume the material to be standard, and therefore characterized by one or two convex potentials along with the dimension of its set of hidden state variables. The approach relies on the Constitutive Relation Error (CRE) concept: the optimal data-driven model minimizes the CRE functional while strictly satisfying all admissibility requirements, particularly the equilibrium equations. Experimental data used for identification may originate from complex 2D or 3D specimens. The proposed method determines whether the computed solution of a new boundary-value problem—solved with new data but using the previously identified material model—is acceptable. This is achieved by evaluating its proximity to experimental data, under the assumption that the identified data-driven material model already provides an accurate fit to that data. We introduce dimensionless acceptability criteria based on the CRE, applicable to any identified material model. These criteria can naturally incorporate additional modeling assumptions such as isotropy or orthotropy. Several numerical examples will be presented, demonstrating the approach on structural computations using a neural-network-based material model for viscoelastic or elasto-(visco)plastic materials.
