A hybrid model–data framework for elastoplasticity with kinematic and isotropic hardening

Data-driven computational mechanics offers an alternative solution methodology to conventional methods by replacing constitutive models with data spaces defining admissible material states. Originally proposed for linear elasticity, its application to plasticity remains challenging. Purely data-driven plasticity schemes are usually restricted to one-dimensional problems due to the excessively large data space required as a result of path dependence. Hybrid frameworks combining constitutive assumptions with data have shown promise but are often limited by their underlying assumptions such as isotropic hardening or their inability to capture strain-path changes. In this work, a new hybrid model–data plasticity framework is proposed that incorporates kinematic and isotropic hardening via data spaces derived from discrete datasets, while adopting Prager’s law for back stress evolution without explicitly defining its functional form. The approach preserves the standard computational plasticity algorithmic procedures, while an implicit return-mapping procedure and a search direction calculation akin to the elastoplastic tangent are performed through the data spaces. Numerical examples in one and three-dimensional problems demonstrate the effectiveness of the proposed framework in more general plasticity problems.