A Monolithic Mixed Finite Element Formulation for Thermomechanical Small-Strain Elastoplasticity with Temperature‑Dependent Properties

Thermomechanical elastoplasticity has been extensively studied; however, many formulations are developed within weakly coupled frameworks and often assume temperature independent material behavior. Fully coupled thermomechanical approaches have also been investigated, but most are formulated in the finite-strain setting and are frequently solved using staggered solution strategies [1]. While temperature-dependent constitutive models have been proposed, they typically are restricted to elastic analyses or consider only a subset of material parameters for inelastic cases. Moreover, existing fully coupled formulations with temperature-dependent properties are commonly developed for specific engineering applications rather than as reproducible benchmark frameworks [2]. Despite these advances, their combined treatment in small-strain thermomechanics remains unexplored, particularly with reproducible benchmark problems. This work presents a fully coupled small-strain thermomechanical formulation for rate-independent elastoplastic materials with combined isotropic and kinematic hardening, in which all constitutive and thermal material properties are explicitly temperature dependent. The governing balance equations and constitutive relations are derived and discretized within a monolithic finite element framework. To avoid volumetric locking associated with nearly incompressible plastic deformation, a mixed displacement–pressure formulation with a stabilization term is employed. The implementation is verified against two benchmark problems with available analytical and semi-analytical solutions, demonstrating excellent agreement. Building on this verification, a suite of benchmark problems is introduced to systematically examine the influence of temperature-dependent material properties on the predicted thermomechanical response. The proposed framework is intended to provide a comprehensive and openly documented benchmark reference for the development, verification, and assessment of numerical methods for coupled thermomechanical problems in small-strain elastoplasticity.

References

1. J. Simo and C. Miehe, Associative coupled thermoplasticity at finite strains: formulation, numerical analysis and implementation, Computer Methods in Applied Mechanics and Engineering, 98(1):41–104, 1992, https://doi.org/10.1016/0045-7825(92)90170-o.
2. B. Ali, Y. Heider, and B. Markert, Predicting residual stresses in slm additive manufacturing using a phase-field thermomechanical modeling framework, Computational Materials Science, 231:112576, 2024, https://doi.org/10.1016/j.commatsci.2023.112576.