Mathematical models for composition–eigenstrain and composition–eigenstrain–stress relationships in MPEAs

Develop effective mathematical models that accurately characterize the continuum-scale relationships mapping (1) composition fields to eigenstrain and (2) composition fields together with eigenstrain to residual stress in multi-principal element alloys, so that these physically meaningful mappings can be quantitatively described beyond data-driven surrogates.

Background

The paper extends AlloyVAE to problems involving eigenstrain by proposing two surrogate frameworks: one mapping composition fields to eigenstrain and another mapping composition fields and eigenstrain to residual stress. While these relationships are physically motivated and relevant for linking composition, lattice distortion, and residual stress, the authors note that there is no existing effective mathematical model capturing them accurately.

The presented generative models demonstrate feasibility using MD-derived datasets, but the absence of established mathematical formulations underscores a gap for theory-driven or mechanistic modeling approaches that can generalize these mappings.