Making coupled-field Abaqus user elements simple

Abstract

Soft materials, energy storage, and advanced manufacturing couple mechanics with transport, reaction, or damage, so their simulation must solve several interacting fields together. In Abaqus, custom coupled formulations are typically implemented through user elements (UELs), and a coupled UEL must supply the residual, an iteration matrix (ideally the consistent tangent), degree-of-freedom maps, and state updates in exactly the form the solver expects. Deriving and debugging these ingredients, especially the unsymmetric cross-field tangent blocks, separates a model on paper from a working simulation, and an implementation error is hard to distinguish from a modeling choice. We present abaqus_ufl, a Python framework in which the user declares the fields and their interpolations and selects and configures supported balance templates for the governing equations. The framework generates a self-contained Fortran UEL and evaluates the required tangent blocks with the established complex-step approximation. Correctness is addressed by layered verification, from Python derivative checks through compiled single-point tests and a lightweight assembly runtime to Abaqus benchmarks, and each demonstration reports the evidence level it actually reached. The examples progress from reproducing an established corrosion element to stabilized, mixed-order, and  locally condensed formulations exercised in three-dimensional morphing.