A Gauge-Theoretic Framework for Finite-Deformation Plasticity in the Dislocation-Dominated Regime

Theories of large elastoplastic deformation in metallic materials have been developed through several complementary approaches: geometric theories of crystal defects, dislocation field mechanics, and defect gauge theory. For finite elastoplastic deformation and the accompanying lattice rotation, however, a formulation integrating a higher-form gauge structure with thermodynamically consistent dissipation remains incomplete. Motivated by large-deformation problems in structural metallic materials, this study constructs a 3+1-dimensional elastoplastic gauge theory for finite deformation and lattice rotation, under the assumptions that dislocations dominate and the elastic strain is small. In three dimensions, the noncommutativity of rotations, the nonconvexity of the finite-deformation energy, and objectivity under rigid rotations prevent a global Lagrangian from being dualized directly. To overcome this difficulty, we propose a framework that, by neglecting disclinations, retains the lattice rotation as an internal degree of freedom and combines a momentum-conserving Kalb--Ramond two-form representation with a local Legendre dualization on the tangent space about a base state. We first construct a conservative backbone that determines the dislocation conservation law, the constraint on dislocation motion, and the stress-induced driving force, and then introduce dissipation based on the thermodynamic dissipation inequality. The resulting framework clearly delineates relations dictated by the geometric and gauge structure from those, such as the hardening law, that must be supplied separately from materials-science considerations.