A variationally consistent mesoscopic Cosserat theory with distributed defects and configurational forces

TL;DR

This paper introduces a variationally consistent mesoscopic Cosserat theory that models defects and configurational forces using independent measures of torsion and curvature, providing a unified geometric framework.

Contribution

It develops a novel variational formulation incorporating defect measures and configurational forces, extending classical Cosserat elasticity to include compatibility-breaking perturbations.

Findings

Defect transport generates configurational forces.

The theory reveals a Maxwell-type structure in defect dynamics.

Numerical examples illustrate defect-induced configurational effects.

Abstract

We develop a variationally consistent mesoscopic extension of Cosserat elasticity motivated by the breakdown of compatibility in classical formulations. By admitting compatibility-breaking perturbations, the classical theory ceases to remain closed under admissible variations, necessitating an enlargement of the constitutive framework. This leads naturally to a formulation in which torsion and curvature are treated as independent distributed measures of defects. The theory is constructed using a Palatini-type variational approach, with the coframe and connection as independent fields. The resulting Euler--Lagrange equations yield both the standard balance laws and defect-related excitation fields. Material invariance gives rise to configurational forces and moments, which emerge as Noether currents and are directly linked to defect transport governed by the Bianchi identities. The framework provides a unified description of defect kinematics, configurational mechanics, and microstructural evolution. Illustrative examples and numerical evaluations demonstrate how defect transport generates configurational forces and highlight the underlying Maxwell-type structure of the theory. The proposed formulation offers a consistent geometric foundation for the analysis of structured solids with evolving internal geometry and provides a basis for future developments in defect dynamics and dissipative processes.