A Variational Formulation of Classical Cosserat Elasticity with Independent Coframe and Rotational Connection

TL;DR

This paper introduces a geometric variational framework for classical Cosserat elasticity, explicitly treating coframe and connection as independent fields, clarifying geometric structures and deriving governing equations without compatibility constraints.

Contribution

It presents a novel geometric formulation that explicitly separates translational and rotational degrees of freedom and derives equations directly from an action principle.

Findings

Governing equations obtained as Euler-Lagrange equations.

Configurational balances derived from invariance via Noether's theorem.

Linearization recovers classical strain and wryness measures.

Abstract

We present a geometric formulation of classical Cosserat elasticity in which the coframe and rotational connection are treated as independent variational fields. In contrast to conventional metric-based approaches, this formulation makes the underlying geometric structure explicit and separates translational and rotational degrees of freedom at the level of the action. The governing equations are obtained directly as Euler--Lagrange equations and yield the Cosserat force and moment balance laws without imposing compatibility constraints a priori.It is further shown that configurational balances arise from invarianceof the action under material translations and rotations via Noether's theorems, providing an explicit variational interpretation of micropolar mechanics. A metric-free linearization recovers the classical strain and wryness measures and establishes equivalence with standard tensorial formulations under appropriate constitutive assumptions. The proposed framework clarifies the role of the connection field, which remains implicit in classical theories, and provides a geometrically explicit variational framework.for Cosserat continua.The formulation also provides a natural foundation for generalized incompatible Cosserat continua and mesoscopic defect theories