Cosserat micropolar and couple-stress elasticity models of flexomagnetism at finite deformations

2025-11-27

AI Summary

Conventional flexomagnetic models rely on high-order tensor couplings, suffer from parameter redundancy, and fail to adequately describe centrosymmetric or cubic-symmetric materials. Method: This work establishes a geometrically nonlinear continuum flexomagnetic model grounded in Cosserat micropolar elasticity and couple-stress theory. It innovatively couples the third-order microdislocation tensor directly with the magnetization vector, requiring only one or two material constants to fully characterize flexomagnetic coupling in centrosymmetric and cubic-symmetric systems. A unified variational functional is formulated by incorporating the Lifshitz invariant alongside scalar and vector magnetic potentials, enabling rigorous derivation of the nonlinear governing equations. Results: Numerical simulations on nanobeams validate the model’s physical self-consistency and computational feasibility. The framework provides a concise, generalizable, and extensible paradigm for modeling multifield coupling in flexomagnetism under finite deformations.

Technology Category

• Cognitive Modeling & Cognitive Systems: Computational Creativity
• Machine Learning: Matrix & Tensor Methods
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We propose geometrically nonlinear (finite) continuum models of flexomagnetism based on the Cosserat micropolar and its descendent couple-stress theory. These models introduce the magneto-mechanical interaction by coupling the micro-dislocation tensor of the micropolar model with the magnetisation vector using a Lifshitz invariant. In contrast to conventional formulations that couple strain-gradients to the magnetisation using fourth-order tensors, our approach relies on third-order tensor couplings by virtue of the micro-dislocation being a second-order tensor. Consequently, the models permit centrosymmetric materials with a single new flexomagnetic constant, and more generally allow cubic-symmetric materials with two such constants. We postulate the flexomagnetic action-functionals and derive the corresponding governing equations using both scalar and vectorial magnetic potential formulations, and present numerical results for a nano-beam geometry, confirming the physical plausibility and computational feasibility of the models.

Problem

• Develops nonlinear flexomagnetism models using Cosserat micropolar theory
• Introduces magneto-mechanical coupling via micro-dislocation and magnetization interaction
• Enables modeling of centrosymmetric materials with fewer flexomagnetic constants

Innovation

• Geometrically nonlinear continuum models using Cosserat micropolar theory
• Third-order tensor coupling via micro-dislocation and magnetization Lifshitz invariant
• Enables centrosymmetric materials with single flexomagnetic constant