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

[2604.12984] A variationally consistent mesoscopic Cosserat theory with distributed defects and configurational forces Skip to main content Search Submit Donate Log in Mathematical Physics arXiv:2604.12984 (math-ph) [Submitted on 14 Apr 2026] Title: A variationally consistent mesoscopic Cosserat theory with distributed defects and configurational forces Authors: Lev Steinberg View PDF HTML (experimental) 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. Subjects: Mathematical Physics (math-ph) MSC classes: 74A05, 74A15, 74E15, 74A30, 53C05 Cite as: arXiv:2604.12984 [math-ph] (or arXiv:2604.12984v1 [math-ph] for this version) https://doi.org/10.48550/arXiv.2604.12984 Focus to learn more arXiv-issued DOI via DataCite Journal reference: European Journal of Mechanics - A/Solids 121 (2027) 106340 Related DOI : https://doi.org/10.1016/j.euromechsol.2026.106340 Focus to learn more DOI(s) linking to related resources Submission history From: Lev Steinberg [ view email ] [v1] Tue, 14 Apr 2026 17:19:30 UTC (355 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math-ph < prev | next > new | recent | 2026-04 Change to browse by: math math.MP References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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