On Physical Components of Tensors in Elasticity and Inelasticity

[2608.14946] On Physical Components of Tensors in Elasticity and Inelasticity Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematical Physics arXiv:2608.14946 (math-ph) [Submitted on 15 Aug 2026] Title: On Physical Components of Tensors in Elasticity and Inelasticity Authors: Souhayl Sadik , Arash Yavari View a PDF of the paper titled On Physical Components of Tensors in Elasticity and Inelasticity, by Souhayl Sadik and Arash Yavari View PDF HTML (experimental) Abstract: Widely used in mechanics and mathematical physics, physical components remove the inherent coordinate-dependent scaling in curvilinear coordinates, yielding components of consistent physical dimension. In orthogonal coordinates, they are constructed by normalizing the coordinate frame and coframe; in general coordinates, however, their construction requires additional, non-trivial choices. In this paper, we extract physical components of arbitrary tensors on arbitrary Riemannian manifolds by orthonormalization of the coordinate frame. We further formulate a general normalization framework distinguishing three requirements: dimensional consistency, dual frame-coframe compatibility, and unit normalization. We show that dimensional consistency alone leaves independent general linear gauge freedoms for the contravariant and covariant components. Further requiring dual compatibility locks these into a single general linear gauge; a dual-compatible frame and coframe are both of unit length if and only if they are orthonormal. Thus, the choice of orthonormal transformations emerges as the only physical-components framework that satisfies all three requirements. We apply this framework to nonlinear elasticity and inelasticity, referring broadly to constitutive responses involving internal distortions, of which we study anelasticity, viscoelasticity, and visco-anelasticity. We examine the deformation gradient, inelastic distortions, strain measures, and stress tensors. We conclude by arguing that physical components remain neither intrinsic nor unique. Subjects: Mathematical Physics (math-ph) Cite as: arXiv:2608.14946 [math-ph] (or arXiv:2608.14946v1 [math-ph] for this version) https://doi.org/10.48550/arXiv.2608.14946 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Arash Yavari [ view email ] [v1] Sat, 15 Aug 2026 00:00:11 UTC (38 KB) Full-text links: Access Paper: View a PDF of the paper titled On Physical Components of Tensors in Elasticity and Inelasticity, by Souhayl Sadik and Arash Yavari View PDF HTML (experimental) TeX Source view license Current browse context: math-ph < prev | next > new | recent | 2026-08 Change to browse by: math math.MP References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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) Major funding support from

Related documents

• The electromagnetic stress tensor in cubic crystals and amorphous solids#973583
• On non-phononic modes and glassy dynamics#1070150
• Regularity of velocity averages in kinetic equations with heterogeneity#155610
• Principal eigenvalues of nonlocal operators with advection: sharp scaling limits and spectral phase transitions#924298
• Principal eigenvalues of nonlocal operators with advection: sharp scaling limits and spectral phase transitions#920067