Irreversibility condition and stability of equilibria in the inverse-deformation approach to fracture

[2512.04479] Irreversibility condition and stability of equilibria in the inverse-deformation approach to fracture Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2512.04479 (math) [Submitted on 4 Dec 2025 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: Irreversibility condition and stability of equilibria in the inverse-deformation approach to fracture Authors: Arnav Gupta View a PDF of the paper titled Irreversibility condition and stability of equilibria in the inverse-deformation approach to fracture, by Arnav Gupta View PDF HTML (experimental) Abstract: We derive an irreversibility condition for fracture in the inverse-deformation approach using the second law of thermodynamics. We consider the problem of brittle failure in one-dimensional, homogeneous, elastic bars undergoing quasistatic motion. Despite the presence of a non-zero interfacial/surface energy, the third derivative of the inverse deformation is discontinuous at crack faces. This is due to the inequality constraint allowing fracture while ensuring that the orientation of matter is preserved. We show that any change in the location of open cracks in their reference configuration result in negative entropy production. We disallow these changes according to the second law of thermodynamics, fixing the location of cracks in their reference domain. The inequality constraint and the irreversibility condition limit the space of admissible variations. We prove second-order conditions for local stability incorporating these restrictions. Their numerical implementation shows that all broken equilibria of the elastic bar under hard loading are locally stable. Subjects: Analysis of PDEs (math.AP) ; Materials Science (cond-mat.mtrl-sci); Mathematical Physics (math-ph) Cite as: arXiv:2512.04479 [math.AP] (or arXiv:2512.04479v2 [math.AP] for this version) https://doi.org/10.48550/arXiv.2512.04479 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Arnav Gupta [ view email ] [v1] Thu, 4 Dec 2025 05:33:11 UTC (1,427 KB) [v2] Sat, 15 Aug 2026 04:30:45 UTC (1,457 KB) Full-text links: Access Paper: View a PDF of the paper titled Irreversibility condition and stability of equilibria in the inverse-deformation approach to fracture, by Arnav Gupta View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2025-12 Change to browse by: cond-mat cond-mat.mtrl-sci math math-ph 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

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