{"paper":{"title":"On the synthesis of complete two-dimensional second-gradient continua: Tri-pantographic fabrics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","math.MP","physics.class-ph"],"primary_cat":"math-ph","authors_text":"Casey Rodriguez, Emilio Barchiesi, Francesco Dell'Isola, Ivan Giorgio, Simon R. Eugster","submitted_at":"2026-08-06T02:02:22Z","abstract_excerpt":"We introduce a notion of completeness for two-dimensional second-gradient elastic continua and propose a microstructural route toward its synthesis. A continuum is said to be complete if the Hessian of the stored energy with respect to the second-gradient variable is locally positive definite, so that every nonzero admissible increment of the placement second gradient is quadratically controlled in the highest-order part of the energy about each configuration. Starting from the Principle of Virtual Work, we derive the constitutive relations, equilibrium equations, and admissible boundary inter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05524","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.05524/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}