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Part I: Closed form expression for the effective higher-order constitutive tensor. arXiv:1305.2365 Submitted, 2013), to define effective second-gradient elastic materials from heterogeneous Cauchy elastic solids, are extended here to the case of phases having non-isotropic tensors of inertia. It is shown that the nonlocal constitutive tensor for the homogenized material depends on both the inertia properties of the RVE and the difference bet"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1306.0421","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-03T14:12:13Z","cross_cats_sorted":["cond-mat.soft","math.MP"],"title_canon_sha256":"0a7f381d29ba91de5b405acf9b2ff779edbdbfc2de48cb0c72781b376a972ce2","abstract_canon_sha256":"b948435366d89b217f83af74ddf68db17d79d4aad4f0c21018b3a4cb269b6c75"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:32.125290Z","signature_b64":"w+Fsmew5HEucnWYDz52ze/mt3dMkejcMm0bhnGrPdljzfjFdpQ/NlduqJmS8cAcgfVDdGzHXVZigOPgUQAo+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b0b28ae4e6d33e3de767009a69c2b0d51035e085f9a29f774108a7817ba4878","last_reissued_at":"2026-05-18T03:03:32.123626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:32.123626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Anisotropic effective higher-order response of heterogeneous Cauchy elastic materials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft","math.MP"],"primary_cat":"math-ph","authors_text":"Daniele Veber, Davide Bigoni, Francesco Dal Corso, Mattia Bacca","submitted_at":"2013-06-03T14:12:13Z","abstract_excerpt":"The homogenization results obtained by Bacca et al. 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