{"paper":{"title":"Two-dimensional FrBD friction models for rolling contact: extension to linear viscoelasticity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Linear viscoelasticity extends the FrBD rolling contact framework to a system of 2(n+1) hyperbolic PDEs that capture relaxation while ensuring well-posedness and passivity.","cross_cats":["cs.NA","math.NA"],"primary_cat":"physics.app-ph","authors_text":"Luigi Romano","submitted_at":"2026-01-20T10:24:35Z","abstract_excerpt":"This paper extends the distributed rolling contact FrBD framework to linear viscoelasticity by considering classic derivative Generalised Maxwell and Kelvin-Voigt rheological representations of the bristle element. With this modelling approach, the dynamics of the bristle, generated friction forces, and internal deformation states are described by a system of 2(n+1) hyperbolic partial differential equations (PDEs), which can capture complex relaxation phenomena originating from viscoelastic behaviours. By appropriately specifying the analytical expressions for the transport and rigid relative "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"With this modelling approach, the dynamics of the bristle, generated friction forces, and internal deformation states are described by a system of 2(n+1) hyperbolic partial differential equations (PDEs), which can capture complex relaxation phenomena originating from viscoelastic behaviours. ... well-posedness and passivity are analysed rigorously, showing that these properties hold for any physically meaningful parametrisation.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that the bristle element can be represented using classic derivative Generalised Maxwell and Kelvin-Voigt rheological models, combined with the ability to specify analytical expressions for the transport and rigid relative velocity that account for different spin excitations.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Extends the FrBD rolling contact model to linear viscoelasticity via Generalized Maxwell and Kelvin-Voigt bristle models, producing a system of 2(n+1) hyperbolic PDEs with proven well-posedness and passivity for linear cases.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Linear viscoelasticity extends the FrBD rolling contact framework to a system of 2(n+1) hyperbolic PDEs that capture relaxation while ensuring well-posedness and passivity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1d58a399d3c4f62917ba55d4631035d37bdba8bbb4fc04d8a696c0ac136e3d00"},"source":{"id":"2601.13818","kind":"arxiv","version":10},"verdict":{"id":"71750589-4db4-471a-b120-501183386b01","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T12:47:36.759764Z","strongest_claim":"With this modelling approach, the dynamics of the bristle, generated friction forces, and internal deformation states are described by a system of 2(n+1) hyperbolic partial differential equations (PDEs), which can capture complex relaxation phenomena originating from viscoelastic behaviours. ... well-posedness and passivity are analysed rigorously, showing that these properties hold for any physically meaningful parametrisation.","one_line_summary":"Extends the FrBD rolling contact model to linear viscoelasticity via Generalized Maxwell and Kelvin-Voigt bristle models, producing a system of 2(n+1) hyperbolic PDEs with proven well-posedness and passivity for linear cases.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that the bristle element can be represented using classic derivative Generalised Maxwell and Kelvin-Voigt rheological models, combined with the ability to specify analytical expressions for the transport and rigid relative velocity that account for different spin excitations.","pith_extraction_headline":"Linear viscoelasticity extends the FrBD rolling contact framework to a system of 2(n+1) hyperbolic PDEs that capture relaxation while ensuring well-posedness and passivity."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.13818/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":2,"snapshot_sha256":"8c7af5f7dd02e2e31a724e31f4c35547ce10a9a34002a498ba5267a1efa8c77e"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}