{"data":{"id":"10.4121/6346fbdb-d79e-4bd7-80b7-4d24d26cfd82","type":"dois","attributes":{"doi":"10.4121/6346fbdb-d79e-4bd7-80b7-4d24d26cfd82","prefix":"10.4121","suffix":"6346fbdb-d79e-4bd7-80b7-4d24d26cfd82","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Khadijeh, Mahmoud","nameType":"Personal","givenName":"Mahmoud","familyName":"Khadijeh","nameIdentifiers":[{"nameIdentifier":"0009-0006-5186-6754","nameIdentifierScheme":"https://orcid.org/"}],"affiliation":[]},{"name":"Kasbergen, Cor","nameType":"Personal","givenName":"Cor","familyName":"Kasbergen","nameIdentifiers":[{"nameIdentifier":"0000-0002-7076-2348","nameIdentifierScheme":"https://orcid.org/"}],"affiliation":[]},{"name":"Erkens, Sandra","nameType":"Personal","givenName":"Sandra","familyName":"Erkens","nameIdentifiers":[{"nameIdentifier":"0000-0002-2465-7643","nameIdentifierScheme":"https://orcid.org/"}],"affiliation":[]},{"name":"Varveri, Aikaterini","nameType":"Personal","givenName":"Aikaterini","familyName":"Varveri","nameIdentifiers":[{"nameIdentifier":"0000-0002-8830-9437","nameIdentifierScheme":"https://orcid.org/"}],"affiliation":[]}],"titles":[{"title":"User-Defined Material Subroutine for Viscoelastic Paving Materials including the Aging Effect"}],"publisher":"4TU.ResearchData","container":{},"publicationYear":2025,"subjects":[{"subject":"Civil Engineering","subjectScheme":"Australian and New Zealand Standard Research Classification (ANZSRC), 2008","classificationCode":"0905"},{"subject":"FOS: Civil engineering","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Chemical Engineering","subjectScheme":"Australian and New Zealand Standard Research Classification (ANZSRC), 2008","classificationCode":"0904"},{"subject":"FOS: Chemical engineering","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Engineering","subjectScheme":"Australian and New Zealand Standard Research Classification (ANZSRC), 2008","classificationCode":"09"},{"subject":"Aging effects"},{"subject":"Carbonyl area index"},{"subject":"Oxidative aging"},{"subject":"Relaxation modulus"},{"subject":"Asphalt materials"}],"contributors":[{"name":"TU Delft, Faculty Civil Engineering and Geosciences, Department of Engineering Structures, Section of Pavement Engineering","nameType":"Organizational","affiliation":[],"contributorType":"Other","nameIdentifiers":[]}],"dates":[{"date":"2025-11-26","dateType":"Issued"}],"language":"en","types":{"ris":"COMP","bibtex":"misc","citeproc":"article","schemaOrg":"SoftwareSourceCode","resourceType":"Software","resourceTypeGeneral":"Software"},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.4121/6346fbdb-d79e-4bd7-80b7-4d24d26cfd82.v1","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":["Fortran Codes (.f); Python codes (.py)"],"version":"1","rightsList":[{"rights":"MIT License","rightsUri":"https://opensource.org/licenses/MIT","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"mit","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"This repository provides a user-defined material subroutine (UMAT) for Abaqus, written in Fortran, that models the linear viscoelastic response of materials with explicit consideration of aging effects. The viscoelastic behavior is represented through a Prony series formulation, enabling accurate simulation of time-dependent stress–strain relationships. To capture long-term material degradation, the subroutine incorporates an aging index based on carbonyl area evolution, which dynamically modifies the stiffness parameters as a function of simulation time. The aging mechanism is governed by a reaction-rate model, allowing the Young’s modulus and relaxation times to evolve with chemical changes in the material microstructure. This UMAT enables realistic prediction of mechanical performance under prolonged loading and environmental exposure, making it particularly suitable for polymers, asphalt binders, and other materials where oxidative aging significantly alters structural integrity.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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