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Model. and Simul. in Eng. Sci."],"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>This work investigates the use of the virtual fields method (VFM) to calibrate the hardening behavior of sheet metals up to rupture. Indeed, a few studies dealing with the VFM in a 2D framework have shown that after necking, the validity of the VFM is compromised, leading to inaccurate descriptions of the material hardening behavior. However, no study has yet quantified the validity of the VFM in a 2D framework. Therefore, it is essential to assess its limitations and, in turn, highlight the advantages of a 3D approach. This study investigates the influence of sample thickness on both 2D and 3D VFM, first by analyzing the evolution of the predicted load and then by evaluating the identification of material parameters in the Swift hardening law. In the first part, the 3D-VFM has shown to yield accurate results while using the 2D-VFM resulted in non-negligible relative errors after necking, showing that the error is correlated to the thickness. In the second part, the identification of the parameters of the Swift law was carried out using different combinations of three manually defined virtual fields. The material parameters identified with the 2D-VFM did not match the reference parameters while the 3D-VFM was able to correctly identify them in every instance.<\/jats:p>","DOI":"10.1186\/s40323-025-00293-7","type":"journal-article","created":{"date-parts":[[2025,4,28]],"date-time":"2025-04-28T14:43:24Z","timestamp":1745851404000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Inverse identification of the hardening behavior with a fully 3D virtual fields method"],"prefix":"10.1186","volume":"12","author":[{"given":"Miguel G.","family":"Oliveira","sequence":"first","affiliation":[]},{"given":"Sandrine","family":"Thuillier","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3988-5606","authenticated-orcid":false,"given":"Ant\u00f3nio","family":"Andrade-Campos","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,28]]},"reference":[{"issue":"1","key":"293_CR1","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/0022-5096(52)90003-3","volume":"1","author":"R Hill","year":"1952","unstructured":"Hill R. 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