{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T18:12:53Z","timestamp":1790359973384,"version":"4.1.0"},"reference-count":95,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,5,10]],"date-time":"2024-05-10T00:00:00Z","timestamp":1715299200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)","award":["AN1113\/2-2"],"award-info":[{"award-number":["AN1113\/2-2"]}]},{"name":"Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)","award":["BR5278\/2-2"],"award-info":[{"award-number":["BR5278\/2-2"]}]},{"name":"Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)","award":["SCHR570\/32-2"],"award-info":[{"award-number":["SCHR570\/32-2"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>A phenomenological material model has been developed to facilitate the efficient numerical analysis of fiber-reinforced high-performance concrete (HPC). The formulation integrates an elasto-plastic phase-field model for simulating fractures within the HPC matrix, along with a superimposed one-dimensional elasto-plasticity model that represents the behavior of the embedded fibers. The Drucker\u2013Prager plasticity and one-dimensional von-Mises plasticity formulations are incorporated to describe the nonlinear material behavior of both the HPC matrix and the fibers, respectively. Specific steps are undertaken during the development and calibration of the phenomenological material model. In the initial step, an experimental and numerical analysis of the pullout test of steel fibers embedded in an HPC matrix is conducted. This process is used to calibrate the micro-mechanical model based on the elasto-plastic phase-field formulation for fracture. In the subsequent step, virtual experiments based on an ellipsoidal unit cell, also with the resolution of fibers (used as a representative volume element, RVE), are simulated to analyze the impact of fiber\u2013matrix interactions and their physical properties on the effective material behavior of fiber-reinforced HPC. In the final step, macroscopic boundary value problems (BVPs) based on a cuboid are simulated on a single scale using the developed phenomenological material model. The resulting macroscopic stress\u2013strain characteristics obtained from both types of simulations, namely simulations of virtual experiments and macroscopic BVPs, are compared. This comparison is utilized for the calibration of material parameters to obtain a regularized solution and to assess the effectiveness of the presented phenomenological material model.<\/jats:p>","DOI":"10.3390\/ma17102247","type":"journal-article","created":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T09:28:25Z","timestamp":1715592505000},"page":"2247","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Development and Calibration of a Phenomenological Material Model for Steel-Fiber-Reinforced High-Performance Concrete Based on Unit Cell Calculations"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4848-2606","authenticated-orcid":false,"given":"Mangesh","family":"Pise","sequence":"first","affiliation":[{"name":"Institute of Mechanics, Faculty of Engineering, Department Civil Engineering, University of Duisburg-Essen, Universit\u00e4tsstr. 12, 45141 Essen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0548-4350","authenticated-orcid":false,"given":"Dominik","family":"Brands","sequence":"additional","affiliation":[{"name":"Institute of Mechanics, Faculty of Engineering, Department Civil Engineering, University of Duisburg-Essen, Universit\u00e4tsstr. 12, 45141 Essen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7960-9553","authenticated-orcid":false,"given":"J\u00f6rg","family":"Schr\u00f6der","sequence":"additional","affiliation":[{"name":"Institute of Mechanics, Faculty of Engineering, Department Civil Engineering, University of Duisburg-Essen, Universit\u00e4tsstr. 12, 45141 Essen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"A\u00eftcin, P.C. 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