An enhanced affine formulation and the corresponding numerical algorithms for the mean-field homogenization of elasto-viscoplastic composites |
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| Affiliation: | 1. Laboratoire d’Etude des Microstructures et de Mécanique des Matériaux, LEM3 – UMR CNRS 7239, Université de Lorraine, Île du Saulcy, 57045 METZ Cedex 1, France;2. Institute of Fundamental Technological Research (IPPT PAN), Pawińskiego 5B, 02-106 Warsaw, Poland;1. University of Liege, Department of Aeronautics and Mechanical Engineering, Computational & Multiscale Mechanics of Materials (CM3), Chemin des Chevreuils 1, B-4000 Liège, Belgium;2. e-Xstream Engineering, Axis Park-Building H, Rue Emile Francqui 9, B-1435 Mont-Saint-Guibert, Belgium;3. Université Catholique de Louvain, Bâtiment Euler, 1348 Louvain-la-Neuve, Belgium;1. LMS International, A Siemens Business, Leuven, Interleuvenlaan 68, B-3001 Leuven, Belgium;2. Department of Metallurgy and Materials Engineering, KU Leuven, Belgium;3. Department of Material Science and Engineering, Ghent University, Belgium;1. College of Aerospace Engineering, Chongqing University, Chongqing, 400044, China;2. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, China;1. Department of Management and Engineering, University of Padova, Stradella S. Nicola 3, 36100 Vicenza, Italy;2. Robert Bosch GmbH, Corporate Sector Research and Advance Engineering, Plastics Engineering, Robert-Bosch-Campus 1, 71272 Renningen, Germany |
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| Abstract: | This paper deals with the prediction of the overall behavior of a class of two-phase elasto-viscoplastic composites, based on mean-field homogenization. For this, important improvements are made to the recently-proposed affine formulation. The latter theory linearizes the rate-dependent inelastic constitutive equations of each phase’s material and transforms them into fictitious linear thermo-elastic relations in the Laplace–Carson domain. The main contributions of the present work are threefold. Firstly, complete mathematical developments including a full treatment of internal variables are carried out, enabling the modeling of the response under unloading and cyclic histories. Secondly, robust and accurate computational algorithms are proposed. Thirdly, an extensive validation of the predictions against reference unit cell finite element results is conducted for a variety of materials and loadings. A good agreement between predictions and reference results is observed. |
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