https://hal.science/hal-01069603Badulescu, ClaudiuClaudiuBadulescuMMA - LBMS - Laboratoire brestois de mécanique et des systèmes - ENIB - École Nationale d'Ingénieurs de Brest - UBO - Université de Brest - ENSTA Bretagne - École Nationale Supérieure de Techniques Avancées BretagneLahellec, NoelNoelLahellecLMA - Laboratoire de Mécanique et d'Acoustique [Marseille] - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche ScientifiqueSuquet, PierrePierreSuquetLMA - Laboratoire de Mécanique et d'Acoustique [Marseille] - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche ScientifiqueField statistics in linear viscoelastic composites and polycrystals.HAL CCSD2015[PHYS.MECA.MEMA] Physics [physics]/Mechanics [physics]/Mechanics of materials [physics.class-ph][SPI.MECA.MEMA] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of materials [physics.class-ph]Lahellec, NoelBlanc - Micromechanical approach of nonlinear ELasto-VIScoplasticity in polycrystalline materials: theory, modeling, and experimental comparison. - - ELVIS2008 - ANR-08-BLAN-0138 - BLANC - VALID - 2014-10-06 14:25:572023-03-24 14:52:592014-10-08 11:39:57enJournal articleshttps://hal.science/hal-01069603/document10.1016/j.euromechsol.2014.07.012application/pdf1The aim of this study is to estimate the effective response, as well as the statistics of the fields (average and fluctuations per phase) in linear viscoelastic heterogeneous materials. To this effect, a variational method based on a rate variational principle (RVP) has recently been introduced by the authors in which, at each time step, the stress or strain fields are approximated by those of a linear thermoelastic comparison composite. In the present study, a different derivation of this estimate is proposed, based on a simple approximation of the stress field along the time steps. The present study also explores the accuracy of the RVP model by comparing its predictions with reference results, either in closed form (for specific two-phase particulate composites) or obtained by full-field simulations (FFT method) for 2D polycrystals. A differential equation for the second moment of the stress field in the individual phases of two-phase particulate composites is given for the first time. These comparisons show that the RVP model delivers a very accurate estimate of the effective behavior as well as of the statistics of the local fields in two-phase particulate composites. For polycrystalline materials subjected to monotonic loading, the effective behavior and the statistics of the local fields are well predicted. The agreement is less accurate for cycling loadings.