Efficiency of boundary conditions on the computation of local fields in a Representative Volume Element

International audienceWithin the framework of numerical homogeneization approaches, we focus on the effectof boundary conditions (BCs) on local mechanical fields computed by the Finite Ele-ment method. The influence of classical BCs (affine displacements, periodic conditions)imposed on the Representative Volume Element (RVE) has been largely studied with re-spect to the effective macroscopic behaviour [1]. When a periodic microstructure can begenerated at the RVE scale (periodic or model materials typically), periodic conditionsproduce more accurate results. However, these conditions come with technical difficultieslinked to the generation of the periodic mesh and additional costs in terms of computationtime.In a multiscale use of numerical homogenization [2], local fields are of great importance todetect phenomena arising at the local scale. Moreover these fields must be computed inreasonable calculation times to make these numerical coupling approaches efficient. Veryfew studies focus on the effects of the BCs on the local behaviour. Affine displacementconditions, which are the computationnally most efficient technique, are subject to lo-cal boundary effects, located on cut inclusions in case of matrix-inclusion composites [3].Different ways are followed in order to improve the ratio precision over cost of such ap-proaches : truncation or filtering [4], homogenization-based Dirichlet values, RVE withoutcut inclusions.REFERENCES[1] T. Kanit, S. Forest, I. Galliet, V. Mounoury, and D. Jeulin. Determination of the size of therepresentative volume element for random composites: statistical and numerical approach.International Journal of Solids and Structures, 40(13):3647-3679, 2003.[2] S. Saeb, P. Steinmann, and A. Javili. Aspects of computational homogenization at finitedeformations: A unifying review from Reuss' to Voigt's bound. Applied Mechanics Reviews,68, 06 2016.[3] M. Salmi, F. Auslender, M. Bornert, and M. Fogli. Apparent and effective mechanicalproperties of linear matrix-inclusion random composites: Improved bounds for the effectivebehavior. International Journal of Solids and Structures, 49(10):1195-1211, 2012.[4] X. Yue and W. E. The local microscale problem in the multiscale modeling of stronglyheterogeneous media: Effects of boundary conditions and cell size. Journal of ComputationalPhysics, 222:556-572, 03 2007