TY - JOUR

T1 - An adaptive multiscale resolution strategy for the finite deformation analysis of microheterogeneous structures

AU - Temizer, I.

AU - Wriggers, P.

N1 - Funding information: Support for this work was provided by the German Research Foundation (DFG) under Grant No. WR 19/36-1 . The assistance of Christian Weißenfels in the numerical example involving the 27-node hexahedral element is much appreciated.

PY - 2010/6/13

Y1 - 2010/6/13

N2 - Standard homogenized formulations of problems posed on microheterogeneous domains provide a lower order of accuracy in regions where highly localized variations are observed in the solution fields. In order to account for this loss of accuracy for the finite deformation analysis of generally inelastic macrostructures, a scale adaptation strategy is developed where a transition from a homogenized description to an explicit microstructural resolution is pursued in designated zones of interest. Motivated by higher-order homogenization techniques, the adaptation zones are identified based on a post-processing step on the homogenized solution and correspond to regions with high strain-gradients. In order to avoid modeling errors emanating from the use of approximate explicit macroscale constitutive formulations, an exact homogenization procedure based on databased and direct multilevel finite element computations is employed. The overall methodology is investigated in a two-dimensional setting where special attention is paid to the underlying multiscale mesh resolution and additionally demonstrated with a three-dimensional problem. Numerical observations suggest the concept of a representative adaptation zone within which scale adaptation effects can be assessed.

AB - Standard homogenized formulations of problems posed on microheterogeneous domains provide a lower order of accuracy in regions where highly localized variations are observed in the solution fields. In order to account for this loss of accuracy for the finite deformation analysis of generally inelastic macrostructures, a scale adaptation strategy is developed where a transition from a homogenized description to an explicit microstructural resolution is pursued in designated zones of interest. Motivated by higher-order homogenization techniques, the adaptation zones are identified based on a post-processing step on the homogenized solution and correspond to regions with high strain-gradients. In order to avoid modeling errors emanating from the use of approximate explicit macroscale constitutive formulations, an exact homogenization procedure based on databased and direct multilevel finite element computations is employed. The overall methodology is investigated in a two-dimensional setting where special attention is paid to the underlying multiscale mesh resolution and additionally demonstrated with a three-dimensional problem. Numerical observations suggest the concept of a representative adaptation zone within which scale adaptation effects can be assessed.

KW - Homogenization

KW - Multiscale analysis

KW - Scale adaptivity

UR - http://www.scopus.com/inward/record.url?scp=78649473789&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2010.06.013

DO - 10.1016/j.cma.2010.06.013

M3 - Article

AN - SCOPUS:78649473789

VL - 200

SP - 2639

EP - 2661

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

IS - 37-40

ER -