TECHNIQUES FOR STRESS-CONTROLLED AND STRAIN-CONTROLLED HOMOGENIZATIONOF INELASTIC PERIODIC COMPOSITES

A framework is developed within the context of the displacement finite element method for applying periodic boundary conditions to uni-perio d basic cells under the influence of applied macroscopically homogeneo us stresses. The resulting approach supplements the more common strain -controlled method which is also presented and which relies on an addi tive decomposition of the displacement field into linear (imposed) and periodic (unknown) contributions. As implemented here, the stress-con trolled method employs a penalty formulation to insure that the displa cement solution satisfies the linear-periodic decomposition. The perfo rmance of both the stress and strain driven methods are demonstrated a nd assessed on a complete set of homogenization computations for an el asto-plastic composite.