Multiple scale eigendeformation-based reduced order homogenization

Multiple scale eigendeformation-based reduced order homogenization method, which provides considerable computational cost saving in comparison to the direct homogenization method, has been developed, verified against the direct homogenization method, and validated against experimental data. The salient feature of the method is in the formulation of the unit cell problem in terms of residual-free stresses, and therefore eliminating the need for costly equilibrium calculations required by the direct homogenization method. This is accomplished by introducing discretized eigendeformation fields at different scales, which are collectively referred to as eigenstrains and eigenseparations, and then precomputing a sequence of elasticity solutions of the unit cell problem subjected to the eigendeformation fields prior to nonlinear analysis.