Multiscale enrichment based on partition of unity for nonperiodic fields and nonlinear problems

We present a generalization of the Multiscale Enrichment based on Partition of Unity (MEPU) formulation originally reported in Fish and Yuan (Int J Numer Methods Eng 62:1341-1359, 2005) to account for boundary layers, nonperiodic fields and nonlinear systems. MEPU is aimed at extending the range of applicability of the mathematical homogenization theory to nonlinear nonperiodic systems with inseparable fine and coarse scales. Performance studies for both continuum and coarse grained discrete systems are conducted to validate the formulation.