A GENERALIZED MICROMORPHIC COMPUTATIONAL HOMOGENIZATION FRAMEWORK FOR HETEROGENEOUS MATERIALS AND STRUCTURES

Abstract

In the absence of a clear separation of length scales, higher-order enrichment is required to capture influence of the underlying rapid fluctuations, otherwise neglected in the conventional FE2 framework. To this end, a novel computational homogenization framework is proposed such that standard continuum models at the micro-scale translate onto the macro-scale to recover a micromorphic continuum. The rapid fluctuations are captured by introducing an additional macro kinematic field characterizing the dominant micro mechanisms. The proposed bottom-up strategy naturally incorporates geometrical and material nonlinearities. A parallel processing algorithm is presented to reduce the computational cost. The excellent predictive capability of the proposed framework is illustrated through several benchmark examples. The micromorphic model is shown to capture size effects originating from dominance of different higher-order modes, and regularize a geometrical softening response. Finally, the micromorphic model is adopted for a tetra-chiral auxetic structure addressing limitations of the first-order approach.