Reduced order modeling in nonlinear homogenization

Two nonlinear reduced order homogenization methods are described: pRBMOR and NUTFA.Both methods are based on the framework of the transformation field analysis (TFA).A comparison of advantages and disadvantages of the two methodologies is presented.Numerical 2D and 3D examples considering complex load paths are provided.Both approaches accurately predict the mechanical response of nonlinear composites. Computationally inexpensive nonlinear homogenization methods are much sought after in academia and industry. However, the accuracy and the accessibility of the methods play an important role. Two nonlinear homogenization methods for microstructured solid materials are investigated in this work: the pRBMOR (Fritzen and Leuschner, 2013; Fritzen et al., 2014) and the NUTFA (Sepe et al., 2013). Both methods are based on ideas of the nonuniform transformation field analysis (NTFA; Michel and Suquet, 2003, 2004). A detailed comparison with respect to accuracy, storage requirements and the evolution of the reduced degrees of freedom is carried out. Numerical examples for two- and three-dimensional problems undergoing nonproportional load paths are presented.

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