Nonlinear analyses with a micromorphic computational homogenization framework for composite materials

A small deformation micromorphic computational homogenization framework for matrix-inclusion composites was recently presented in Biswas and Poh (2017), where standard continuum models at the micro-scale are translated consistently onto the macro-scale to recover a micromorphic continuum. In this contribution, the micromorphic framework is extended to the regime of significant geometrical and material nonlinearities. Following the small deformation framework, an additional degree of freedom is introduced to capture the influence of rapid fluctuations within a unit cell. In this contribution, we elaborate on the specific choice of decomposition for the kinematic fields, where certain higher-order modes are deliberately neglected. Several examples are considered to illustrate the influence of different higher-order modes, and how the corresponding size effect emerges naturally in the homogenized micromorphic model. In the regime of geometrical softening, the higher order term provides a regularizing effect to give mesh independent solutions, albeit with a stiffer response. A detailed discussion on this phenomenon is provided. The homogenization framework is implemented using a client-server based parallel processing algorithm to reduce the computational time. The excellent predictive capability and efficiency of the micromorphic approach are demonstrated with a mixed loading problem on a composite plate with non-uniform cross-section. Furthermore, the micromorphic solutions are shown to be independent of the choice of a unit cell. (C) 2019 Elsevier B.V. All rights reserved.