Micromorphic two-scale modelling of periodic grid structures

The present contribution focuses on the numerical homogenization of periodic grid structures. In order to investigate the micro-to-macroscale transition, a consistent numerical homogenization scheme will be presented, replacing a heterogeneous Cauchy microcontinuum by a homogeneous micromorphic substitute continuum on the macroscale. The extended degrees of freedom, namely, the microdeformation and its gradient, are to be interpreted in terms of geometrical deformation modes and the related loading conditions of the underlying unit cells. Assuming strain energy equivalence of the macro- and the microscale, the effective constitutive properties of a square and a honeycomb grid structure are identified and quantitatively validated in comparison to reference calculations with microscopic resolution. © 2013 by Begell House, Inc.

Subjects

Cellular materials

FE method 2

Homogenization

Micromorphic media

Size effects

DDC Class

620: Ingenieurwissenschaften

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Micromorphic two-scale modelling of periodic grid structures