Numerical homogenisation of micromorphic media

Abstract

Due to their underlying microtopology, cellular materials are known to show a complex mechanical behaviour. For the material modelling, the heterogeneous microcontinuum is commonly replaced by a homogeneous macrocontinuum involving extended kinematics. An appropriate homogenisation methodology will be introduced in order to replace a heterogeneous Cauchy microcontinuum by a homogeneous micromorphic macrocontinuum. For an artificial 2-D periodic microstructure, the present contribution draws a comparison between extended two-scale calculations on the one hand, and a reference solution as well as a first-order FE2 calculation on the other hand.