Effective properties of a viscoplastic constitutive model obtained by homogenisation

Heterogeneous materials are used more and more frequent due to their enhanced mechanical properties. If the relation between the microscopic deformation and the macroscopic mechanical behaviour can be obtained, it can be used to design new materials with desired properties such as high strength, high stiffness or high toughness. A method for obtaining this relation is called homogenisation, by which the heterogeneous material is replaced by an equivalent homogeneous continuum. In the paper, a homogenisation method is proposed which offers the possibility to determine effective material properties for the homogeneous equivalent continuum, modelled by Perzyna's viscoplastic constitutive law. To this end, finite element calculations are performed on a representative volume element, the geometry of which is defined by the microstructure of the considered material. The mechanical behaviour of this RVE is also described by a viscoplastic model, clearly with a given parameter set. The proposed homogenisation strategy provides a way to acquire the constitutive parameters for the equivalent medium. To validate the results of the homogenisation, finite element calculations of the deformation behaviour of a perforated plate that is subjected to different loading histories are performed. The global mechanical behaviour of the homogenised simulations and direct calculations, where the heterogeneous structure is completely discretised, are compared