Homogenisation of heterogeneous viscoplastic materials

Heterogeneous materials are used more and more 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 this paper, a numerical homogenisation method is presented 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. To assess the validaty of the homogenisation method, finite element calculations of the deformation behaviour of a heterogeneous plate with a regular cubic as well as a random perforation pattern are performed. The global mechanical behaviour of the homogenised simulations and direct calculations, where the heterogeneous structure is completely discretised, will be compared.